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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 inpainting problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
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   "source": [
    "options(warn=-1) # turns off warnings, to turn on: \"options(warn=0)\"\n",
    "\n",
    "library(pracma)\n",
    "library(imager)\n",
    "\n",
    "# Importing the libraries\n",
    "for (f in list.files(path=\"nt_toolbox/toolbox_general/\", pattern=\"*.R\")) {\n",
    "    source(paste(\"nt_toolbox/toolbox_general/\", f, sep=\"\"))\n",
    "}\n",
    "for (f in list.files(path=\"nt_toolbox/toolbox_signal/\", pattern=\"*.R\")) {\n",
    "    source(paste(\"nt_toolbox/toolbox_signal/\", f, sep=\"\"))\n",
    "}"
   ]
  },
  {
   "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": 2,
   "metadata": {
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   "outputs": [],
   "source": [
    "n = 128\n",
    "f0 = load_image(\"nt_toolbox/data/lena.png\")\n",
    "f0 = t(f0[,])\n",
    "f0 = rescale(f0[(256 - n / 2 + 1):(256 + n / 2), (256 - n / 2 + 1) : (256 + n / 2)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
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M0PPvhgm/635H8VOJdHth+diCca7bzx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\n9t8AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Image f_0\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=4, repr.plot.height=4)\n",
    "imageplot(f0, 'Image f_0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Amount of removed pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "rho = 0.7"
   ]
  },
  {
   "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": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "set.seed(1)\n",
    "Omega = c(matrix(0, n, n))\n",
    "sel = sample(n**2)\n",
    "Omega[sel[1:as.integer(rho * n**2)]] = 1\n",
    "Omega = matrix(Omega, n, n)"
   ]
  },
  {
   "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": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Phi = function(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": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "y = Phi(f0, Omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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l7XvPLKK+UWVBv14lS4RJSoREzgco3JeamqN9oZ0O/QpC3QCkM3zmI/exuzCtTn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\nAQ1k3flaJ9VPM9tnn33KjWhnUjj4P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9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\nJWiAKUEDTAkaYErQAFOCBpgSNMBUsmGm9IG3a/kAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Observations y\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "SoftThresh = function(x, T)\n",
    "{\n",
    "    if (!is.null(dim(x)))\n",
    "    {\n",
    "        return(x * pmax(1 - T / abs(x), 1e-10 * array(1, dim=dim(x)), array(0, dim=dim(x))))\n",
    "    }\n",
    "    else\n",
    "    {\n",
    "        return(x * pmax(1 - T / abs(x), 1e-10 * rep(1, length(x)), rep(0, length(x))))\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display a curve of the 1D soft thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T09PUMc43a7Jfn9/hBtGrZLl1RcrIQEbdpkegoAh3BSoBcuXCjpzTffHOKY3bt3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\nEWgAsBSBBgBL/T+3ydDynkXWNwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = seq(-1, 1, length=1000)\n",
    "\n",
    "plot(x, SoftThresh(x, .5), col=4, type=\"l\", ylab=\"\", xlab=\"\")"
   ]
  },
  {
   "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": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Psi = function(a){perform_wavelet_transf(a, Jmin, -1, ti=0)}\n",
    "PsiS = function(f){perform_wavelet_transf(f, Jmin, +1, ti=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": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "SoftThreshPsi = function(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": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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E35pYkvQSD6pI5n1en9Zda7rWrI/lgG/NQpldMqdOqcxT1MtcLoe0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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 15,
   "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": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ProjC = function(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": 17,
   "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": 18,
   "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": 19,
   "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": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GfIt/3tmzGsoI0xplGsoJtjxYoVu+22W9ZWE7M01FYVqubS/ahgjUXmFWUal9Ty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\nQmCC",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "source(\"nt_solutions/inverse_5_inpainting_sparsity/exo1.R\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true,
    "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": 22,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Insert your code here."
   ]
  },
  {
   "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": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wjs7kw6ds57tPudRut1Gk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",
      "text/plain": [
       "Plot with title \"Sparsity inpainting, SNR =  17.3 dB\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "source(\"nt_solutions/inverse_5_inpainting_sparsity/exo2.R\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true,
    "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": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "J = Jmax - Jmin + 1\n",
    "u = c(4**(-J), 4**(floor(-1 * seq(J + 2./3,1,by=-1 /3.) + 1)))\n",
    "U = array(0, dim=c(n, n, length(u)))\n",
    "for (i in 1:length(u))\n",
    "{\n",
    "    U[,,i] = u[i]\n",
    "}\n",
    "U = aperm(U, c(3, 1, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Choose a value of the regularization parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "lambd = .01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut for the wavelet transform and the reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Xi = function(a){perform_wavelet_transf(a, Jmin, -1, ti=1)}\n",
    "PsiS = function(f){perform_wavelet_transf(f, Jmin, + 1, ti=1)}\n",
    "Psi = function(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": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "tau = 1.9 * min(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": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "a = U * PsiS(fSpars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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ebNAODoiPvvx4AB6N8f/fqhc2fodGJTEzWUlgq6lhUrViQlJTk7O7/zzjtPPPFE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\nwlcnZ+yAgAAA5eXl5oPKTeU4NjmTp6am4vfDe2oMGjQIwMWLF6W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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VAWORNMCx9rFQ5NVEMksp19UFhs0WoYGpvWd/rocWTp1q1bo0SZQT3U7KlV7gjm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",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "source(\"nt_solutions/inverse_5_inpainting_sparsity/exo3.R\")"
   ]
  },
  {
   "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": 34,
   "metadata": {
    "collapsed": true,
    "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": 35,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "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": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yB9iJj1VlrYCsehhN6YACODPBbyUj4RT03kYXO0RU+oAWKIHMz2FnrlMEzm3cBx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c/v+yFo7dOtgZZD1adxDzZz6ffKTno5lZ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\n/BctZITyrYi0XQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Sparsity inpainting TI, SNR = 21.2 dB\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "source(\"nt_solutions/inverse_5_inpainting_sparsity/exo4.R\")"
   ]
  },
  {
   "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": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "HardThresh = function(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": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AOAJRHQAKAoAhoAFEVAA4Ci9LsP+moe/rAbgBWxgwYARRHQAKAoAjo4IiMjR/7X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\nty5UBE7AWAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = seq(-1, 1, length=1000)\n",
    "\n",
    "plot(x, HardThresh(x, .5), col=4, type=\"l\", xlab=\"\", ylab=\"\")"
   ]
  },
  {
   "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": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "lambda_list = seq(1, 0, length=niter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fHard = y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OlggE1Sce+995pZcrySk+WHP/wh7oWE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//XU+7SMngwZYSga9zu3tbbLd49Ks+fff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\nDxP92d3nirsJAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Inpainting hard thresh., SNR = 23.1 dB\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "source(\"nt_solutions/inverse_5_inpainting_sparsity/exo5.R\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<script>\n",
    "  $(document).ready(function(){\n",
    "      $('div.prompt').hide();\n",
    "  });\n",
    "</script>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<script>\n",
    "  $(document).ready(function(){\n",
    "      $('div.prompt').hide();\n",
    "  });\n",
    "</script>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<script>\n",
    "  $(document).ready(function(){\n",
    "      $('div.prompt').hide();\n",
    "  });\n",
    "</script>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}