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    "Inpainting using Sparse Regularization\n",
    "======================================\n",
    "\n",
    "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n",
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This numerical tour explores the use of\n",
    "sparse energies to regularize the image inpaiting problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
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   "outputs": [],
   "source": [
    "using PyPlot\n",
    "using NtToolBox\n",
    "# using Autoreload\n",
    "# arequire(\"NtToolBox\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Here we consider inpainting of damaged observation without noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Sparse Regularization\n",
    "---------------------\n",
    "This tour consider measurements $y=\\Phi f_0 + w$\n",
    "where $\\Phi$ is a masking operator\n",
    "and $w$ is an additive noise.\n",
    "\n",
    "\n",
    "This tour is focused on using sparsity to recover an image from the\n",
    "measurements $y$. It considers a synthesis-based regularization, that\n",
    "compute a sparse set of coefficients $ (a_m^{\\star})_m $\n",
    "in a frame $\\Psi = (\\psi_m)_m$ that solves\n",
    "$$a^{\\star} \\in \\text{argmin}_a \\: \\frac{1}{2}\\|y-\\Phi \\Psi a\\|^2 + \\lambda J(a)$$\n",
    "\n",
    "\n",
    "where $\\lambda$ should be adapted to the noise level $\\|w\\|$.\n",
    "Since in this tour we consider damaged observation without noise, i.e.\n",
    "$w=0$, we use either a very small value of $\\lambda$, or we decay its\n",
    "value through the iterations of the recovery process.\n",
    "\n",
    "\n",
    "Here we use the notation\n",
    "$$\\Psi a = \\sum_m a_m \\psi_m$$\n",
    "to indicate the reconstruction operator, and $J(a)$ is the $\\ell^1$\n",
    "sparsity prior\n",
    "$$J(a)=\\sum_m \\|a_m\\|.$$\n",
    "\n",
    "\n",
    "Missing Pixels and Inpainting\n",
    "-----------------------------\n",
    "Inpainting corresponds to filling holes in images.\n",
    "This corresponds to a linear ill posed inverse problem.\n",
    "\n",
    "\n",
    "You might want to do first the numerical tour _Variational image inpaiting_\n",
    "that use Sobolev and TV priors to performs the inpainting.\n",
    "\n",
    "\n",
    "First we load the image to be inpainted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "source": [
    "n = 128\n",
    "f0 = load_image(\"NtToolBox/src/data/lena.png\")\n",
    "f0 = rescale(f0[256 - Base.div(n, 2) + 1 : 256 + Base.div(n, 2), 256 - Base.div(n, 2) + 1 : 256 + Base.div(n, 2)]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": true
   },
   "source": [
    "Display it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
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    "deletable": true,
    "editable": true
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   "outputs": [
    {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001F0B7908>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x000000002566FA58>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(f0, L\"Image $f_0$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Amount of removed pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho = .7;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Then we construct a mask $\\Omega$ made of random pixel locations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omega = zeros(n, n)\n",
    "sel = randperm(n^2)\n",
    "Omega[sel[1:Int(round(rho*n^2))]] = 1;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The damaging operator put to zeros the pixel locations $x$ for which $\\Omega(x)=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#21) (generic function with 1 method)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi = (f, Omega) -> f.*(1 - Omega);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The damaged observations reads $y = \\Phi f_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.817734  0.0       0.0     \n",
       " 0.571429  0.0       0.591133  0.610838     0.0       0.0       0.812808\n",
       " 0.581281  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.561576  0.0       0.0       0.586207     0.0       0.802956  0.0     \n",
       " 0.0       0.0       0.522168  0.0          0.0       0.0       0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.802956  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.561576  0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.472906  0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.0       0.0       0.182266     0.0       0.0       0.0     \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.832512\n",
       " 0.44335   0.0       0.0       0.0          0.0       0.812808  0.0     \n",
       " 0.0       0.0       0.0       0.369458     0.807882  0.0       0.827586\n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.0       0.0       0.0       0.472906     0.955665  0.932677  0.0     \n",
       " 0.0       0.0       0.541872  0.0          0.0       0.935961  0.876847\n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.0       0.497537  0.0          0.0       0.0       0.91133 \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.906404\n",
       " 0.0       0.0       0.0       0.0          0.0       0.955665  0.0     \n",
       " 0.0       0.0       0.0       0.689655     0.0       0.0       0.0     \n",
       " 0.0       0.487685  0.0       0.0          0.990148  0.0       0.916256\n",
       " 0.0       0.0       0.0       0.788177     1.0       0.0       0.916256\n",
       " 0.0       0.0       0.0       0.0       …  1.0       0.97537   0.91133 \n",
       " 0.0       0.0       0.0       0.561576     0.0       0.0       0.916256\n",
       " 0.0       0.0       0.0       0.738916     0.945813  0.0       0.0     "
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = Phi(f0, Omega);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000002552AAC8>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x0000000025309A90>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(y, \"Observations y\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Soft Thresholding in a Basis\n",
    "----------------------------\n",
    "The soft thresholding operator is at the heart of $\\ell^1$ minimization\n",
    "schemes. It can be applied to coefficients $a$, or to an image $f$\n",
    "in an ortho-basis.\n",
    "\n",
    "\n",
    "The soft thresholding is a 1-D functional that shrinks the value of\n",
    "coefficients.\n",
    "$$ s_T(u)=\\max(0,1-T/|u|)u $$\n",
    "\n",
    "\n",
    "Define a shortcut for this soft thresholding 1-D functional."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#23) (generic function with 1 method)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SoftThresh = (x,T) -> x.*max( 0, 1 - T./max(abs(x), 1e-10) );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display a curve of the 1D soft thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000250FB4A8>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1, 1, 1000)\n",
    "\n",
    "figure(figsize = (7, 5))\n",
    "plot(x, SoftThresh(x, .5))\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Note that the function SoftThresh can also be applied to vector which defines an\n",
    "operator on coefficients:\n",
    "$$ S_T(a) = ( s_T(a_m) )_m. $$\n",
    "\n",
    "\n",
    "In the next section, we use an orthogonal wavelet basis $\\Psi$.\n",
    "\n",
    "\n",
    "We set the parameters of the wavelet transform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Jmax = log2(n) - 1\n",
    "Jmin = (Jmax - 3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut for $\\Psi$ and $\\Psi^*$ in the orthogonal case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Psi = a -> NtToolBox.perform_wavelet_transf(a, Jmin, -1, \"9-7\", 0, 0)\n",
    "PsiS = f -> NtToolBox.perform_wavelet_transf(f, Jmin, +1, \"9-7\", 0, 0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The soft thresholding opterator in the basis $\\Psi$ is defined as\n",
    "$$S_T^\\Psi(f) = \\sum_m s_T( \\langle f,\\psi_m \\rangle ) \\psi_m $$\n",
    "\n",
    "\n",
    "It thus corresponds to applying the transform $\\Psi^*$, thresholding\n",
    "the coefficients using $S_T$ and then undoing the transform using\n",
    "$\\Psi$.\n",
    "$$ S_T^\\Psi(f) = \\Psi \\circ S_T \\circ \\Psi^*$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "SoftThreshPsi = (f, T) -> Psi(SoftThresh(PsiS(f), T));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This soft thresholding corresponds to a denoising operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000254DC550>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(clamP(SoftThreshPsi(f0, 0.1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Inpainting using Orthogonal Wavelet Sparsity\n",
    "--------------------------------------------\n",
    "If $\\Psi$ is an orthogonal basis, a change of variable shows that the\n",
    "synthesis prior is also an analysis prior, that reads\n",
    "$$f^{\\star} \\in \\text{argmin}_f \\: E(f) = \\frac{1}{2}\\|y-\\Phi f\\|^2 + \\lambda \\sum_m \\|\\langle f,\\psi_m \\rangle\\|. $$\n",
    "\n",
    "\n",
    "To solve this non-smooth optimization problem, one can use\n",
    "forward-backward splitting, also known as iterative soft thresholding.\n",
    "\n",
    "\n",
    "It computes a series of images $f^{(\\ell)}$ defined as\n",
    "$$ f^{(\\ell+1)} = S_{\\tau\\lambda}^{\\Psi}( f^{(\\ell)} - \\tau \\Phi^{*} (\\Phi f^{(\\ell)} - y)  ) $$\n",
    "\n",
    "\n",
    "Set up the value of the threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "lambd = .03;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In our setting, we have $ \\Phi^* = \\Phi $ which is an operator of norm\n",
    "1.\n",
    "\n",
    "\n",
    "For $f^{(\\ell)}$ to converge to a solution of the problem, the gradient\n",
    "step size should be chosen as\n",
    "$$\\tau < \\frac{2}{\\|\\Phi^* \\Phi\\|} = 2$$\n",
    "\n",
    "\n",
    "In the following we use:\n",
    "$$\\tau = 1$$\n",
    "\n",
    "\n",
    "Since we use $ \\tau=1 $ and $ \\Phi = \\Phi^* = \\text{diag}(1-\\Omega) $,  the gradient descent step\n",
    "is a projection on the inpainting constraint\n",
    "$$ C = \\{ f \\backslash \\forall \\Omega(x)=0, f(x)=y(x) \\} $$\n",
    "One thus has\n",
    "$$ f - \\tau \\Phi^{*} (\\Phi f - y)  = \\text{Proj}_C(f) $$\n",
    "\n",
    "\n",
    "For the sake of simplicity, we define a shortcut for this projection\n",
    "operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ProjC = (f, Omega) -> Omega.*f + (1 - Omega).*y;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Each iteration of the forward-backward (iterative thresholding) algorithm\n",
    "thus reads:\n",
    "$$ f^{(\\ell+1)} = S_{\\lambda}^\\Psi( \\text{Proj}_C(f^{(\\ell)}) ). $$\n",
    "\n",
    "\n",
    "Initialize the iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fSpars = y;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "First step: gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fSpars = ProjC(fSpars, Omega);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Second step: denoise the solution by thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fSpars = SoftThreshPsi(fSpars, lambd);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 1__\n",
    "\n",
    "Perform the iterative soft thresholding.\n",
    "Monitor the decay of the energy $E$ you are minimizing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000024F76518>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo1.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000024D2ACC0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(clamP(fSpars))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 2__\n",
    "\n",
    "Since there is no noise, one should in theory take $\\lambda\n",
    "\\rightarrow 0$.\n",
    "To do this, decay the value of $\\lambda$ through the iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001ED83860>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x0000000024F89518>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo2.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Inpainting using Translation Invariant Wavelet Sparsity\n",
    "-------------------------------------------------------\n",
    "Orthogonal sparsity performs a poor regularization because of the lack of\n",
    "translation invariance. This regularization is enhanced by considering\n",
    "$\\Psi$ as a redundant tight frame of translation invariant wavelets.\n",
    "\n",
    "\n",
    "One thus looks for optimal coefficients $a^\\star$ that solves\n",
    "$$a^{\\star} \\in \\text{argmin}_a \\: E(a) = \\frac{1}{2}\\|y-\\Phi \\Psi a\\|^2 + \\lambda J(a)$$\n",
    "\n",
    "\n",
    "*Important*: The operator $\\Psi^*$ is the forward translation invariant wavelet transform.\n",
    "It computes the inner product with the unit norm wavelet atoms:\n",
    "$$ (\\Psi^* f)_m = \\langle f,\\psi_m \\rangle \\quad \\text{with} \\quad \\|\\psi_m\\|=1. $$\n",
    "\n",
    "\n",
    "The reconstruction operator $\\Xi$ satisfies $ \\Xi \\Psi^* f = f $, and\n",
    "is the pseudo inverse of the analysis operator $ \\Xi = (\\Psi^*)^+ $.\n",
    "\n",
    "\n",
    "For our algorithm, we will need to use $\\Psi$ and not $\\Xi$. Lukily,\n",
    "for the wavelet transform, one has\n",
    "$$ \\Xi = \\Psi \\text{diag(U)} f $$\n",
    "where $U_m$ account for the redundancy of the scale of the atom\n",
    "$\\psi_m$.\n",
    "\n",
    "\n",
    "Compute the scaling factor (inverse of the redundancy)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " ⋮                                   ⋱  ⋮                                 \n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       "\n",
       "...\n",
       "\n",
       "[:, :, 11] =\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " ⋮                             ⋮     ⋱                    ⋮               \n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       "\n",
       "[:, :, 12] =\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " ⋮                             ⋮     ⋱                    ⋮               \n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       "\n",
       "[:, :, 13] =\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " ⋮                             ⋮     ⋱                    ⋮               \n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J = Jmax - Jmin + 1;\n",
    "\n",
    "u = reshape([4^(-J); 4.^(-floor(J+2/3:-1/3:1))], (1, 1, 13))\n",
    "\n",
    "U = repeat(u, inner = [n, n, 1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Choose a value of the regularization parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambd = .01;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut for the wavelet transform and the reconstruction.\n",
    "\n",
    "\n",
    "\n",
    "*Important:* Scilab users have to create files |Xi.m|, |PsiS.m| and |Psi.m| to implement this\n",
    "function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Xi = a -> NtToolBox.perform_wavelet_transf(a, Jmin, -1, \"9-7\", 0, 1)\n",
    "PsiS = f -> NtToolBox.perform_wavelet_transf(f, Jmin, + 1, \"9-7\", 0, 1)\n",
    "Psi = a -> Xi(a./U);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The forward-backward algorithm now compute a series of wavelet\n",
    "coefficients $a^{(\\ell)}$ computed as\n",
    "$$a^{(\\ell+1)} = S_{\\tau\\lambda}( a^{(\\ell)} + \\Psi^*\\Phi( y - \\Phi\\Psi a^{(\\ell)} )  ). $$\n",
    "\n",
    "\n",
    "The soft thresholding is defined as:\n",
    "$$\\forall m, \\quad S_T(a)_m = \\max(0, 1-T/\\|a_m\\|)a_m. $$\n",
    "\n",
    "\n",
    "The step size should satisfy:\n",
    "$$\\tau < \\frac{2}{\\|\\Psi\\Phi \\|} \\leq 2 \\min( u ). $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007421875"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tau = 1.9*minimum(u);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialize the wavelet coefficients with those of the previous reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128×13 Array{Float64,3}:\n",
       "[:, :, 1] =\n",
       " 0.0323998  0.0323408  0.032198   …  0.0497627  0.0497896  0.0498026\n",
       " 0.0323222  0.0322629  0.0321195     0.049747   0.0497735  0.0497863\n",
       " 0.0320984  0.0320383  0.0318918     0.0497036  0.0497298  0.0497425\n",
       " 0.031718   0.0316577  0.0315087     0.0496433  0.0496698  0.0496825\n",
       " 0.0311659  0.0311074  0.0309599     0.0495708  0.0495982  0.0496111\n",
       " 0.0304433  0.0303877  0.0302443  …  0.0494936  0.0495219  0.0495349\n",
       " 0.0295714  0.0295197  0.0293834     0.0494165  0.0494451  0.049458 \n",
       " 0.0285937  0.0285468  0.0284203     0.0493344  0.0493626  0.0493751\n",
       " 0.0275173  0.0274758  0.0273607     0.0492568  0.0492838  0.0492956\n",
       " 0.026379   0.0263437  0.0262417     0.0491961  0.0492221  0.0492333\n",
       " 0.0252068  0.0251783  0.0250907  …  0.0491663  0.0491926  0.0492036\n",
       " 0.0239974  0.0239752  0.0239017     0.0491732  0.0492007  0.0492117\n",
       " 0.0227982  0.022781   0.0227206     0.0492064  0.0492362  0.049248 \n",
       " ⋮                                ⋱  ⋮                              \n",
       " 0.0382111  0.0381686  0.0379823     0.0554137  0.0557831  0.0559001\n",
       " 0.0386472  0.0385807  0.0383335     0.0555067  0.0558895  0.0560103\n",
       " 0.0389726  0.0388838  0.0385819     0.0555916  0.0559873  0.0561121\n",
       " 0.039167   0.0390565  0.038703      0.0556713  0.056079   0.0562073\n",
       " 0.0392543  0.0391239  0.0387253  …  0.0557556  0.0561754  0.0563073\n",
       " 0.0392432  0.039097   0.0386641     0.0558498  0.0562819  0.0564178\n",
       " 0.0391019  0.0389432  0.0384843     0.055957   0.056401   0.0565408\n",
       " 0.038889   0.0387209  0.038244      0.0560627  0.0565176  0.0566608\n",
       " 0.0387639  0.038588   0.0380964     0.0561424  0.0566062  0.0567523\n",
       " 0.0387139  0.0385291  0.0380195  …  0.056187   0.0566565  0.0568045\n",
       " 0.0387146  0.0385229  0.0379989     0.0562012  0.056674   0.056823 \n",
       " 0.0387365  0.0385424  0.038014      0.0562015  0.0566757  0.0568252\n",
       "\n",
       "[:, :, 2] =\n",
       "  0.00517647    0.00517974    0.00520866   …   0.000453717   0.000450113\n",
       "  0.00494234    0.00494263    0.00496545       0.000460674   0.000457591\n",
       "  0.00430781    0.00430343    0.00431392       0.000493755   0.000492376\n",
       "  0.003369      0.00336223    0.00336226       0.000513809   0.000514249\n",
       "  0.002139      0.00212951    0.00211789       0.000498846   0.000500436\n",
       "  0.000783836   0.00077358    0.000752523  …   0.00046975    0.000472512\n",
       " -0.000455605  -0.000464663  -0.000491254      0.000428269   0.000432135\n",
       " -0.00151366   -0.00152437   -0.00155787       0.000335391   0.000340167\n",
       " -0.00234035   -0.00235136   -0.00238571       0.000150589   0.000155272\n",
       " -0.00277925   -0.00278589   -0.0028116       -8.79292e-5   -8.46004e-5 \n",
       " -0.00278339   -0.00278594   -0.00280389   …  -0.000359     -0.000358327\n",
       " -0.00249213   -0.00249172   -0.00250609      -0.00060884   -0.000610867\n",
       " -0.00190337   -0.00189785   -0.00190492      -0.000821571  -0.000825059\n",
       "  ⋮                                        ⋱                            \n",
       "  0.00361317    0.0035157     0.00327191      -0.000156927  -0.000157751\n",
       "  0.00311397    0.00302163    0.00280189       7.32275e-5    7.75564e-5 \n",
       "  0.00262674    0.00254535    0.00235944       0.000221212   0.000229091\n",
       "  0.00191046    0.00184993    0.00170897       0.000311088   0.000320092\n",
       "  0.00101829    0.000980576   0.00088745   …   0.000377979   0.00038726 \n",
       "  3.51231e-5    2.00672e-5   -2.05707e-5       0.00041864    0.00042811 \n",
       " -0.00106653   -0.00106246   -0.00105575       0.000405405   0.000414133\n",
       " -0.00205521   -0.00204404   -0.00200543       0.000322731   0.000330442\n",
       " -0.00278134   -0.00276769   -0.00270948       0.000213383   0.000219765\n",
       " -0.00340196   -0.00338264   -0.00330966   …   0.000131161   0.000135772\n",
       " -0.00381386   -0.00379104   -0.00371005       9.1912e-5     9.55647e-5 \n",
       " -0.00393484   -0.00391203   -0.00382998       8.23326e-5    8.59554e-5 \n",
       "\n",
       "[:, :, 3] =\n",
       "  0.00138346    0.00134712    0.00132677   …  0.000294635  0.000295266\n",
       "  0.00135317    0.00131994    0.00130722      0.000291986  0.000292514\n",
       "  0.00126775    0.00123879    0.00123711      0.00029099   0.000291185\n",
       "  0.00117381    0.00114881    0.00115346      0.000299619  0.000300178\n",
       "  0.00112772    0.00110504    0.00110927      0.000316047  0.00031857 \n",
       "  0.00113961    0.00111067    0.0010943    …  0.000339363  0.000343832\n",
       "  0.00117624    0.00113606    0.00108741      0.000364889  0.000369789\n",
       "  0.00121848    0.00116595    0.00108587      0.000383485  0.000387823\n",
       "  0.0012667     0.00120006    0.00108392      0.000396432  0.000398699\n",
       "  0.00129647    0.0012172     0.00106779      0.000404625  0.000404162\n",
       "  0.00130226    0.0012131     0.00103741   …  0.0004126    0.000409924\n",
       "  0.00125916    0.00116201    0.000964115     0.00042561   0.000420912\n",
       "  0.00111489    0.00101673    0.000814625     0.000437259  0.000431794\n",
       "  ⋮                                        ⋱                          \n",
       " -0.00701353   -0.00645471   -0.00488546      0.00423701   0.00419635 \n",
       " -0.0061419    -0.00556284   -0.00394824      0.00463457   0.00461425 \n",
       " -0.00523841   -0.00464047   -0.00298138      0.00500965   0.00500903 \n",
       " -0.00434972   -0.00373374   -0.00203747      0.00536678   0.00538489 \n",
       " -0.00349784   -0.00286825   -0.00114521   …  0.00571198   0.00574873 \n",
       " -0.00268225   -0.00204489   -0.00030208      0.0060428    0.00609817 \n",
       " -0.00197506   -0.00133154    0.000422803     0.00636174   0.00643585 \n",
       " -0.00138652   -0.000738818   0.00102683      0.00664149   0.00673154 \n",
       " -0.000848183  -0.000201675   0.0015706       0.00686179   0.00696506 \n",
       " -0.000418623   0.000221834   0.00199185   …  0.00701477   0.00712807 \n",
       " -0.000118745   0.000514737   0.00227896      0.00709912   0.00721828 \n",
       "  8.54528e-6    0.000639047   0.00239924      0.00712595   0.00724738 \n",
       "\n",
       "...\n",
       "\n",
       "[:, :, 11] =\n",
       "  0.00917278    0.0059813    -0.0003906    …   2.6135e-5    -0.00727329 \n",
       " -0.00578015   -0.00345774   -9.64634e-5       2.88868e-6    0.00466319 \n",
       "  0.000226373  -0.00015325    0.000920243     -0.00055009   -0.000929758\n",
       "  0.00289008    0.00186457    4.47425e-5       1.84094e-6   -0.00195206 \n",
       " -0.0011004    -0.000295352  -0.000969456      0.00134247    0.00332507 \n",
       " -3.05964e-6    0.000455492   9.06466e-6   …  -2.87702e-6    0.00015365 \n",
       " -0.00648117   -0.00686412    0.00171912      -0.0038552    -0.00532766 \n",
       "  0.012836      0.0127208     5.0436e-6        0.00529647    0.00647929 \n",
       " -0.00939992   -0.0143707    -0.00260384      -0.00197791   -0.00421301 \n",
       "  2.57869e-6    0.0121628    -9.07698e-6      -1.95516e-6    5.58853e-5 \n",
       "  0.00194427   -0.00793574    0.00106706   …  -0.000226475   0.0101109  \n",
       " -1.61525e-5    0.00201233    1.54474e-6      -0.000125637  -0.0156778  \n",
       " -0.000253978   0.00230396   -0.000617237     -0.00123861    0.00256596 \n",
       "  ⋮                                        ⋱                            \n",
       " -0.0113686    -0.0107581    -0.00820473       0.00462062    0.00193607 \n",
       " -1.5835e-6     0.000135531   0.000844468      0.000351036  -0.0010109  \n",
       "  0.00553721    0.0118431     0.0120688       -0.0017466     0.00297146 \n",
       "  1.89804e-5   -0.0135594    -0.0155274       -6.6132e-6    -0.00105747 \n",
       " -0.00669351    0.00859285    0.00832474   …  -0.000579034  -0.00308679 \n",
       "  1.24352e-5   -0.00573448   -1.0406e-7        0.00178989    0.00218958 \n",
       "  0.0247506     0.00643042   -0.000939542     -0.00130609    0.00198111 \n",
       " -0.0406369    -0.00350874   -7.5799e-6       -0.000372674  -0.00223376 \n",
       "  0.024568     -0.00146143   -0.00114894       0.00132469    0.00165565 \n",
       "  9.05832e-7   -4.31222e-6   -3.18369e-6   …  -1.46323e-5   -0.00127304 \n",
       " -0.00402011    0.0061899     0.000796783     -0.000598393  -0.00490415 \n",
       " -5.99336e-7   -0.00909471    4.52905e-6       7.73119e-8    0.00990787 \n",
       "\n",
       "[:, :, 12] =\n",
       " -0.00449085    0.00396476   -0.00232793   …  -0.004166      0.000106307\n",
       " -0.00319138    0.00245479   -0.00263145      -0.00319149    0.00150597 \n",
       "  0.000276887  -4.09888e-7   -0.0035307       -5.42174e-5    1.72207e-6 \n",
       " -0.000669645   0.00224556   -0.00571916       0.000406822  -0.000740761\n",
       "  0.00156905    8.3065e-7    -0.00376568      -0.00287511    0.00385917 \n",
       "  0.0121829    -0.0107244     0.00396029   …  -0.00337479    0.0040742  \n",
       "  0.00143818    3.64192e-6   -0.00286217      -0.000834918  -3.2223e-6  \n",
       " -0.0150026     0.0160502    -0.0109862        0.00254461   -0.00426762 \n",
       " -0.00333856    1.73205e-5    0.0149371        0.000350724  -8.21148e-6 \n",
       "  0.0063219    -0.0110108     0.0278823       -0.0072361     0.0127171  \n",
       "  0.00264213    1.18644e-6   -0.000154913  …  -0.00335475    0.00419147 \n",
       "  0.00187368    0.00315936   -0.0111698        0.00271088   -0.0100405  \n",
       "  0.00291421    1.52903e-6   -0.00382745      -0.00441138    0.00492219 \n",
       "  ⋮                                        ⋱                            \n",
       " -0.00155628   -2.30734e-6    0.00878927       0.0111443    -0.0242021  \n",
       " -0.00695112   -0.000924208   0.0135361        0.00185189   -0.0106929  \n",
       " -0.00444753    1.7005e-7     0.00510469      -0.0030131    -0.000350499\n",
       " -0.00283263   -4.38726e-5    0.00161316      -0.000740089  -0.00451854 \n",
       " -0.00464792   -3.13702e-5    0.0019732    …   0.00214606   -0.00986261 \n",
       "  0.00208197    0.000606016  -0.0084714       -0.00184894   -0.00279289 \n",
       " -0.0057928    -2.36751e-6    0.00556668      -0.00336604   -0.000118007\n",
       " -0.0150847    -0.000946847   0.0154178        0.00298061   -0.0110905  \n",
       "  0.00436221   -7.43884e-6   -0.0181692        0.00729842   -0.0202426  \n",
       "  0.011324      0.000659877  -0.0245522    …   0.00633017   -0.0198908  \n",
       "  0.000485084  -1.67179e-7   -0.0091768        0.00173709   -0.00808405 \n",
       " -0.00203203   -0.000379899  -0.00998926      -0.00163171    0.0013418  \n",
       "\n",
       "[:, :, 13] =\n",
       "  0.00355613   -0.00148139    0.00109446   …   0.00567658   -0.011787   \n",
       " -0.00390518    0.00225513   -0.000823849     -0.00585691    0.00992344 \n",
       "  0.00291568   -0.00260679    0.00092917       0.00384719   -0.00452704 \n",
       "  0.000769272  -4.32777e-5   -0.000172785      0.000322157  -0.0015609  \n",
       " -0.00507854    0.0045675    -0.00264505      -0.00148378    0.0028184  \n",
       " -0.000486914  -2.54141e-6    0.000993943  …   0.000106665  -2.74196e-5 \n",
       "  0.0223541    -0.0205873     0.0111644       -0.000694964  -1.35017e-5 \n",
       " -0.037605      0.0342995    -0.0187872        0.000727461  -0.000130751\n",
       "  0.0284017    -0.0205045    -0.00207004       0.00220342   -0.00411383 \n",
       " -0.0131143    -1.62847e-6    0.0304887        6.58912e-5   -3.36512e-6 \n",
       "  0.00633852    0.00410443   -0.025955     …  -0.011318      0.0199959  \n",
       " -0.00288937    3.68533e-6    0.00357207       0.0198394    -0.0331738  \n",
       " -0.00139255   -0.000999686   0.00773926      -0.0161178     0.0205128  \n",
       "  ⋮                                        ⋱                            \n",
       "  0.00140687   -0.00146856    0.00183502      -0.00371426    0.00227529 \n",
       " -0.000101363  -2.76017e-6   -0.000649082      0.00185308   -0.00307042 \n",
       " -0.00647417    0.000397433   0.00787183      -0.00345536    0.00705918 \n",
       "  0.0127634     2.95358e-5   -0.0174405        5.61066e-5   -0.000509055\n",
       " -0.0132811    -0.000300215   0.019811     …   0.00292933   -0.0052473  \n",
       "  0.00418413    1.09733e-5   -0.00906009       0.000416578  -0.000188827\n",
       "  0.0167908     0.00120511   -0.0217332       -0.00517419    0.00816235 \n",
       " -0.0329837    -0.00200856    0.0501814        0.00375625   -0.00551317 \n",
       "  0.0230317     0.00119328   -0.0384689       -0.000278776   0.000643716\n",
       " -4.47471e-6    8.36188e-7   -8.85988e-6   …  -0.000206552  -0.000759992\n",
       " -0.0103651    -0.000191526   0.0237438        0.00282315   -0.00670209 \n",
       "  0.0106138    -5.11262e-7   -0.0282697       -0.00561311    0.014263   "
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = U.*PsiS(fSpars) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128×13 Array{Float64,3}:\n",
       "[:, :, 1] =\n",
       " 0.0323998  0.0323408  0.032198   …  0.0497627  0.0497896  0.0498026\n",
       " 0.0323222  0.0322629  0.0321195     0.049747   0.0497735  0.0497863\n",
       " 0.0320984  0.0320383  0.0318918     0.0497036  0.0497298  0.0497425\n",
       " 0.031718   0.0316577  0.0315087     0.0496433  0.0496698  0.0496825\n",
       " 0.0311659  0.0311074  0.0309599     0.0495708  0.0495982  0.0496111\n",
       " 0.0304433  0.0303877  0.0302443  …  0.0494936  0.0495219  0.0495349\n",
       " 0.0295714  0.0295197  0.0293834     0.0494165  0.0494451  0.049458 \n",
       " 0.0285937  0.0285468  0.0284203     0.0493344  0.0493626  0.0493751\n",
       " 0.0275173  0.0274758  0.0273607     0.0492568  0.0492838  0.0492956\n",
       " 0.026379   0.0263437  0.0262417     0.0491961  0.0492221  0.0492333\n",
       " 0.0252068  0.0251783  0.0250907  …  0.0491663  0.0491926  0.0492036\n",
       " 0.0239974  0.0239752  0.0239017     0.0491732  0.0492007  0.0492117\n",
       " 0.0227982  0.022781   0.0227206     0.0492064  0.0492362  0.049248 \n",
       " ⋮                                ⋱  ⋮                              \n",
       " 0.0382111  0.0381686  0.0379823     0.0554137  0.0557831  0.0559001\n",
       " 0.0386472  0.0385807  0.0383335     0.0555067  0.0558895  0.0560103\n",
       " 0.0389726  0.0388838  0.0385819     0.0555916  0.0559873  0.0561121\n",
       " 0.039167   0.0390565  0.038703      0.0556713  0.056079   0.0562073\n",
       " 0.0392543  0.0391239  0.0387253  …  0.0557556  0.0561754  0.0563073\n",
       " 0.0392432  0.039097   0.0386641     0.0558498  0.0562819  0.0564178\n",
       " 0.0391019  0.0389432  0.0384843     0.055957   0.056401   0.0565408\n",
       " 0.038889   0.0387209  0.038244      0.0560627  0.0565176  0.0566608\n",
       " 0.0387639  0.038588   0.0380964     0.0561424  0.0566062  0.0567523\n",
       " 0.0387139  0.0385291  0.0380195  …  0.056187   0.0566565  0.0568045\n",
       " 0.0387146  0.0385229  0.0379989     0.0562012  0.056674   0.056823 \n",
       " 0.0387365  0.0385424  0.038014      0.0562015  0.0566757  0.0568252\n",
       "\n",
       "[:, :, 2] =\n",
       "  0.00517647    0.00517974    0.00520866   …   0.000453717   0.000450113\n",
       "  0.00494234    0.00494263    0.00496545       0.000460674   0.000457591\n",
       "  0.00430781    0.00430343    0.00431392       0.000493755   0.000492376\n",
       "  0.003369      0.00336223    0.00336226       0.000513809   0.000514249\n",
       "  0.002139      0.00212951    0.00211789       0.000498846   0.000500436\n",
       "  0.000783836   0.00077358    0.000752523  …   0.00046975    0.000472512\n",
       " -0.000455605  -0.000464663  -0.000491254      0.000428269   0.000432135\n",
       " -0.00151366   -0.00152437   -0.00155787       0.000335391   0.000340167\n",
       " -0.00234035   -0.00235136   -0.00238571       0.000150589   0.000155272\n",
       " -0.00277925   -0.00278589   -0.0028116       -8.79292e-5   -8.46004e-5 \n",
       " -0.00278339   -0.00278594   -0.00280389   …  -0.000359     -0.000358327\n",
       " -0.00249213   -0.00249172   -0.00250609      -0.00060884   -0.000610867\n",
       " -0.00190337   -0.00189785   -0.00190492      -0.000821571  -0.000825059\n",
       "  ⋮                                        ⋱                            \n",
       "  0.00361317    0.0035157     0.00327191      -0.000156927  -0.000157751\n",
       "  0.00311397    0.00302163    0.00280189       7.32275e-5    7.75564e-5 \n",
       "  0.00262674    0.00254535    0.00235944       0.000221212   0.000229091\n",
       "  0.00191046    0.00184993    0.00170897       0.000311088   0.000320092\n",
       "  0.00101829    0.000980576   0.00088745   …   0.000377979   0.00038726 \n",
       "  3.51231e-5    2.00672e-5   -2.05707e-5       0.00041864    0.00042811 \n",
       " -0.00106653   -0.00106246   -0.00105575       0.000405405   0.000414133\n",
       " -0.00205521   -0.00204404   -0.00200543       0.000322731   0.000330442\n",
       " -0.00278134   -0.00276769   -0.00270948       0.000213383   0.000219765\n",
       " -0.00340196   -0.00338264   -0.00330966   …   0.000131161   0.000135772\n",
       " -0.00381386   -0.00379104   -0.00371005       9.1912e-5     9.55647e-5 \n",
       " -0.00393484   -0.00391203   -0.00382998       8.23326e-5    8.59554e-5 \n",
       "\n",
       "[:, :, 3] =\n",
       "  0.00138346    0.00134712    0.00132677   …  0.000294635  0.000295266\n",
       "  0.00135317    0.00131994    0.00130722      0.000291986  0.000292514\n",
       "  0.00126775    0.00123879    0.00123711      0.00029099   0.000291185\n",
       "  0.00117381    0.00114881    0.00115346      0.000299619  0.000300178\n",
       "  0.00112772    0.00110504    0.00110927      0.000316047  0.00031857 \n",
       "  0.00113961    0.00111067    0.0010943    …  0.000339363  0.000343832\n",
       "  0.00117624    0.00113606    0.00108741      0.000364889  0.000369789\n",
       "  0.00121848    0.00116595    0.00108587      0.000383485  0.000387823\n",
       "  0.0012667     0.00120006    0.00108392      0.000396432  0.000398699\n",
       "  0.00129647    0.0012172     0.00106779      0.000404625  0.000404162\n",
       "  0.00130226    0.0012131     0.00103741   …  0.0004126    0.000409924\n",
       "  0.00125916    0.00116201    0.000964115     0.00042561   0.000420912\n",
       "  0.00111489    0.00101673    0.000814625     0.000437259  0.000431794\n",
       "  ⋮                                        ⋱                          \n",
       " -0.00701353   -0.00645471   -0.00488546      0.00423701   0.00419635 \n",
       " -0.0061419    -0.00556284   -0.00394824      0.00463457   0.00461425 \n",
       " -0.00523841   -0.00464047   -0.00298138      0.00500965   0.00500903 \n",
       " -0.00434972   -0.00373374   -0.00203747      0.00536678   0.00538489 \n",
       " -0.00349784   -0.00286825   -0.00114521   …  0.00571198   0.00574873 \n",
       " -0.00268225   -0.00204489   -0.00030208      0.0060428    0.00609817 \n",
       " -0.00197506   -0.00133154    0.000422803     0.00636174   0.00643585 \n",
       " -0.00138652   -0.000738818   0.00102683      0.00664149   0.00673154 \n",
       " -0.000848183  -0.000201675   0.0015706       0.00686179   0.00696506 \n",
       " -0.000418623   0.000221834   0.00199185   …  0.00701477   0.00712807 \n",
       " -0.000118745   0.000514737   0.00227896      0.00709912   0.00721828 \n",
       "  8.54528e-6    0.000639047   0.00239924      0.00712595   0.00724738 \n",
       "\n",
       "...\n",
       "\n",
       "[:, :, 11] =\n",
       "  0.00917278    0.0059813    -0.0003906    …   2.6135e-5    -0.00727329 \n",
       " -0.00578015   -0.00345774   -9.64634e-5       2.88868e-6    0.00466319 \n",
       "  0.000226373  -0.00015325    0.000920243     -0.00055009   -0.000929758\n",
       "  0.00289008    0.00186457    4.47425e-5       1.84094e-6   -0.00195206 \n",
       " -0.0011004    -0.000295352  -0.000969456      0.00134247    0.00332507 \n",
       " -3.05964e-6    0.000455492   9.06466e-6   …  -2.87702e-6    0.00015365 \n",
       " -0.00648117   -0.00686412    0.00171912      -0.0038552    -0.00532766 \n",
       "  0.012836      0.0127208     5.0436e-6        0.00529647    0.00647929 \n",
       " -0.00939992   -0.0143707    -0.00260384      -0.00197791   -0.00421301 \n",
       "  2.57869e-6    0.0121628    -9.07698e-6      -1.95516e-6    5.58853e-5 \n",
       "  0.00194427   -0.00793574    0.00106706   …  -0.000226475   0.0101109  \n",
       " -1.61525e-5    0.00201233    1.54474e-6      -0.000125637  -0.0156778  \n",
       " -0.000253978   0.00230396   -0.000617237     -0.00123861    0.00256596 \n",
       "  ⋮                                        ⋱                            \n",
       " -0.0113686    -0.0107581    -0.00820473       0.00462062    0.00193607 \n",
       " -1.5835e-6     0.000135531   0.000844468      0.000351036  -0.0010109  \n",
       "  0.00553721    0.0118431     0.0120688       -0.0017466     0.00297146 \n",
       "  1.89804e-5   -0.0135594    -0.0155274       -6.6132e-6    -0.00105747 \n",
       " -0.00669351    0.00859285    0.00832474   …  -0.000579034  -0.00308679 \n",
       "  1.24352e-5   -0.00573448   -1.0406e-7        0.00178989    0.00218958 \n",
       "  0.0247506     0.00643042   -0.000939542     -0.00130609    0.00198111 \n",
       " -0.0406369    -0.00350874   -7.5799e-6       -0.000372674  -0.00223376 \n",
       "  0.024568     -0.00146143   -0.00114894       0.00132469    0.00165565 \n",
       "  9.05832e-7   -4.31222e-6   -3.18369e-6   …  -1.46323e-5   -0.00127304 \n",
       " -0.00402011    0.0061899     0.000796783     -0.000598393  -0.00490415 \n",
       " -5.99336e-7   -0.00909471    4.52905e-6       7.73119e-8    0.00990787 \n",
       "\n",
       "[:, :, 12] =\n",
       " -0.00449085    0.00396476   -0.00232793   …  -0.004166      0.000106307\n",
       " -0.00319138    0.00245479   -0.00263145      -0.00319149    0.00150597 \n",
       "  0.000276887  -4.09888e-7   -0.0035307       -5.42174e-5    1.72207e-6 \n",
       " -0.000669645   0.00224556   -0.00571916       0.000406822  -0.000740761\n",
       "  0.00156905    8.3065e-7    -0.00376568      -0.00287511    0.00385917 \n",
       "  0.0121829    -0.0107244     0.00396029   …  -0.00337479    0.0040742  \n",
       "  0.00143818    3.64192e-6   -0.00286217      -0.000834918  -3.2223e-6  \n",
       " -0.0150026     0.0160502    -0.0109862        0.00254461   -0.00426762 \n",
       " -0.00333856    1.73205e-5    0.0149371        0.000350724  -8.21148e-6 \n",
       "  0.0063219    -0.0110108     0.0278823       -0.0072361     0.0127171  \n",
       "  0.00264213    1.18644e-6   -0.000154913  …  -0.00335475    0.00419147 \n",
       "  0.00187368    0.00315936   -0.0111698        0.00271088   -0.0100405  \n",
       "  0.00291421    1.52903e-6   -0.00382745      -0.00441138    0.00492219 \n",
       "  ⋮                                        ⋱                            \n",
       " -0.00155628   -2.30734e-6    0.00878927       0.0111443    -0.0242021  \n",
       " -0.00695112   -0.000924208   0.0135361        0.00185189   -0.0106929  \n",
       " -0.00444753    1.7005e-7     0.00510469      -0.0030131    -0.000350499\n",
       " -0.00283263   -4.38726e-5    0.00161316      -0.000740089  -0.00451854 \n",
       " -0.00464792   -3.13702e-5    0.0019732    …   0.00214606   -0.00986261 \n",
       "  0.00208197    0.000606016  -0.0084714       -0.00184894   -0.00279289 \n",
       " -0.0057928    -2.36751e-6    0.00556668      -0.00336604   -0.000118007\n",
       " -0.0150847    -0.000946847   0.0154178        0.00298061   -0.0110905  \n",
       "  0.00436221   -7.43884e-6   -0.0181692        0.00729842   -0.0202426  \n",
       "  0.011324      0.000659877  -0.0245522    …   0.00633017   -0.0198908  \n",
       "  0.000485084  -1.67179e-7   -0.0091768        0.00173709   -0.00808405 \n",
       " -0.00203203   -0.000379899  -0.00998926      -0.00163171    0.0013418  \n",
       "\n",
       "[:, :, 13] =\n",
       "  0.00355613   -0.00148139    0.00109446   …   0.00567658   -0.011787   \n",
       " -0.00390518    0.00225513   -0.000823849     -0.00585691    0.00992344 \n",
       "  0.00291568   -0.00260679    0.00092917       0.00384719   -0.00452704 \n",
       "  0.000769272  -4.32777e-5   -0.000172785      0.000322157  -0.0015609  \n",
       " -0.00507854    0.0045675    -0.00264505      -0.00148378    0.0028184  \n",
       " -0.000486914  -2.54141e-6    0.000993943  …   0.000106665  -2.74196e-5 \n",
       "  0.0223541    -0.0205873     0.0111644       -0.000694964  -1.35017e-5 \n",
       " -0.037605      0.0342995    -0.0187872        0.000727461  -0.000130751\n",
       "  0.0284017    -0.0205045    -0.00207004       0.00220342   -0.00411383 \n",
       " -0.0131143    -1.62847e-6    0.0304887        6.58912e-5   -3.36512e-6 \n",
       "  0.00633852    0.00410443   -0.025955     …  -0.011318      0.0199959  \n",
       " -0.00288937    3.68533e-6    0.00357207       0.0198394    -0.0331738  \n",
       " -0.00139255   -0.000999686   0.00773926      -0.0161178     0.0205128  \n",
       "  ⋮                                        ⋱                            \n",
       "  0.00140687   -0.00146856    0.00183502      -0.00371426    0.00227529 \n",
       " -0.000101363  -2.76017e-6   -0.000649082      0.00185308   -0.00307042 \n",
       " -0.00647417    0.000397433   0.00787183      -0.00345536    0.00705918 \n",
       "  0.0127634     2.95358e-5   -0.0174405        5.61066e-5   -0.000509055\n",
       " -0.0132811    -0.000300215   0.019811     …   0.00292933   -0.0052473  \n",
       "  0.00418413    1.09733e-5   -0.00906009       0.000416578  -0.000188827\n",
       "  0.0167908     0.00120511   -0.0217332       -0.00517419    0.00816235 \n",
       " -0.0329837    -0.00200856    0.0501814        0.00375625   -0.00551317 \n",
       "  0.0230317     0.00119328   -0.0384689       -0.000278776   0.000643716\n",
       " -4.47471e-6    8.36188e-7   -8.85988e-6   …  -0.000206552  -0.000759992\n",
       " -0.0103651    -0.000191526   0.0237438        0.00282315   -0.00670209 \n",
       "  0.0106138    -5.11262e-7   -0.0282697       -0.00561311    0.014263   "
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fTI = Psi(a)\n",
    "a = a + tau.*PsiS(Phi(y-Phi(fTI, Omega), Omega));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Soft threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128×13 Array{Float64,3}:\n",
       "[:, :, 1] =\n",
       " 0.0323256  0.0322666  0.0321238  …  0.0496885  0.0497154  0.0497284\n",
       " 0.032248   0.0321887  0.0320453     0.0496728  0.0496992  0.0497121\n",
       " 0.0320242  0.0319641  0.0318176     0.0496294  0.0496555  0.0496682\n",
       " 0.0316437  0.0315835  0.0314344     0.0495691  0.0495955  0.0496082\n",
       " 0.0310917  0.0310332  0.0308857     0.0494966  0.049524   0.0495368\n",
       " 0.0303691  0.0303135  0.0301701  …  0.0494194  0.0494477  0.0494607\n",
       " 0.0294972  0.0294455  0.0293092     0.0493423  0.0493709  0.0493838\n",
       " 0.0285195  0.0284726  0.0283461     0.0492602  0.0492884  0.0493009\n",
       " 0.0274431  0.0274016  0.0272865     0.0491826  0.0492095  0.0492214\n",
       " 0.0263047  0.0262695  0.0261674     0.0491219  0.0491479  0.0491591\n",
       " 0.0251326  0.0251041  0.0250165  …  0.0490921  0.0491183  0.0491293\n",
       " 0.0239232  0.0239009  0.0238275     0.049099   0.0491264  0.0491375\n",
       " 0.0227239  0.0227068  0.0226463     0.0491322  0.049162   0.0491738\n",
       " ⋮                                ⋱  ⋮                              \n",
       " 0.0381369  0.0380944  0.0379081     0.0553394  0.0557089  0.0558259\n",
       " 0.038573   0.0385065  0.0382593     0.0554324  0.0558153  0.0559361\n",
       " 0.0388984  0.0388096  0.0385077     0.0555174  0.0559131  0.0560379\n",
       " 0.0390928  0.0389823  0.0386288     0.0555971  0.0560048  0.0561331\n",
       " 0.03918    0.0390497  0.0386511  …  0.0556814  0.0561011  0.0562331\n",
       " 0.039169   0.0390228  0.0385898     0.0557755  0.0562076  0.0563436\n",
       " 0.0390277  0.0388689  0.0384101     0.0558827  0.0563268  0.0564666\n",
       " 0.0388148  0.0386467  0.0381698     0.0559885  0.0564434  0.0565866\n",
       " 0.0386897  0.0385137  0.0380221     0.0560682  0.056532   0.0566781\n",
       " 0.0386397  0.0384549  0.0379453  …  0.0561127  0.0565823  0.0567303\n",
       " 0.0386404  0.0384486  0.0379247     0.0561269  0.0565998  0.0567488\n",
       " 0.0386623  0.0384681  0.0379398     0.0561273  0.0566014  0.056751 \n",
       "\n",
       "[:, :, 2] =\n",
       "  0.00510226    0.00510552    0.00513444   …   0.000379498   0.000375894\n",
       "  0.00486813    0.00486841    0.00489124       0.000386455   0.000383373\n",
       "  0.00423359    0.00422921    0.0042397        0.000419537   0.000418157\n",
       "  0.00329478    0.00328801    0.00328804       0.000439591   0.00044003 \n",
       "  0.00206479    0.0020553     0.00204367       0.000424627   0.000426217\n",
       "  0.000709618   0.000699362   0.000678304  …   0.000395531   0.000398293\n",
       " -0.000381386  -0.000390444  -0.000417035      0.000354051   0.000357917\n",
       " -0.00143944   -0.00145015   -0.00148365       0.000261173   0.000265948\n",
       " -0.00226614   -0.00227714   -0.00231149       7.63704e-5    8.10535e-5 \n",
       " -0.00270503   -0.00271167   -0.00273738      -1.37104e-5   -1.03817e-5 \n",
       " -0.00270917   -0.00271172   -0.00272967   …  -0.000284781  -0.000284108\n",
       " -0.00241791   -0.0024175    -0.00243187      -0.000534622  -0.000536648\n",
       " -0.00182916   -0.00182363   -0.0018307       -0.000747352  -0.00075084 \n",
       "  ⋮                                        ⋱                            \n",
       "  0.00353895    0.00344148    0.00319769      -8.27083e-5   -8.35321e-5 \n",
       "  0.00303975    0.00294742    0.00272767       0.0           3.33761e-6 \n",
       "  0.00255252    0.00247113    0.00228522       0.000146993   0.000154873\n",
       "  0.00183624    0.00177572    0.00163476       0.000236869   0.000245873\n",
       "  0.000944073   0.000906358   0.000813231  …   0.000303761   0.000313041\n",
       "  0.0           0.0          -0.0              0.000344421   0.000353891\n",
       " -0.000992316  -0.000988242  -0.000981535      0.000331186   0.000339915\n",
       " -0.001981     -0.00196982   -0.00193121       0.000248512   0.000256223\n",
       " -0.00270712   -0.00269348   -0.00263526       0.000139164   0.000145546\n",
       " -0.00332774   -0.00330843   -0.00323545   …   5.69425e-5    6.15534e-5 \n",
       " -0.00373964   -0.00371682   -0.00363583       1.76932e-5    2.1346e-5  \n",
       " -0.00386062   -0.00383781   -0.00375576       8.11381e-6    1.17366e-5 \n",
       "\n",
       "[:, :, 3] =\n",
       "  0.00130924    0.00127291    0.00125255   …  0.000220417  0.000221047\n",
       "  0.00127895    0.00124572    0.001233        0.000217767  0.000218295\n",
       "  0.00119353    0.00116457    0.00116289      0.000216771  0.000216966\n",
       "  0.00109959    0.00107459    0.00107924      0.000225401  0.000225959\n",
       "  0.0010535     0.00103082    0.00103505      0.000241829  0.000244351\n",
       "  0.0010654     0.00103645    0.00102008   …  0.000265144  0.000269613\n",
       "  0.00110202    0.00106184    0.00101319      0.00029067   0.00029557 \n",
       "  0.00114426    0.00109173    0.00101165      0.000309267  0.000313605\n",
       "  0.00119248    0.00112585    0.0010097       0.000322214  0.000324481\n",
       "  0.00122225    0.00114298    0.000993568     0.000330406  0.000329943\n",
       "  0.00122804    0.00113888    0.000963195  …  0.000338382  0.000335706\n",
       "  0.00118494    0.00108779    0.000889896     0.000351391  0.000346693\n",
       "  0.00104067    0.000942508   0.000740406     0.00036304   0.000357576\n",
       "  ⋮                                        ⋱                          \n",
       " -0.00693931   -0.00638049   -0.00481124      0.00416279   0.00412214 \n",
       " -0.00606768   -0.00548862   -0.00387402      0.00456035   0.00454003 \n",
       " -0.0051642    -0.00456625   -0.00290716      0.00493543   0.00493481 \n",
       " -0.00427551   -0.00365952   -0.00196325      0.00529256   0.00531067 \n",
       " -0.00342362   -0.00279403   -0.001071     …  0.00563776   0.00567451 \n",
       " -0.00260803   -0.00197067   -0.000227861     0.00596858   0.00602395 \n",
       " -0.00190084   -0.00125732    0.000348584     0.00628752   0.00636163 \n",
       " -0.0013123    -0.000664599   0.000952607     0.00656727   0.00665733 \n",
       " -0.000773965  -0.000127456   0.00149638      0.00678757   0.00689084 \n",
       " -0.000344404   0.000147616   0.00191763   …  0.00694055   0.00705385 \n",
       " -4.45263e-5    0.000440518   0.00220474      0.0070249    0.00714406 \n",
       "  0.0           0.000564828   0.00232503      0.00705173   0.00717317 \n",
       "\n",
       "...\n",
       "\n",
       "[:, :, 11] =\n",
       "  0.00909856    0.00590708   -0.000316382  …   0.0          -0.00719907 \n",
       " -0.00570593   -0.00338352   -2.22446e-5       0.0           0.00458897 \n",
       "  0.000152154  -7.90309e-5    0.000846024     -0.000475871  -0.000855539\n",
       "  0.00281586    0.00179035    0.0              0.0          -0.00187784 \n",
       " -0.00102618   -0.000221133  -0.000895237      0.00126825    0.00325085 \n",
       " -0.0           0.000381273   0.0          …  -0.0           7.94315e-5 \n",
       " -0.00640695   -0.0067899     0.0016449       -0.00378098   -0.00525344 \n",
       "  0.0127618     0.0126466     0.0              0.00522225    0.00640507 \n",
       " -0.0093257    -0.0142965    -0.00252962      -0.0019037    -0.00413879 \n",
       "  0.0           0.0120885    -0.0             -0.0           0.0        \n",
       "  0.00187006   -0.00786152    0.000992838  …  -0.000152256   0.0100367  \n",
       " -0.0           0.00193811    0.0             -5.14187e-5   -0.0156036  \n",
       " -0.00017976    0.00222974   -0.000543018     -0.00116439    0.00249174 \n",
       "  ⋮                                        ⋱                            \n",
       " -0.0112943    -0.0106839    -0.00813051       0.0045464     0.00186185 \n",
       " -0.0           6.13123e-5    0.000770249      0.000276817  -0.000936678\n",
       "  0.00546299    0.0117689     0.0119946       -0.00167239    0.00289724 \n",
       "  0.0          -0.0134852    -0.0154532       -0.0          -0.000983246\n",
       " -0.00661929    0.00851863    0.00825052   …  -0.000504815  -0.00301257 \n",
       "  0.0          -0.00566026   -0.0              0.00171567    0.00211536 \n",
       "  0.0246764     0.0063562    -0.000865324     -0.00123187    0.00190689 \n",
       " -0.0405626    -0.00343452   -0.0             -0.000298456  -0.00215954 \n",
       "  0.0244938    -0.00138722   -0.00107472       0.00125047    0.00158143 \n",
       "  0.0          -0.0          -0.0          …  -0.0          -0.00119882 \n",
       " -0.00394589    0.00611568    0.000722564     -0.000524174  -0.00482993 \n",
       " -0.0          -0.00902049    0.0              0.0           0.00983365 \n",
       "\n",
       "[:, :, 12] =\n",
       " -0.00441663    0.00389054   -0.00225371  …  -0.00409178    3.20887e-5 \n",
       " -0.00311716    0.00238057   -0.00255723     -0.00311727    0.00143175 \n",
       "  0.000202668  -0.0          -0.00345648     -0.0           0.0        \n",
       " -0.000595426   0.00217134   -0.00564495      0.000332604  -0.000666543\n",
       "  0.00149483    0.0          -0.00369146     -0.00280089    0.00378495 \n",
       "  0.0121087    -0.0106502     0.00388607  …  -0.00330057    0.00399998 \n",
       "  0.00136396    0.0          -0.00278795     -0.000760699  -0.0        \n",
       " -0.0149284     0.015976     -0.010912        0.00247039   -0.0041934  \n",
       " -0.00326434    0.0           0.0148629       0.000276505  -0.0        \n",
       "  0.00624769   -0.0109366     0.027808       -0.00716188    0.0126429  \n",
       "  0.00256791    0.0          -8.06943e-5  …  -0.00328053    0.00411725 \n",
       "  0.00179946    0.00308514   -0.0110956       0.00263666   -0.00996628 \n",
       "  0.00283999    0.0          -0.00375323     -0.00433716    0.00484797 \n",
       "  ⋮                                       ⋱                            \n",
       " -0.00148207   -0.0           0.00871505      0.0110701    -0.0241279  \n",
       " -0.0068769    -0.000849989   0.0134619       0.00177767   -0.0106187  \n",
       " -0.00437331    0.0           0.00503047     -0.00293888   -0.00027628 \n",
       " -0.00275841   -0.0           0.00153894     -0.00066587   -0.00444432 \n",
       " -0.0045737    -0.0           0.00189899  …   0.00207184   -0.00978839 \n",
       "  0.00200775    0.000531797  -0.00839718     -0.00177472   -0.00271867 \n",
       " -0.00571858   -0.0           0.00549247     -0.00329182   -4.37879e-5 \n",
       " -0.0150105    -0.000872628   0.0153435       0.00290639   -0.0110163  \n",
       "  0.00428799   -0.0          -0.018095        0.0072242    -0.0201684  \n",
       "  0.0112498     0.000585658  -0.024478    …   0.00625595   -0.0198166  \n",
       "  0.000410866  -0.0          -0.00910258      0.00166287   -0.00800983 \n",
       " -0.00195781   -0.000305681  -0.00991504     -0.00155749    0.00126758 \n",
       "\n",
       "[:, :, 13] =\n",
       "  0.00348191   -0.00140717    0.00102024   …   0.00560236   -0.0117128  \n",
       " -0.00383096    0.00218091   -0.00074963      -0.0057827     0.00984923 \n",
       "  0.00284146   -0.00253257    0.000854952      0.00377297   -0.00445282 \n",
       "  0.000695053  -0.0          -9.85663e-5       0.000247939  -0.00148669 \n",
       " -0.00500433    0.00449328   -0.00257083      -0.00140956    0.00274418 \n",
       " -0.000412696  -0.0           0.000919725  …   3.24464e-5   -0.0        \n",
       "  0.0222799    -0.0205131     0.0110902       -0.000620745  -0.0        \n",
       " -0.0375308     0.0342253    -0.018713         0.000653242  -5.65321e-5 \n",
       "  0.0283275    -0.0204303    -0.00199582       0.0021292    -0.00403962 \n",
       " -0.0130401    -0.0           0.0304144        0.0          -0.0        \n",
       "  0.0062643     0.00403021   -0.0258808    …  -0.0112437     0.0199217  \n",
       " -0.00281515    0.0           0.00349786       0.0197651    -0.0330996  \n",
       " -0.00131833   -0.000925467   0.00766504      -0.0160436     0.0204386  \n",
       "  ⋮                                        ⋱                            \n",
       "  0.00133265   -0.00139434    0.0017608       -0.00364004    0.00220107 \n",
       " -2.71445e-5   -0.0          -0.000574863      0.00177886   -0.0029962  \n",
       " -0.00639995    0.000323214   0.00779761      -0.00338114    0.00698496 \n",
       "  0.0126892     0.0          -0.0173663        0.0          -0.000434836\n",
       " -0.0132069    -0.000225997   0.0197367    …   0.00285511   -0.00517308 \n",
       "  0.00410991    0.0          -0.00898587       0.000342359  -0.000114609\n",
       "  0.0167165     0.00113089   -0.021659        -0.00509997    0.00808813 \n",
       " -0.0329095    -0.00193434    0.0501072        0.00368203   -0.00543895 \n",
       "  0.0229575     0.00111906   -0.0383947       -0.000204558   0.000569497\n",
       " -0.0           0.0          -0.0          …  -0.000132334  -0.000685773\n",
       " -0.0102909    -0.000117307   0.0236696        0.00274893   -0.00662787 \n",
       "  0.0105395    -0.0          -0.0281955       -0.00553889    0.0141887  "
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = SoftThresh(a, lambd*tau);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 3__\n",
    "\n",
    "Perform the iterative soft thresholding. Monitor the decay of the\n",
    "energy $E$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000250835F8>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo3.jl\")\n",
    "\n",
    "# niter = 1000\n",
    "# a = U.*PsiS(fSpars)\n",
    "# E = []\n",
    "# for i in 1 : niter\n",
    "#     fTI = Psi(a)\n",
    "#     d = y - Phi(fTI, Omega)\n",
    "#     E = [E; 1/2.*vecnorm(d )^2 + lambd*sum(abs(a))]\n",
    "#     # step \n",
    "#     a = SoftThresh(a + tau.*PsiS(Phi(d, Omega)), lambd*tau)\n",
    "# end\n",
    "\n",
    "# figure(figsize = (7, 5))    \n",
    "# plot(E)\n",
    "# show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Perform the reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.5959    0.595353  0.595991  0.599185  …  0.807213  0.808388  0.808516\n",
       " 0.584907  0.588184  0.595149  0.599971     0.806676  0.808078  0.808128\n",
       " 0.57642   0.578371  0.584624  0.59133      0.805662  0.80676   0.80688 \n",
       " 0.553808  0.557782  0.563702  0.575164     0.804513  0.804783  0.806422\n",
       " 0.526524  0.527638  0.531838  0.545507     0.802583  0.805117  0.810185\n",
       " 0.515926  0.507072  0.512286  0.511787  …  0.801578  0.802938  0.805109\n",
       " 0.535189  0.514696  0.511119  0.498153     0.797553  0.801766  0.801545\n",
       " 0.490022  0.548615  0.486463  0.4634       0.799584  0.809141  0.811728\n",
       " 0.476114  0.453588  0.431169  0.393877     0.798867  0.803229  0.803014\n",
       " 0.426983  0.410282  0.35747   0.199237     0.797629  0.803465  0.808521\n",
       " 0.416674  0.400481  0.384433  0.374821  …  0.796928  0.805276  0.816949\n",
       " 0.429307  0.413717  0.373537  0.33173      0.801037  0.811888  0.804466\n",
       " 0.385212  0.386148  0.384318  0.368313     0.803085  0.809197  0.817707\n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.580924  0.568513  0.543235  0.486878     0.961058  0.931482  0.879598\n",
       " 0.545986  0.544897  0.540175  0.517487     0.967928  0.931906  0.889483\n",
       " 0.515031  0.523947  0.534806  0.539136     0.965063  0.933182  0.911034\n",
       " 0.493114  0.493515  0.509994  0.589143     0.96075   0.94113   0.917824\n",
       " 0.479228  0.499803  0.535113  0.551319  …  0.969464  0.946206  0.917224\n",
       " 0.477929  0.490436  0.529352  0.613429     0.963602  0.947622  0.925302\n",
       " 0.481471  0.490679  0.535707  0.686777     0.973385  0.94616   0.926498\n",
       " 0.476539  0.501362  0.550068  0.481006     0.987526  0.94981   0.921532\n",
       " 0.501373  0.517568  0.600884  0.776717     0.998177  0.962172  0.91704 \n",
       " 0.530728  0.546292  0.586503  0.622514  …  0.994391  0.968419  0.916097\n",
       " 0.546093  0.563104  0.596076  0.570503     0.96796   0.954034  0.923728\n",
       " 0.540378  0.556386  0.599143  0.728456     0.9488    0.941611  0.930387"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fTI = Psi(a);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000024D13470>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(clamP(fTI))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 4__\n",
    "\n",
    "Perform the iteration with a decaying value of $\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000025B1CF60>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x0000000025B44048>"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo4.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Inpainting using Iterative Hard Thresholding\n",
    "--------------------------------------------\n",
    "To improve the sparsity of the solution, it is possible to replace the\n",
    "soft thresholding by a hard threshdoling. In this case, the resulting\n",
    "algorihtm does not perform anymore a variational minimization of an\n",
    "energy.\n",
    "\n",
    "\n",
    "The hard thresholding is defined as $h_T(x)=0$ if $-T < x < T$\n",
    "and $h_T(x)=x$ otherwise. It thus defines a thresholding operator of\n",
    "wavelet coefficients as $H_T(a)_m = h_T(a_m)$.\n",
    "\n",
    "\n",
    "Define a shortcut for this vectorialized hard thresholding\n",
    "\n",
    "\n",
    "\n",
    "*Important:* Scilab users have to create a file |HardThresh.m| to implement this\n",
    "function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#103) (generic function with 1 method)"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HardThresh = (x, t) -> x.*(abs(x) .> t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display a curve of the 1-D Hard thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MvkJQAwCgDliffUj/7/+26/DxEgUFWPX4wA768/VtZWXCQL1GUAMAwI8Vl1XouU93a/7GnyVJ7SOaavbQ69Q5mmdVNwQENQAA/NRuh0vjFm1Tdv5xSdKIpNZKu62TggMDTK4MlwtBDQAAP+N2G5q/8Wc9l75bpeVuhTcN0ov3xqtfxwizS8NlRlADAMCPHHIVa+LS7/SPH45Ikvp3jNDz93ZTeFObyZXBDAQ1AAD8xOc7HZq0bLuOnSyTrZFVU+7orD8lXi2LhQkDDRVBDQAAk50sLdczq3Zp0eYcSVLnlna9OixBsRHNTK4MZiOoAQBgoqxfnBq3eKt+PFIki0V6+PftlPqHa2VrxIQBENQAADBFhdvQmxv2aebne1TuNhRlD9bM++PVJzbc7NLgRwhqAABcZrmFp5S6ZJs2/VQgSbo1Lkoz7umqsJAgkyuDvyGoAQBwGX383UE9sSJLx4vLFRIUoKfu6qL7urdiwgAqRVADAOAyOF5cpmkf7dTyLbmSpPiYMM1OSVCb8CYmVwZ/RlADAMDHMvcXaPySbTpQcEpWizS2X6we699egQFWs0uDnyOoAQDgI+UVbs1Zt1dz1v0gtyG1uqKxXklJUM82zc0uDXUEQQ0AAB/IOXpS45Zs1dacQknS3dddpemDusgeHGhyZahLCGoAANQiwzC0bEuupn24Q0WlFWoW3EjPDo7ToISrzC4NdRBBDQCAWuI8WaYnVmRpdVaeJKlXm+aamRKvVleEmFwZ6iqCGgAAtWDjviOa+MF3ynMWq5HVogm3XKsxfa9RgJVlN3DpCGoAANRAablbM9fs0Zsb9skwpLbhTTQrJUHxMWFml4Z6gKAGAMAl2nvohMYv2aoduS5J0tCeMXryjs5qYuPXK2oHP0kAAFSTYRhasClHz67+XsVlboWFBOq5e7ppYFyU2aWhniGoAQBQDUdPlGjSsu36YtchSdINseF6+f54RdqDTa4M9RFBDQCAKlqffUj/7/+26/DxEgUFWPX4wA768/VtZWXCAHzksjy74vXXX1ebNm0UHBysxMREbd68+bxt169fL4vFcs7mcDi82i1dulQdO3ZUcHCwunbtqk8++cTX3QAANFDFZRV66qOdGvnuNzp8vETtI5pq5aPX66HftyOkwad8HtSWLFmi1NRUTZs2TVu2bFF8fLwGDBigQ4cOXfC47Oxs5eXlebaIiAjPexs3btSwYcM0atQobd26VYMHD9bgwYO1Y8cOX3cHANDA7Ha4NOi1rzV/48+SpBFJrfXxYzeoc7Td3MLQIFgMwzB8+QGJiYnq2bOnXnvtNUmS2+1WTEyMHnvsMU2ePPmc9uvXr1e/fv107NgxhYVVPrU5JSVFRUVFWrVqlWdf7969lZCQoLlz5160JpfLpdDQUDmdTtnt/EEDAJzL7TY0f+PPei59t0rL3QpvGqQX741Xv44RFz8YOMulZg+fjqiVlpYqMzNTycnJv32g1ark5GRlZGRc8NiEhAS1bNlSt9xyi77++muv9zIyMrzOKUkDBgw47zlLSkrkcrm8NgAALuTZ1bv09KrvVVruVv+OEUoffyMhDZedT4PakSNHVFFRocjISK/9kZGR59xzdlrLli01d+5cLVu2TMuWLVNMTIxuuukmbdmyxdPG4XBU65wzZsxQaGioZ4uJialhzwAA9d2WnGOSpLH9YvX2iB4Kb2ozuSI0RH4367NDhw7q0KGD53WfPn20b98+vfLKK/qf//mfSzpnWlqaUlNTPa9dLhdhDQBwQafvDPpd6zBZLEwYgDl8GtTCw8MVEBCg/Px8r/35+fmKiqr6ooC9evXSP//5T8/rqKioap3TZrPJZuP/hAAAVXf6Bm6LCGkwj08vfQYFBal79+5au3atZ5/b7dbatWuVlJRU5fNs27ZNLVu29LxOSkryOqckrVmzplrnBADgQtyn59qR02Ain1/6TE1N1YgRI9SjRw/16tVLs2bNUlFRkR588EFJv16WzM3N1fvvvy9JmjVrltq2basuXbqouLhYb7/9ttatW6fPP//cc85x48apb9++evnll3X77bdr8eLF+vbbb/XWW2/5ujsAgAbidE6zctkTJvJ5UEtJSdHhw4c1depUORwOJSQkKD093TMZIC8vTzk5OZ72paWlmjhxonJzcxUSEqJu3brpiy++UL9+/Txt+vTpo4ULF2rKlCl64okn1L59e61cuVJxcXG+7g4AoIFwM6AGP+DzddT8EeuoAQAuZuCsDdrtOK7/HZWoG9qHm10O6ji/XEcNAIC6ynOLGkNqMBFBDQCAShj/nvdJUIOZCGoAAFTit0mfJDWYh6AGAEAlTi/PwYgazERQAwCgEqdn2rE8B8xEUAMAoBJMJoA/IKgBAFCJ06tXWQlqMBFBDQCASrg9q4yS1GAeghoAAJU4vTwHI2owE0ENAIBKuN2//tPCTWowEUENAIALIKbBTAQ1AAAq8dtkAqIazENQAwCgEm6W54AfIKgBAFAJnvUJf0BQAwCgEm6e9Qk/QFADAKASp59MYOU3JUzEjx8AAJU4PZmAETWYiaAGAEAlfnsou6lloIEjqAEAUAm3wWQCmI+gBgBAJQye9Qk/QFADAKASvy14a3IhaNAIagAAVMLwLHhLUoN5CGoAAFSCyQTwBwQ1AAAq4WZ5DvgBghoAAJUweNYn/ABBDQCASrA8B/wBQQ0AgEqcvkeNyQQwE0ENAIDKnH7WJzkNJiKoAQBQCSYTwB8Q1AAAqATLc8AfENQAAKiE2zPt09w60LAR1AAAqIThuUeNpAbzENQAADiL8dsT2RlQg6kuS1B7/fXX1aZNGwUHBysxMVGbN28+b9vly5frlltuUYsWLWS325WUlKTPPvvMq838+fNlsVi8tuDgYF93AwDQQJyR01ieA6byeVBbsmSJUlNTNW3aNG3ZskXx8fEaMGCADh06VGn7DRs26JZbbtEnn3yizMxM9evXT3feeae2bt3q1c5utysvL8+z7d+/39ddAQA0EO4zkhqTCWCmRr7+gJkzZ2r06NF68MEHJUlz587V6tWrNW/ePE2ePPmc9rNmzfJ6/Z//+Z/68MMP9fHHH+u6667z7LdYLIqKivJt8QCABumMATWW54CpfDqiVlpaqszMTCUnJ//2gVarkpOTlZGRUaVzuN1uHT9+XM2bN/faf+LECbVu3VoxMTEaNGiQdu7ced5zlJSUyOVyeW0AAJyP16VP7uaGiXz643fkyBFVVFQoMjLSa39kZKQcDkeVzvHSSy/pxIkTuv/++z37OnTooHnz5unDDz/U//7v/8rtdqtPnz765ZdfKj3HjBkzFBoa6tliYmIuvVMAgHrPzWQC+Am//v+EhQsXavr06frggw8UERHh2Z+UlKQHHnhACQkJ6tu3r5YvX64WLVrozTffrPQ8aWlpcjqdnu3AgQOXqwsAgDqO5TlgJp/eoxYeHq6AgADl5+d77c/Pz7/o/WWLFy/WQw89pKVLl3pdOq1MYGCgrrvuOu3du7fS9202m2w2W/WKBwA0WF4jauQ0mMinI2pBQUHq3r271q5d69nndru1du1aJSUlnfe4RYsW6cEHH9SiRYt0++23X/RzKioqlJWVpZYtW9ZK3QCAhs3rHjUufsJEPp/1mZqaqhEjRqhHjx7q1auXZs2apaKiIs8s0LS0NOXm5ur999+X9OvlzhEjRmj27NlKTEz03MvWuHFjhYaGSpKefvpp9e7dW7GxsSosLNSLL76o/fv366GHHvJ1dwAADQAjavAXPg9qKSkpOnz4sKZOnSqHw6GEhASlp6d7Jhjk5eUpJyfH0/6tt95SeXm5Hn30UT366KOe/SNGjND8+fMlSceOHdPo0aPlcDh0xRVXqHv37tq4caM6d+7s6+4AABoAr+U5CGowkcU48zkZDYTL5VJoaKicTqfsdrvZ5QAA/IzzZJnin/5ckvTD329VYIBfz71DHXCp2YOfPAAAzmKI5TngHwhqAACc5cxrTSzPATMR1AAAOAuTCeAvCGoAAJzFezIBSQ3mIagBAHCW0yNqZDSYjaAGAMDZ/j2kRk6D2QhqAACcxf3voMZEApiNoAYAwFlOL89BToPZCGoAAJzl9IgaEwlgNoIaAABnOf3QHmIazEZQAwDgLAb3qMFPENQAADiL4bn0aW4dAEENAICzeCYTmFwHQFADAOAsLM8Bf0FQAwDgLIbBirfwDwQ1AADOwoga/AVBDQCAc7DgLfwDQQ0AgLOwPAf8BUENAICzuLlFDX6CoAYAwFl41if8BUENAICzuN2//pNnfcJsBDUAAM7CgrfwFwQ1AADOwmQC+AuCGgAAZ+FZn/AXBDUAAM7i/ndSY0QNZiOoAQBwFsPsAoB/I6gBAHCW08/6ZEANZiOoAQBwFp71CX9BUAMA4ByMqME/ENQAADgLI2rwFwQ1AADOYvCsT/gJghoAAGdxM5kAfoKgBgDAWX5b8JakBnNdlqD2+uuvq02bNgoODlZiYqI2b958wfbr16/X7373O9lsNsXGxmr+/PnntFm6dKk6duyo4OBgde3aVZ988omPqgcANDSGZ8FbkwtBg+fzoLZkyRKlpqZq2rRp2rJli+Lj4zVgwAAdOnSo0vY//fSTbr/9dvXr10/btm3T+PHj9dBDD+mzzz7ztNm4caOGDRumUaNGaevWrRo8eLAGDx6sHTt2+Lo7AIAG4PSCtxbuUoPJLMbp/23wkcTERPXs2VOvvfaaJMntdismJkaPPfaYJk+efE77SZMmafXq1V6ha+jQoSosLFR6erokKSUlRUVFRVq1apWnTe/evZWQkKC5c+detCaXy6XQ0FA5nU7Z7faadhENXIXb0NacYyouc5tdCoBasuOgU899ulsdo5opffyNZpeDeuBSs0cjH9ak0tJSZWZmKi0tzbPParUqOTlZGRkZlR6TkZGh5ORkr30DBgzQ+PHjvdqkpqae02blypWVnrOkpEQlJSWe1y6Xq9p9Ac7ntXV79coXe8wuA4APBHDtEybzaVA7cuSIKioqFBkZ6bU/MjJSu3fvrvQYh8NRaXuXy6VTp06pcePG523jcDgqPeeMGTM0ffr0GvQEOL+cgpOSpPCmNoU3DTK5GgC1xWKx6MHr25pdBho4nwY1f5GWluY1AudyuRQTE2NiRahPjH/fzTL69231l77XmFwNAKA+8WlQCw8PV0BAgPLz87325+fnKyoqqtJjoqKiKm1vt9vVuHHjC7Y53zltNptsNtuldgO4IIMVzAEAPuLTWZ9BQUHq3r271q5d69nndru1du1aJSUlVXpMUlKSV3tJWrNmjVf7qrQBLheDhTEBAD7i8+U5UlNT9d///d967733tGvXLj3yyCMqKirSgw8+KOnXy5IPPPCAp/2YMWP0448/6vHHH9fu3bv1xhtv6IMPPtCECRM8bcaNG6f09HS9/PLL2r17t5566il9++23Gjt2rK+7A5zDzcKYAAAf8fk9aikpKTp8+LCmTp0qh8OhhIQEpaeneyYD5OXlKScnx9O+bdu2Wr16tSZMmKDZs2erVatWevvttzVgwABPmz59+mjhwoWaMmWKnnjiCbVv314rV65UXFycr7sDnOO39ZYAAKhdPl9HzR+xjhpq09iFW7Rqe56m3dmZGWIAgEpdavbgWZ9ADTGZAADgKwQ1oIZOL89BTgMA1DaCGlBD7n8/OYrJBACA2kZQA2rIM6Jmch0AgPqHoAbUkJt71AAAPkJQA2rI8KyjZm4dAID6h6AG1BiXPgEAvkFQA2qIS58AAF8hqAE15FkzmpwGAKhlBDWghhhRAwD4CkENqCGe9QkA8BWCGlBDpy99WvnTBACoZfxqAWrot1vUGFMDANQughpQQzzrEwDgKwQ1oIZ41icAwFcIakAN8axPAICvENSAGmJ5DgCArxDUgJriWZ8AAB8hqAE15D69PAdBDQBQywhqQA0Znn8jqQEAahdBDaghRtQAAL5CUANqyLPgLTepAQBqGUENqKHTlz4ZUQMA1DaCGlBDp5/1yYAaAKC2EdSAGuJZnwChMnl4AAAgAElEQVQAXyGoATXkZkQNAOAjBDWghphMAADwFYIaUEMszwEA8BWCGlBLuEcNAFDbCGpADRmeh7KbWwcAoP4hqAE15P5t2icAALWKoAbU0G8L3pLUAAC1y2dBraCgQMOHD5fdbldYWJhGjRqlEydOnLd9WVmZJk2apK5du6pJkyaKjo7WAw88oIMHD3q1u+mmm2SxWLy2MWPG+KobwEV5lucwuQ4AQP3js6A2fPhw7dy5U2vWrNGqVau0YcMGPfzww+dtf/LkSW3ZskVPPvmktmzZouXLlys7O1t33XXXOW1Hjx6tvLw8z/bCCy/4qhvAxbE8BwDARxr54qS7du1Senq6vvnmG/Xo0UOSNGfOHN1222166aWXFB0dfc4xoaGhWrNmjde+1157Tb169VJOTo6uvvpqz/6QkBBFRUX5onSg2lieAwDgKz4ZUcvIyFBYWJgnpElScnKyrFarNm3aVOXzOJ1OWSwWhYWFee1fsGCBwsPDFRcXp7S0NJ08ebLWageq6/Q9agyoAQBqm09G1BwOhyIiIrw/qFEjNW/eXA6Ho0rnKC4u1qRJkzRs2DDZ7XbP/j/+8Y9q3bq1oqOjtX37dk2aNEnZ2dlavnz5ec9VUlKikpISz2uXy1XNHgHnx5MJAAC+Uq2gNnnyZD3//PMXbLNr164aFST9OrHg/vvvl2EY+q//+i+v9868z61r166Kjo7WzTffrH379umaa66p9HwzZszQ9OnTa1wXUBkmEwAAfKVaQW3ixIkaOXLkBdu0a9dOUVFROnTokNf+8vJyFRQUXPTestMhbf/+/Vq3bp3XaFplevXqJUnau3fveYNaWlqaUlNTPa9dLpdiYmIueF6gqn5b8JaoBgCoXdUKai1atFCLFi0u2i4pKUmFhYXKzMxU9+7dJUnr1q2T2+1WYmLieY87HdJ++OEHffnll7ryyisv+lnbtm2TJLVs2fK8bWw2m2w220XPBVwK4/SIGjkNAFDLfDKZoFOnTho4cKBGjx6tzZs36+uvv9bYsWM1dOhQrxmfHTt21IoVKyT9GtLuvfdeffvtt1qwYIEqKirkcDjkcDhUWloqSdq3b5+eeeYZZWZm6ueff9ZHH32kBx54QDfeeKO6devmi64AF8WCtwAAX/HJZALp15mZY8eOVf/+/WW1WjVkyBC9+uqrXm2ys7PldDolSbm5ufroo48kSQkJCV7tvvzyS910000KCgrSF198oVmzZqmoqEgxMTEaMmSIpkyZ4qtuABfleYQUAAC1zGdBrXnz5lq4cOEF2xhn/IJr06aN1+vKxMTE6KuvvqqV+oDa8tusT3PrAADUPzzrE6ghLn0CAHyFoAbUEJMJAAC+QlADaojlOQAAvkJQA2qIBW8BAL5CUANq6LdnfRLVAAC1i6AG1JDbzT1qAADfIKgBNeQZUTO1CgBAfURQA2qIyQQAAF8hqAE1xPIcAABfIagBNcSCtwAAXyGoATXEsz4BAL5CUANqyHOPmpURNQBA7SKoATXkeSi7uWUAAOohghpQQ8a/71LjHjUAQG0jqAE15D49okZOAwDUMoIaUEMGz/oEAPgIQQ2oIZ71CQDwFYIaUEMGlz4BAD5CUANqwDhjDTUmEwAAahtBDagB9xlr3RLTAAC1jaAG1AAjagAAXyKoATVw5ogaQ2oAgNpGUANqwNCZI2omFgIAqJcIakANnPk8dpbnAADUNoIaUAMGkwkAAD5EUANqwPvSJ1ENAFC7CGpADXgtz0FOAwDUMoIaUANnLs9BUAMA1DaCGlAD3gvektQAALWLoAbUxBlBjeU5AAC1jaAG1MCZkwlYngMAUNsIakANuBlRAwD4EEENqAHvyQQkNQBA7fJZUCsoKNDw4cNlt9sVFhamUaNG6cSJExc8ZuTIkbJYLF7bwIEDvdoUFxfr0Ucf1ZVXXqmmTZtqyJAhys/P91U3gAvyetYnAAC1zGdBbfjw4dq5c6fWrFmjVatWacOGDXr44YcvetzAgQOVl5fn2RYtWuT1/oQJE/Txxx9r6dKl+uqrr3Tw4EHdc889vuoGcEGn71HjsicAwBca+eKku3btUnp6ur755hv16NFDkjRnzhzddttteumllxQdHX3eY202m6Kioip9z+l06p133tHChQt18803S5LeffddderUSf/617/Uu3fv2u8McAGnr3xy2RMA4As+GVHLyMhQWFiYJ6RJUnJysqxWqzZt2nTBY9evX6+IiAh16NBBjzzyiI4ePep5LzMzU2VlZUpOTvbs69ixo66++mplZGSc95wlJSVyuVxeG1AbTgc1RtQAAL7gk6DmcDgUERHhta9Ro0Zq3ry5HA7HeY8bOHCg3n//fa1du1bPP/+8vvrqK916662qqKjwnDcoKEhhYWFex0VGRl7wvDNmzFBoaKhni4mJqUHvgF8dchXr8WXbJUlBAczLAQDUvmr9dpk8efI5N/ufve3evfuSixk6dKjuuusude3aVYMHD9aqVav0zTffaP369Zd8TklKS0uT0+n0bAcOHKjR+YDPdzo0cPY/tGHPYdkaWTXtri5mlwQAqIeqdY/axIkTNXLkyAu2adeunaKionTo0CGv/eXl5SooKDjv/WfnO1d4eLj27t2r/v37KyoqSqWlpSosLPQaVcvPz7/geW02m2w2W5U/Fzifk6Xlenb1Li3clCNJ6tzSrtlDE9Q+spnJlQEA6qNqBbUWLVqoRYsWF22XlJSkwsJCZWZmqnv37pKkdevWye12KzExscqf98svv+jo0aNq2bKlJKl79+4KDAzU2rVrNWTIEElSdna2cnJylJSUVJ2uANWW9YtT4xZv1Y9HiiRJD9/YThP/cK1sjQJMrgwAUF9ZjDNX7KxFt956q/Lz8zV37lyVlZXpwQcfVI8ePbRw4UJPm44dO2rGjBm6++67deLECU2fPl1DhgxRVFSU9u3bp8cff1zHjx9XVlaWZ0TskUce0SeffKL58+fLbrfrsccekyRt3LixyrW5XC6FhobK6XTKbrfXbsdR71S4Db214Ue9/Hm2yt2GouzBevn+eF0fG252aQCAOuJSs4dPlueQpAULFmjs2LHq37+/rFarhgwZoldffdWrTXZ2tpxOpyQpICBA27dv13vvvafCwkJFR0frD3/4g5555hmvy5avvPKK53wlJSUaMGCA3njjDV91Aw3cwcJTmrBkmzb9VCBJujUuSv95d1dd0STI5MoAAA2Bz0bU/BkjaqiKj787qL+tyJKruFwhQQF66s4uuq9HK9ZMAwBUm9+NqAF11fHiMk37aKeWb8mVJMXHhGl2SoLahDcxuTIAQENDUAPOkLn/mMYv2aoDBadktUhj+8Xqsf7tFcg6aQAAExDUAEnlFW7NWbdXr325VxVuQ1eFNdasoQnq2aa52aUBABowghoavJyjJzV+yVZtySmUJA1OiNbTg+NkDw40uTIAQENHUEODZRiGlm/J1dQPd6iotELNbI307N1xGpRwldmlAQAgiaCGBsp5skxPrMzS6u15kqRebZprZkq8Wl0RYnJlAAD8hqCGBidj31GlfrBNec5iNbJaNOGWazWm7zUKsLLsBgDAvxDU0GCUlrs1c80evblhnwxDahveRLNSEhQfE3bxgwEAMAFBDQ3CvsMnNG7xVu3IdUmShvaM0ZN3dFYTG38EAAD+i99SqNcMw9DCzTl6ZtX3Ki5zKywkUM/d01UD41qaXRoAABdFUEO9dfREiSYty9IXu/IlSTfEhuul++IVFRpscmUAAFQNQQ310ld7DuuvS7/T4eMlCgqw6vGBHfTn69vKyoQBAEAdQlBDvVJcVqHn03fr3a9/liS1j2iq2UOvU+foqj8AFwAAf0FQQ72x2+HSuEXblJ1/XJI0Iqm10m7rpODAAJMrAwDg0hDUUOe53Ybmb/xZz6XvVmm5W+FNg/TivfHq1zHC7NIAAKgRghrqtEOuYv31/7Zrw57DkqSbO0bohXu7KbypzeTKAACoOYIa6qzPdzo0eXmWCopKZWtk1ZQ7OutPiVfLYmHCAACgfiCooc45WVquZ1fv0sJNOZKkzi3tenVYgmIjmplcGQAAtYughjol6xenxi3eqh+PFEmSHr6xnSb+4VrZGjFhAABQ/xDUUCdUuA29teFHvfx5tsrdhqLswXr5/nhdHxtudmkAAPgMQQ1+72DhKU1Ysk2bfiqQJN0aF6X/vLurrmgSZHJlAAD4FkENfu3j7w7qbyuy5CouV0hQgJ66s4vu69GKCQMAgAaBoAa/dLy4TNM+2qnlW3IlSfExYZqdkqA24U1MrgwAgMuHoAa/k7n/mMYv2aoDBadktUhj+8Xqsf7tFRhgNbs0AAAuK4Ia/EZ5hVtz1u3Va1/uVYXb0FVhjTVraIJ6tmludmkAAJiCoAa/kHP0pMYv2aotOYWSpMEJ0Xp6cJzswYEmVwYAgHkIajCVYRhaviVXUz/coaLSCjWzNdKzd8dpUMJVZpcGAIDpCGowjfNkmZ5YmaXV2/MkSb3aNNfMlHi1uiLE5MoAAPAPBDWYImPfUaV+sE15zmI1slo04ZZrNabvNQqwsuwGAACnEdRwWZWWuzVzzR69uWGfDENqG95Es1ISFB8TZnZpAAD4HYIaLpt9h09o3OKt2pHrkiQN7RmjJ+/orCY2fgwBAKgMvyHhc4ZhaOHmHD2z6nsVl7kVFhKo5+7ppoFxUWaXBgCAXyOowaeOnijRpGVZ+mJXviTphthwvXx/vCLtwSZXBgCA//PZUu8FBQUaPny47Ha7wsLCNGrUKJ04ceKCx1gslkq3F1980dPmpptuOuf9MWPG+KobqIGv9hzWwNn/0Be78hUUYNWU2zvp/T/3IqQBAFBFPhtRGz58uPLy8rRmzRqVlZXpwQcf1MMPP6yFCxee95i8vDyv159++qlGjRqlIUOGeO0fPXq0nn76ac/rkBCWc/AnxWUVej59t979+mdJUvuIppo99Dp1jrabWxgAAHWMT4Larl27lJ6erm+++UY9evSQJM2ZM0e33XabXnrpJUVHR1d6XFSU9z1LH374ofr166d27dp57Q8JCTmnLfzDbodL4xZtU3b+cUnSiKTWSrutk4IDA0yuDACAuscnlz4zMjIUFhbmCWmSlJycLKvVqk2bNlXpHPn5+Vq9erVGjRp1znsLFixQeHi44uLilJaWppMnT17wXCUlJXK5XF4bapfbbWjeP3/SXa99rez84wpvGqR3R/bU9EFxhDQAAC6RT0bUHA6HIiIivD+oUSM1b95cDoejSud477331KxZM91zzz1e+//4xz+qdevWio6O1vbt2zVp0iRlZ2dr+fLl5z3XjBkzNH369Op3BFVyyFWsv/7fdm3Yc1iSdHPHCL1wbzeFN7WZXBkAAHVbtYLa5MmT9fzzz1+wza5du2pU0Gnz5s3T8OHDFRzsfeP5ww8/7Pn3rl27Kjo6WjfffLP27duna665ptJzpaWlKTU11fPa5XIpJiamVups6D7f6dDk5VkqKCqVrZFVU+7orD8lXi2LhScMAABQU9UKahMnTtTIkSMv2KZdu3aKiorSoUOHvPaXl5eroKCgSveW/eMf/1B2draWLFly0ba9evWSJO3du/e8Qc1ms8lmY3SnNp0sLdezq3dp4aYcSVLnlna9OixBsRHNTK4MAID6o1pBrUWLFmrRosVF2yUlJamwsFCZmZnq3r27JGndunVyu91KTEy86PHvvPOOunfvrvj4+Iu23bZtmySpZcuWF22L2pH1i1PjFm/Vj0eKJEkP39hOE/9wrWyNuBcNAIDa5JPJBJ06ddLAgQM1evRobd68WV9//bXGjh2roUOHes347Nixo1asWOF1rMvl0tKlS/XQQw+dc959+/bpmWeeUWZmpn7++Wd99NFHeuCBB3TjjTeqW7duvugKzlDhNvRf6/fp7je+1o9HihRlD9aChxL1xG2dCGkAAPiAz9ZRW7BggcaOHav+/fvLarVqyJAhevXVV73aZGdny+l0eu1bvHixDMPQsGHDzjlnUFCQvvjiC82aNUtFRUWKiYnRkCFDNGXKFF91A/92sPCUJizZpk0/FUiSbo2L0ox7uiosJMjkygAAqL8shmEYZhdxublcLoWGhsrpdMpuZxHWi/n4u4P624osuYrLFRIUoKfu6qL7urdiwgAAAFV0qdmDZ33ivI4Xl2naRzu1fEuuJCk+JkyzUxLUJryJyZUBANAwENRQqcz9xzR+yVYdKDglq0Ua2y9Wj/Vvr8AAnz0eFgAAnIWgBi/lFW7NWbdXr325VxVuQ62uaKxXUhLUs01zs0sDAKDBIajBI+foSY1fslVbcgolSXdfd5WmD+oie3CgyZUBANAwEdQgwzC0fEuupn64Q0WlFWpma6Rn747ToISrzC4NAIAGjaDWwDlPlumJlVlavT1PktSrTXPNTIlXqytCTK4MAAAQ1BqwjH1HlfrBNuU5i9XIatGEW67VmL7XKMDKshsAAPgDgloDVFru1sw1e/Tmhn0yDKlteBPNSklQfEyY2aUBAIAzENQamH2HT2jc4q3akeuSJA3tGaMn7+isJjZ+FAAA8Df8dm4gDMPQws05embV9youcyssJFDP3dNNA+OizC4NAACcB0GtATh6okSTlmXpi135kqQbYsP18v3xirQHm1wZAAC4EIJaPffVnsP669LvdPh4iYICrHp8YAf9+fq2sjJhAAAAv0dQq6eKyyr0fPpuvfv1z5Kk9hFNNXvodeoczUPoAQCoKwhq9dBuh0vjFm1Tdv5xSdKIpNZKu62TggMDTK4MAABUB0GtHnG7Dc3f+LOeS9+t0nK3wpsG6cV749WvY4TZpQEAgEtAUKsnDrmK9df/264New5Lkm7uGKEX7u2m8KY2kysDAACXiqBWD3y+06HJy7NUUFQqWyOrptzRWX9KvFoWCxMGAACoywhqddjJ0nI9u3qXFm7KkSR1bmnXq8MSFBvRzOTKAABAbSCo1VFZvzg1bvFW/XikSJL0lxvbKfUP18rWiAkDAADUFwS1OqbCbeitDT/q5c+zVe42FGUP1sv3x+v62HCzSwMAALWMoFaHHCw8pQlLtmnTTwWSpFvjojTjnq4KCwkyuTIAAOALBLU64uPvDupvK7LkKi5XSFCAnrqri+7r3ooJAwAA1GMENT93vLhM0z7aqeVbciVJ8TFhmp2SoDbhTUyuDAAA+BpBzY9l7j+m8Uu26kDBKVkt0th+sXqsf3sFBljNLg0AAFwGBDU/VF7h1px1e/Xal3tV4TbU6orGeiUlQT3bNDe7NAAAcBkR1PxMztGTGr9kq7bkFEqS7r7uKk0f1EX24ECTKwMAAJcbQc1PGIah5VtyNfXDHSoqrVCz4EZ6dnCcBiVcZXZpAADAJAQ1P+A8WaYnVmZp9fY8SVKvNs01MyVera4IMbkyAABgJoKayTL2HVXqB9uU5yxWI6tFE265VmP6XqMAK8tuAADQ0BHUTFJa7tbMNXv05oZ9MgypbXgTzUpJUHxMmNmlAQAAP0FQM8G+wyc0bvFW7ch1SZKG9ozRk3d0VhMbXwcAAPgNyeAyMgxDCzfn6JlV36u4zK2wkEA9d083DYyLMrs0AADghwhql8nREyWatCxLX+zKlyTdEBuul++PV6Q92OTKAACAv/LZEvd///vf1adPH4WEhCgsrGr3XRmGoalTp6ply5Zq3LixkpOT9cMPP3i1KS4u1qOPPqorr7xSTZs21ZAhQ5Sfn++LLtSar/Yc1sDZ/9AXu/IVFGDVlNs76f0/9yKkAQCAC/JZUCstLdV9992nRx55pMrHvPDCC3r11Vc1d+5cbdq0SU2aNNGAAQNUXFzsaTNhwgR9/PHHWrp0qb766isdPHhQ99xzjy+6UGPFZRWa/vFOjZi3WYePl6h9RFOtfPR6PfT7drIyqxMAAFyExTAMw5cfMH/+fI0fP16FhYUXbGcYhqKjozVx4kT99a9/lSQ5nU5FRkZq/vz5Gjp0qJxOp1q0aKGFCxfq3nvvlSTt3r1bnTp1UkZGhnr37l2lmlwul0JDQ+V0OmW322vWwfPY7XBp3KJtys4/LkkakdRaabd1UnBggE8+DwAA+K9LzR5+83Tvn376SQ6HQ8nJyZ59oaGhSkxMVEZGhiQpMzNTZWVlXm06duyoq6++2tOmMiUlJXK5XF6bL313oFB3vfa1svOPK7xpkN4d2VPTB8UR0gAAQLX4zWQCh8MhSYqMjPTaHxkZ6XnP4XAoKCjonHvezmxTmRkzZmj69Om1XPH5xV0VqoSYMDWzNdLz93ZTeFPbZftsAABQf1RrRG3y5MmyWCwX3Hbv3u2rWi9ZWlqanE6nZztw4IBPPy/AatE7I3ro7RE9CGkAAOCSVWtEbeLEiRo5cuQF27Rr1+6SComK+nUtsfz8fLVs2dKzPz8/XwkJCZ42paWlKiws9BpVy8/P9xxfGZvNJpvt8gamZsGBl/XzAABA/VOtoNaiRQu1aNHCJ4W0bdtWUVFRWrt2rSeYuVwubdq0yTNztHv37goMDNTatWs1ZMgQSVJ2drZycnKUlJTkk7oAAADM4rN71HJyclRQUKCcnBxVVFRo27ZtkqTY2Fg1bdpU0q8TAWbMmKG7775bFotF48eP17PPPqv27durbdu2evLJJxUdHa3BgwdL+nVywahRo5SamqrmzZvLbrfrscceU1JSUpVnfAIAANQVPgtqU6dO1Xvvved5fd1110mSvvzyS910002Sfh0NczqdnjaPP/64ioqK9PDDD6uwsFA33HCD0tPTFRz828Kwr7zyiqxWq4YMGaKSkhINGDBAb7zxhq+6AQAAYBqfr6Pmjy7HOmoAAACn1fl11AAAAOCNoAYAAOCnCGoAAAB+iqAGAADgpwhqAAAAfoqgBgAA4KcIagAAAH6KoAYAAOCnCGoAAAB+ymePkPJnpx/G4HK5TK4EAAA0BKczR3UfCNUgg9rx48clSTExMSZXAgAAGpLjx48rNDS0yu0b5LM+3W63Dh48qGbNmslisfjkM1wul2JiYnTgwIEG9TzRhtjvhthniX43pH43xD5L9Lsh9fty9NkwDB0/flzR0dGyWqt+51mDHFGzWq1q1arVZfksu93eYH7Qz9QQ+90Q+yzR74akIfZZot8Nia/7XJ2RtNOYTAAAAOCnCGoAAAB+KuCpp556yuwi6quAgADddNNNatSoYV1hboj9boh9luh3Q+p3Q+yzRL8bUr/9tc8NcjIBAABAXcClTwAAAD9FUAMAAPBTBDUAAAA/RVADAADwUwS1S/T3v/9dffr0UUhIiMLCwqp0jGEYmjp1qlq2bKnGjRsrOTlZP/zwg1eb4uJiPfroo7ryyivVtGlTDRkyRPn5+b7owiUpKCjQ8OHDZbfbFRYWplGjRunEiRMXPMZisVS6vfjii542N9100znvjxkzxtfdqZJL6fPIkSPP6c/AgQO92tS377qsrEyTJk1S165d1aRJE0VHR+uBBx7QwYMHvdr523f9+uuvq02bNgoODlZiYqI2b958wfbr16/X7373O9lsNsXGxmr+/PnntFm6dKk6duyo4OBgde3aVZ988omPqr901en38uXLdcstt6hFixay2+1KSkrSZ5995tVm/vz553yvwcHBvu5GtVSnz+vXr6/07y2Hw+HVrr5915X93WWxWNSlSxdPG3//rjds2KA777xT0dHRslgsWrly5UWP8es/1wYuydSpU42ZM2caqampRmhoaJWOee6554zQ0FBj5cqVxnfffWfcddddRtu2bY1Tp0552owZM8aIiYkx1q5da3z77bdG7969jT59+viqG9U2cOBAIz4+3vjXv/5l/OMf/zBiY2ONYcOGXfCYvLw8r23evHmGxWIx9u3b52nTt29fY/To0V7tnE6nr7tTJZfS5xEjRhgDBw706k9BQYFXm/r2XRcWFhrJycnGkiVLjN27dxsZGRlGr169jO7du3u186fvevHixUZQUJAxb948Y+fOncbo0aONsLAwIz8/v9L2P/74oxESEmKkpqYa33//vTFnzhwjICDASE9P97T5+uuvjYCAAOOFF14wvv/+e2PKlClGYGCgkZWVdbm6dVHV7fe4ceOM559/3ti8ebOxZ88eIy0tzQgMDDS2bNniafPuu+8adrvd63t1OByXq0sXVd0+f/nll4YkIzs726tPFRUVnjb18bsuLCz06u+BAweM5s2bG9OmTfO08ffv+pNPPjH+9re/GcuXLzckGStWrLhge3//c01Qq6F33323SkHN7XYbUVFRxosvvujZV1hYaNhsNmPRokWe14GBgcbSpUs9bXbt2mVIMjIyMmq/+Gr6/vvvDUnGN99849n36aefGhaLxcjNza3yeQYNGmTcfPPNXvv69u1rjBs3rtZqrS2X2ucRI0YYgwYNOu/7DeW73rx5syHJ2L9/v2efP33XvXr1Mh599FHP64qKCiM6OtqYMWNGpe0ff/xxo0uXLl77UlJSjAEDBnhe33///cbtt9/u1SYxMdH4y1/+UouV10x1+12Zzp07G9OnT/e8rurfhWapbp9PB7Vjx46d95wN4btesWKFYbFYjJ9//tmzz9+/6zNVJaj5+59rLn1eJj/99JMcDoeSk5M9+0JDQ5WYmKiMjAxJUmZmpsrKyrzadOzYUVdffbWnjZkyMjIUFhamHj16ePYlJyfLarVq06ZNVTpHfn6+Vq9erVGjRp3z3oIFCxQeHq64uDilpaXp5MmTtVb7papJn9evX6+IiAh16NBBjzzyiI4ePep5ryF815LkdDplsVjOuT3AH77r0tJSZWZmen0HVqtVycnJ5/0OMjIyvNpL0oABA7zaV6WNmS6l32dzu93/v737C2mqD+MA/pQ6nZjYsKZmjjRbYcqUWMwLlbSwiPxzIVrJCsqLCCpKlCDCukkYeRFiRlkSif1B3EWEIDPIMMFYGWuONsSCUqnQJmeMdIEAAAcfSURBVPkn7ftehOf1tGnb/NN59z4fEDy/PTv7PTw77uHs/I7kdDpJoVCIxsfGxkilUtHGjRspLy+PLBbLks7dV4vJWaPRUHR0NO3evZueP38ueuz/UOtbt25RTk4OqVQq0bhUa+0LqR/X0rr9rh+bva5BqVSKxpVKpfDY4OAgyWQylw+1uTF/0+DgIK1fv140FhgYSAqFwuP5NTY20po1a6iwsFA0fvDgQVKpVBQTE0O9vb1UUVFBNpuNWlpalmz+vvA159zcXCosLKRNmzaRw+Gg8+fP0969e6mrq4sCAgL+F7WemJigiooKKikpEf2TY6nU+vPnzzQzM+P2mOzr63P7nMHBQbfx3759o/HxcZLL5fPGSKGuRL7l/TuDwUBjY2NUVFQkjKnVampoaKCUlBQaHR0lg8FA6enpZLFYKDY2dklz8JYvOUdHR9P169dpx44dNDk5STdv3qSsrCzq7u6mtLQ0Ipr//eAvtf748SM9efKEmpqaRONSrrUvpH5cc6M2R2VlJVVXVy8YY7VaaevWrSs0o5Xhad5LoaGhgQ4dOuRy4WlZWZnwe3JyMsXExNCuXbvI4XBQQkLCkrz2XMudc3FxsfB7cnIypaSkUEJCAj19+pSys7N93u9irVStf/z4QUVFRQSA6urqRI+tdK3Z0mpqaqKqqioyGo2iZl6n05FOpxO209PTadu2bVRfX0+XL1/+G1NdFLVaTWq1WthOT08nh8NBNTU1dPfu3b84s5XT2NhIERERlJ+fLxr3t1pLHTdqc5w9e5aOHDmyYEx8fLxP+46KiiKiX1/9RUdHC+NDQ0Ok0WiEmKmpKRoZGRGdaRkaGhKevxw8zTsqKoqGh4dF49PT0/T161eP5vfs2TOy2Wx0//79P8ZqtVoiIrLb7cvy4b1SOc/dV2RkJNntdsrOzvbrWs82aQMDA2QymURn09xZ7lrPJzIykgICAlxW2i5Ug6ioKLfx4eHhJJfLF4xZzrp6w5e8ZzU3N9OxY8fo4cOHLl8D/S4oKIhSU1PJbrcves6LtZic59JqtdTZ2Sls+3OtAVBDQwOVlpaSTCZbMFZKtfaF5I/rZb8Kzs95u5jAYDAIY6Ojo24XEzx69EiI6evrk9wF5j09PcJYW1ubxxeY6/V6lxWA8+ns7AQR4fXr1z7PdyksNudZHz58wKpVq2A0GgH4b62npqaQn5+PpKQkDA8Pe/Raf7PWWq0WJ0+eFLZnZmawYcOGBRcTbN++XTRWUlLictHx/v37RTE6nU5yF5h7kzcANDU1ISQkBK2trR69xvT0NNRqNc6cObPo+S4FX3L+XU5ODgoKCoRtf6018O9iCk9WNUqt1nORh4sJpHxcc6Pmo4GBAZjNZlRVVSEsLAxmsxlmsxlOp1OIUavVaGlpEbavXLmCiIgIGI1G9Pb2Ii8vz+3tOeLi4mAymdDT0wOdTgedTreiuS0kNzcXqamp6O7uRmdnJxITE11u2fB73sCvpjQ0NBR1dXUu+7Tb7bh06RJ6enrQ398Po9GI+Ph4ZGRkLGsunvI2Z6fTiXPnzqGrqwv9/f1ob29HWloaEhMTMTExITzH32o9NTWFAwcOIDY2Fq9evRIt3Z+cnAQgvVo3NzcjODgYd+7cwdu3b1FWVoaIiAjhVgOVlZUoLS0V4meX8ZeXl8NqtaK2ttbtMv7AwEAYDAZYrVZcvHhRkrds8Cbve/fuITAwELW1taK6joyMCDFVVVVoa2uDw+HAy5cvUVxcjJCQEFgslhXPzx1vc66pqUFrayvevXuHN2/e4NSpU1i9ejXa29uFGH+s9azDhw9j586dbvcp9Vo7nU7hM5mIcPXqVZjNZmH1+X/tuOZGzUd6vR5E5PLT0dEhxBARbt++LWz//PkTFy5cgFKpRHBwMLKzs2Gz2UT7HR8fx4kTJ7B27VqEhoaioKAAnz59WqGs/uzLly8oKSlBWFgYwsPDcfToUVFzCrjmDQD19fWQy+WiP+yz3r9/j4yMDCgUCgQHB2Pz5s0oLy+XzH3UvM35+/fv2LNnD9atW4egoCCoVCocP37c5T5D/lbr/v5+t8fE3ONCirW+du0a4uLiIJPJoNVq8eLFC+ExvV6PzMxMUXxHRwc0Gg1kMhni4+Nd3usA8ODBA2zZsgUymQxJSUl4/PjxMmfhPW/yzszMdFtXvV4vxJw+fVrYn1KpxL59+0T3WZMCb3Kurq5GQkICQkJCoFAokJWVBZPJ5LJPf6s18OuMv1wux40bN9zuT+q1nj0bON/79b92XK8CgGX+dpUxxhhjjPmA76PGGGOMMSZR3KgxxhhjjEkUN2qMMcYYYxLFjRpjjDHGmERxo8YYY4wxJlHcqDHGGGOMSRQ3aowxxhhjEsWNGmOMMcaYRHGjxhhjjDEmUdyoMcYYY4xJFDdqjDHGGGMSxY0aY4wxxphE/QNEsPd8GvkPyAAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000025A7A828>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1, 1, 1000)\n",
    "\n",
    "figure(figsize = (7, 5))\n",
    "plot(x, HardThresh(x, .5))\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The hard thresholding in the translation invariant wavelet basis $\\Psi$\n",
    "reads\n",
    "$$ H_T^\\Psi(f) = \\Xi \\circ H_T \\circ \\Psi^* (f) $$\n",
    "where $\\Xi = (\\Phi^*)^+$ is the reconstruction operator.\n",
    "\n",
    "\n",
    "We follow the MCA paradigm of Jean-Luc Starck, that alternates between a\n",
    "gradient descent step and a hard thresholding denoising, using a decaying\n",
    "threshold.\n",
    "$$f^{(\\ell+1)} = H_{\\tau\\lambda_\\ell}^\\Psi( f^{(\\ell)} - \\tau \\Phi^*(\\Phi f^{(\\ell)} - y)  ). $$\n",
    "\n",
    "\n",
    "Number of iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "niter = 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "List of thresholds. One must start by a large enough initial threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500-element LinSpace{Float64}:\n",
       " 1.0,0.997996,0.995992,0.993988,…,0.00601202,0.00400802,0.00200401,0.0"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_list = linspace(1, 0, niter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.817734  0.0       0.0     \n",
       " 0.571429  0.0       0.591133  0.610838     0.0       0.0       0.812808\n",
       " 0.581281  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.561576  0.0       0.0       0.586207     0.0       0.802956  0.0     \n",
       " 0.0       0.0       0.522168  0.0          0.0       0.0       0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.802956  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.561576  0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.472906  0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.0       0.0       0.182266     0.0       0.0       0.0     \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.832512\n",
       " 0.44335   0.0       0.0       0.0          0.0       0.812808  0.0     \n",
       " 0.0       0.0       0.0       0.369458     0.807882  0.0       0.827586\n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.0       0.0       0.0       0.472906     0.955665  0.932677  0.0     \n",
       " 0.0       0.0       0.541872  0.0          0.0       0.935961  0.876847\n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.0       0.497537  0.0          0.0       0.0       0.91133 \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.906404\n",
       " 0.0       0.0       0.0       0.0          0.0       0.955665  0.0     \n",
       " 0.0       0.0       0.0       0.689655     0.0       0.0       0.0     \n",
       " 0.0       0.487685  0.0       0.0          0.990148  0.0       0.916256\n",
       " 0.0       0.0       0.0       0.788177     1.0       0.0       0.916256\n",
       " 0.0       0.0       0.0       0.0       …  1.0       0.97537   0.91133 \n",
       " 0.0       0.0       0.0       0.561576     0.0       0.0       0.916256\n",
       " 0.0       0.0       0.0       0.738916     0.945813  0.0       0.0     "
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fHard = y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.817734  0.0       0.0     \n",
       " 0.571429  0.0       0.591133  0.610838     0.0       0.0       0.812808\n",
       " 0.581281  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.561576  0.0       0.0       0.586207     0.0       0.802956  0.0     \n",
       " 0.0       0.0       0.522168  0.0          0.0       0.0       0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.802956  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.561576  0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.472906  0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.0       0.0       0.182266     0.0       0.0       0.0     \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.832512\n",
       " 0.44335   0.0       0.0       0.0          0.0       0.812808  0.0     \n",
       " 0.0       0.0       0.0       0.369458     0.807882  0.0       0.827586\n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.0       0.0       0.0       0.472906     0.955665  0.932677  0.0     \n",
       " 0.0       0.0       0.541872  0.0          0.0       0.935961  0.876847\n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.0       0.497537  0.0          0.0       0.0       0.91133 \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.906404\n",
       " 0.0       0.0       0.0       0.0          0.0       0.955665  0.0     \n",
       " 0.0       0.0       0.0       0.689655     0.0       0.0       0.0     \n",
       " 0.0       0.487685  0.0       0.0          0.990148  0.0       0.916256\n",
       " 0.0       0.0       0.0       0.788177     1.0       0.0       0.916256\n",
       " 0.0       0.0       0.0       0.0       …  1.0       0.97537   0.91133 \n",
       " 0.0       0.0       0.0       0.561576     0.0       0.0       0.916256\n",
       " 0.0       0.0       0.0       0.738916     0.945813  0.0       0.0     "
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fHard = ProjC(fHard, Omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Hard threshold (here $\\lambda=\\lambda_0$) is used)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       "  3.66494e-5    0.000114282   3.83719e-5   …   1.48864e-5   -1.52949e-5 \n",
       "  0.571531     -9.20383e-5    0.591257        -2.28221e-5    0.812817   \n",
       "  0.581632     -0.000467075   0.000137072     -4.51812e-5    3.25829e-6 \n",
       "  0.560358      0.000902527  -0.000436964      0.802976     -6.8564e-5  \n",
       "  0.000264716  -0.000460029   0.522475         0.000223522   0.822554   \n",
       " -4.61803e-5   -0.000139511   0.00022262   …   0.802417      0.000101539\n",
       " -0.000100566  -2.66475e-5    6.36337e-7       0.00029115   -6.52386e-5 \n",
       "  4.16665e-5    0.561575     -0.000171974      0.822604     -7.24068e-5 \n",
       "  0.472961     -1.94345e-5   -9.283e-5        -0.000170705  -0.000214937\n",
       " -6.30669e-5   -1.12377e-5    3.03863e-5      -0.000520495  -0.000549995\n",
       " -2.24487e-6   -6.98895e-5    0.000103071  …   0.00121376    0.833889   \n",
       "  0.44338      -5.18721e-6    0.000131892      0.812257     -0.000614638\n",
       " -0.00046031    0.00051018   -6.4683e-5       -0.000247252   0.827269   \n",
       "  ⋮                                        ⋱                            \n",
       "  0.000178969   0.000110926  -3.71198e-5       0.932618     -5.27957e-5 \n",
       " -7.94895e-5    2.71154e-5    0.541936         0.936001      0.876884   \n",
       " -6.81682e-6    4.09405e-5    6.37876e-6       3.43327e-5    3.08629e-5 \n",
       "  3.13311e-5   -8.60576e-6    0.497441         9.4948e-6     0.911338   \n",
       "  0.000105544   0.507468      1.86034e-5   …   3.39909e-6    0.906405   \n",
       "  0.000192037   0.000134476   0.000117835      0.955668     -7.16564e-7 \n",
       "  0.000124403   0.000190191   0.000154254      5.12116e-6    3.36553e-7 \n",
       "  8.35522e-5    0.487518     -0.000471817     -4.15121e-5    0.916294   \n",
       "  4.45437e-5    0.000100549   0.000114492     -3.95922e-5    0.916275   \n",
       " -0.000195955  -0.000119247  -5.10633e-5   …   0.975452      0.911199   \n",
       "  0.00021258    0.000195805  -2.00267e-5       0.000369328   0.915838   \n",
       "  0.000278678   0.000204671  -8.39566e-5      -0.00090505    0.000835345"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fHard = Xi(HardThresh(PsiS(fHard), tau*lambda_list[1]));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 5__\n",
    "\n",
    "Perform the iteration with a decaying value of $\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000025083550>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo5.jl\")\n",
    "\n",
    "# lambda_list = linspace(1, 0, niter)\n",
    "# fHard = y\n",
    "\n",
    "# for i in 1 : niter\n",
    "#     fHard = Xi(HardThresh(PsiS(ProjC(fHard, Omega)), lambda_list[i]))\n",
    "# end\n",
    "\n",
    "    \n",
    "# figure(figsize = (6, 6))\n",
    "# imageplot(clamP(fSpars), @sprintf(\"Inpainting hard thresh., SNR = %.1f dB\", snr(f0, fHard)))\n"
   ]
  },
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   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
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   "cell_type": "raw",
   "metadata": {},
   "source": [
    "<script>\n",
    "  $(document).ready(function(){\n",
    "      $('div.prompt').hide();\n",
    "  });\n",
    "</script>"
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