{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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",
    "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n",
    "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n",
    "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n",
    "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n",
    "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n",
    "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n",
    "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n",
    "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n",
    "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n",
    "$\\newcommand{\\choice}[1]{ \\left\\{  \\begin{array}{l} #1 \\end{array} \\right. }$\n",
    "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n",
    "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n",
    "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n",
    "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n",
    "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n",
    "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n",
    "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n",
    "$\\newcommand{\\CC}{\\mathbb{C}}$\n",
    "$\\newcommand{\\RR}{\\mathbb{R}}$\n",
    "$\\newcommand{\\EE}{\\mathbb{E}}$\n",
    "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n",
    "$\\newcommand{\\Ww}{\\mathcal{W}}$\n",
    "$\\newcommand{\\Vv}{\\mathcal{V}}$\n",
    "$\\newcommand{\\Nn}{\\mathcal{N}}$\n",
    "$\\newcommand{\\NN}{\\mathcal{N}}$\n",
    "$\\newcommand{\\Hh}{\\mathcal{H}}$\n",
    "$\\newcommand{\\Bb}{\\mathcal{B}}$\n",
    "$\\newcommand{\\Ee}{\\mathcal{E}}$\n",
    "$\\newcommand{\\Cc}{\\mathcal{C}}$\n",
    "$\\newcommand{\\Gg}{\\mathcal{G}}$\n",
    "$\\newcommand{\\Ss}{\\mathcal{S}}$\n",
    "$\\newcommand{\\Pp}{\\mathcal{P}}$\n",
    "$\\newcommand{\\Ff}{\\mathcal{F}}$\n",
    "$\\newcommand{\\Xx}{\\mathcal{X}}$\n",
    "$\\newcommand{\\Mm}{\\mathcal{M}}$\n",
    "$\\newcommand{\\Ii}{\\mathcal{I}}$\n",
    "$\\newcommand{\\Dd}{\\mathcal{D}}$\n",
    "$\\newcommand{\\Ll}{\\mathcal{L}}$\n",
    "$\\newcommand{\\Tt}{\\mathcal{T}}$\n",
    "$\\newcommand{\\si}{\\sigma}$\n",
    "$\\newcommand{\\al}{\\alpha}$\n",
    "$\\newcommand{\\la}{\\lambda}$\n",
    "$\\newcommand{\\ga}{\\gamma}$\n",
    "$\\newcommand{\\Ga}{\\Gamma}$\n",
    "$\\newcommand{\\La}{\\Lambda}$\n",
    "$\\newcommand{\\si}{\\sigma}$\n",
    "$\\newcommand{\\Si}{\\Sigma}$\n",
    "$\\newcommand{\\be}{\\beta}$\n",
    "$\\newcommand{\\de}{\\delta}$\n",
    "$\\newcommand{\\De}{\\Delta}$\n",
    "$\\newcommand{\\phi}{\\varphi}$\n",
    "$\\newcommand{\\th}{\\theta}$\n",
    "$\\newcommand{\\om}{\\omega}$\n",
    "$\\newcommand{\\Om}{\\Omega}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This numerical tour explores the use of\n",
    "sparse energies to regularize the image inpaiting problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Base.UTF8String is deprecated, use String instead.\n",
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      "\u001b[1m\u001b[31mWARNING: readall is deprecated, use readstring instead.\u001b[0m\n",
      " in depwarn(::String, ::Symbol) at .\\deprecated.jl:64\n",
      " in readall(::IOStream, ::Vararg{IOStream,N}) at .\\deprecated.jl:30\n",
      " in #parse_file#6(::Array{Any,1}, ::Function, ::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\files.jl:63\n",
      " in parse_file(::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\files.jl:61\n",
      " in #arequire#10(::Symbol, ::Array{String,1}, ::Function, ::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\Autoreload.jl:65\n",
      " in arequire(::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\Autoreload.jl:47\n",
      " in include_string(::String, ::String) at .\\loading.jl:441\n",
      " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\execute_request.jl:157\n",
      " in eventloop(::ZMQ.Socket) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\eventloop.jl:8\n",
      " in (::IJulia.##13#19)() at .\\task.jl:360\n",
      "while loading In[1], in expression starting on line 4\n",
      "WARNING: replacing module NtToolBox\n"
     ]
    }
   ],
   "source": [
    "using PyPlot\n",
    "using NtToolBox\n",
    "using Autoreload\n",
    "arequire(\"NtToolBox\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we consider inpainting of damaged observation without noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float32,2}:\n",
       " 0.586207  0.610838  0.600985  0.596059  …  0.817734  0.802956  0.802956\n",
       " 0.571429  0.566503  0.591133  0.610838     0.807882  0.807882  0.812808\n",
       " 0.581281  0.561576  0.581281  0.591133     0.802956  0.82266   0.827586\n",
       " 0.561576  0.586207  0.566503  0.586207     0.827586  0.802956  0.812808\n",
       " 0.369458  0.453202  0.522168  0.551724     0.79803   0.79803   0.82266 \n",
       " 0.408867  0.369458  0.310345  0.334975  …  0.788177  0.802956  0.817734\n",
       " 0.517241  0.46798   0.418719  0.325123     0.82266   0.812808  0.817734\n",
       " 0.546798  0.561576  0.53202   0.453202     0.82266   0.82266   0.832512\n",
       " 0.472906  0.44335   0.438424  0.394089     0.827586  0.842365  0.812808\n",
       " 0.472906  0.349754  0.216749  0.182266     0.812808  0.817734  0.82266 \n",
       " 0.413793  0.310345  0.187192  0.152709  …  0.817734  0.827586  0.832512\n",
       " 0.44335   0.374384  0.344828  0.310345     0.812808  0.812808  0.837439\n",
       " 0.453202  0.44335   0.472906  0.369458     0.807882  0.817734  0.827586\n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.689655  0.482759  0.472906  0.472906     0.955665  0.932677  0.852217\n",
       " 0.605911  0.463054  0.541872  0.507389     0.970443  0.935961  0.876847\n",
       " 0.522168  0.472906  0.522168  0.507389     0.977012  0.950739  0.891626\n",
       " 0.492611  0.477833  0.497537  0.507389     0.97537   0.945813  0.91133 \n",
       " 0.482759  0.507389  0.492611  0.546798  …  0.977012  0.955665  0.906404\n",
       " 0.517241  0.517241  0.522168  0.635468     0.985222  0.955665  0.91133 \n",
       " 0.551724  0.53202   0.541872  0.689655     0.985222  0.960591  0.91133 \n",
       " 0.487685  0.487685  0.625616  0.802956     0.990148  0.965517  0.916256\n",
       " 0.458128  0.458128  0.625616  0.788177     1.0       0.960591  0.916256\n",
       " 0.463054  0.418719  0.507389  0.566503  …  1.0       0.97537   0.91133 \n",
       " 0.551724  0.502463  0.512315  0.561576     0.97537   0.950739  0.916256\n",
       " 0.689655  0.674877  0.694581  0.738916     0.945813  0.935961  0.896552"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": {},
   "source": [
    "Display it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001E390860>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x000000001E407320>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(f0, L\"Image $f_0$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amount of removed pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho = .7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we construct a mask $\\Omega$ made of random pixel locations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 12,
     "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\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The damaging operator put to zeros the pixel locations $x$ for which $\\Omega(x)=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#1) (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi = (f, Omega) -> f.*(1 - Omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The damaged observations reads $y = \\Phi f_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.0       0.802956  0.802956\n",
       " 0.571429  0.0       0.0       0.0          0.807882  0.0       0.0     \n",
       " 0.0       0.0       0.581281  0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.566503  0.0          0.827586  0.0       0.0     \n",
       " 0.0       0.0       0.0       0.551724     0.0       0.79803   0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.418719  0.0          0.82266   0.812808  0.0     \n",
       " 0.546798  0.0       0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.349754  0.0       0.182266     0.0       0.0       0.82266 \n",
       " 0.413793  0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.0       0.374384  0.0       0.0          0.812808  0.812808  0.837439\n",
       " 0.0       0.0       0.0       0.369458     0.0       0.0       0.0     \n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.689655  0.482759  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.463054  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.472906  0.0       0.507389     0.977012  0.0       0.0     \n",
       " 0.492611  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.522168  0.0          0.0       0.0       0.91133 \n",
       " 0.551724  0.0       0.0       0.689655     0.0       0.960591  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.458128  0.458128  0.0       0.0          1.0       0.0       0.916256\n",
       " 0.0       0.418719  0.0       0.566503  …  0.0       0.97537   0.0     \n",
       " 0.0       0.0       0.0       0.0          0.97537   0.0       0.916256\n",
       " 0.0       0.0       0.694581  0.0          0.0       0.0       0.0     "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = Phi(f0, Omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001E35D320>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x000000001E7076D8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(y, \"Observations y\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#3) (generic function with 1 method)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# SoftThresh = lambda x, T: x*np.maximum(1-T/np.maximum(abs(x), 1e-10*np.ones(np.shape(x))), np.zeros(np.shape(x)))\n",
    "SoftThresh = (x,T) -> x.*max( 0, 1 - T./max(abs(x), 1e-10) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display a curve of the 1D soft thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GjdKECRO0atUqpaamauDAgTp48GCN45ctW6YBAwboww8/1MqVK3XllVfq+uuv1+rVqz0dFQAAn/L+2v2au2qfghzStCFpigwPsR0JdeAwxhhPPkB6erouvvhi/eUvf5Ekud1uJSUl6eGHH9bYsWNrdR89evRQZmamxo8ff9axRUVFio6OVmFhoaKi+GouAMA/HSg8qYHTlqmotFK/vaqzRl3Noqy21Ld7ePSdsPLycq1cuVIZGRn/fcCgIGVkZCg7O7tW9+F2u1VcXKzY2Ngaby8rK1NRUVG1CwAA/sztNho9a42KSiuV2iZaD/fvYjsS6sGjJezw4cNyuVyKj4+vtj0+Pl55eXm1uo8pU6aopKREQ4YMqfH2SZMmKTo6uuqSlJR0zrkBAPBmf/t8h77cdkQRIU5Ny0xTiJPv2fkirz5q77zzjiZOnKhZs2apZcuWNY4ZN26cCgsLqy579uxp5JQAADSeDfuL9NzCTZKk8dd3V8e4ZpYTob6CPXnnLVq0kNPpVH5+frXt+fn5SkhIOOO+M2fO1C9/+UvNnj272seZPxYWFqawsLAGyQsAgDcrrXBpRNZqlbvcGtA9XkMv5tMfX+bRd8JCQ0PVu3dvLVq0qGqb2+3WokWL1Ldv39Pu989//lP33HOP/vnPf+raa6/1ZEQAAHzG5AW52pxfohbNwvTszSlyOFgV35d59J0wSRo1apSGDRumiy66SH369NH06dN1/Phx3XPPPZK++zhx3759+vvf/y7pu48ghw0bphkzZig9Pb3q3LGIiAhFR0d7Oi4AAF5p2eZDeuOLnZKk527rpebN+BTI13m8hGVmZurQoUMaP3688vLylJaWpgULFlSdrH/gwAHt3r27avyrr76qyspKPfjgg3rwwQertg8bNkxvvvmmp+MCAOB1Co6X65HZayRJd/VtpyuTaz5PGr7F4+uENTbWCQMA+BNjjH79j1VasD5PnVs2078fukwRoU7bsfADXrlOGAAAODezV+7VgvV5CnE6ND0zjQLmRyhhAAB4qV1Hjmvie+slSaMGJKtna86N9ieUMAAAvFCly60RWTk6Xu5SeodY3X95R9uR0MAoYQAAeKG/LNmq1buPKTI8WFMz0+QMYjkKf0MJAwDAy6zafVQvLN4qSfrDjT3VOibCciJ4AiUMAAAvcrysUiOzcuRyGw1OS9TgtNa2I8FDKGEAAHiRp/+9QbuOnFDrmAg9Pbin7TjwIEoYAABeYsG3ecpasUcOh/T8kFRFR4TYjgQPooQBAOAFDhaVatzctZKkX13eSZd0bG45ETyNEgYAgGVut9Ejc9bq6IkK9UiM0qgB59uOhEZACQMAwLK/Z+/Uss2HFBYcpBlD0xQazMtzIOAoAwBg0eb8Yk36KFeS9MS13dS5ZaTlRGgslDAAACwpq3Rp+MwclVW61S85Tnde0s52JDQiShgAAJZM/XizNh4oUmzTUP3p1l5yOFgVP5BQwgAAsODLbYf16mfbJUmTb+mllpHhlhOhsVHCAABoZIUnKjR61hoZI93ep60GdI+3HQkWUMIAAGhExhg9MX+dDhSWqkOLpnryum62I8ESShgAAI1ofs4+vb/2gJxBDk3LTFOT0GDbkWAJJQwAgEayp+CExs9fL0ka0b+L0pJiLCeCTZQwAAAagcttNHrWGhWXVap3u/P0636dbEeCZZQwAAAawSv/2ablOwvULCxY04akKdjJS3Cg4zcAAAAPW7e3UNM+2SxJeuqGHmrbvInlRPAGlDAAADzoZLlLw7NWq9JtdE1Kgm65sLXtSPASlDAAADzomQ83aPuh44qPCtMfb0phVXxUoYQBAOAhi3Pz9Y+vdkuSnr8tTTFNQi0ngjehhAEA4AGHS8r02Jy1kqR7L+ugy7q0sJwI3oYSBgBAAzPGaMyctTpcUq6uCZF6dGCy7UjwQpQwAAAa2DvLd2tR7kGFOoM0fWiawkOctiPBC1HCAABoQNsOlej372+QJD02KFldE6IsJ4K3ooQBANBAKlxujZiZo9IKty7r3EK/+EkH25HgxShhAAA0kBmfbtG6fYWKjgjRlNtSFRTEchQ4PUoYAAAN4JudBXpp6VZJ0qSbU5QQHW45EbwdJQwAgHNUVFqhETNz5DbSrb3b6JqUVrYjwQdQwgAAOEdPvbte+46dVFJshCZc3912HPgIShgAAOfg32v2a+7qfQpySNMz0xQZHmI7EnwEJQwAgHo6UHhST8xbJ0l66MrO6t0u1nIi+BJKGAAA9eB2G42etUZFpZVKTYrRw/272I4EH0MJAwCgHv72+Q59ue2IIkKcmp6ZphAnL6moG35jAACoow37i/Tcwk2SpPHXd1eHFk0tJ4IvooQBAFAHpRUujcharXKXWwO6x2voxUm2I8FHUcIAAKiDyQtytTm/RC2ahenZm1PkcLAqPuqHEgYAQC0t23xIb3yxU5L03G291LxZmN1A8GmUMAAAaqHgeLkemb1GkjSsbztdmdzSciL4OkoYAABnYYzR43PX6WBxmTq3bKaxP+tmOxL8ACUMAICzmL1irxasz1OI06HpmWmKCHXajgQ/QAkDAOAMdh05rqf+vV6SNPrqZPVsHW05EfwFJQwAgNOodLk1IitHJ8pdSu8Qq/t+2tF2JPgRShgAAKfxlyVbtXr3MUWGB2tqZpqcQSxHgYZDCQMAoAardh/VC4u3SpL+cGNPtY6JsJwI/oYSBgDAjxwvq9TIrBy53EaD0xI1OK217UjwQ5QwAAB+5Ol/b9CuIyfUOiZCTw/uaTsO/BQlDACAH1jwbZ6yVuyRwyE9PyRV0REhtiPBT1HCAAD4/w4WlWrc3LWSpF9d3kmXdGxuORH8GSUMAABJbrfRI3PW6uiJCvVIjNKoAefbjgQ/RwkDAEDS37N3atnmQwoLDtKMoWkKDeYlEp7FbxgAIOBtzi/WHz/KlSQ9cW03dW4ZaTkRAgElDAAQ0MoqXRo+M0fllW71S47TnZe0sx0JAYISBgAIaFM/3qyNB4oU2zRUf7q1lxwOVsVH46CEAQAC1pfbDuvVz7ZLkibf0kstI8MtJ0IgaZQS9uKLL6p9+/YKDw9Xenq6li9ffsbxS5cu1YUXXqiwsDB17txZb775ZmPEBAAEkMITFRo9a42MkW7v01YDusfbjoQA4/ESlpWVpVGjRmnChAlatWqVUlNTNXDgQB08eLDG8Tt27NC1116rK6+8Ujk5ORoxYoR++ctfauHChZ6OCgAIEMYYPTF/nQ4UlqpDi6Z68rputiMhADmMMcaTD5Cenq6LL75Yf/nLXyRJbrdbSUlJevjhhzV27NhTxo8ZM0YffPCBvv3226ptQ4cO1bFjx7RgwYKzPl5RUZGio6NVWFioqKiohpsIApLbbbRq91GVVrhtRwHQgD7bekh//c92OYMcmvvrS5WaFGM7EnxYfbtHsAczqby8XCtXrtS4ceOqtgUFBSkjI0PZ2dk17pOdna2MjIxq2wYOHKgRI0bUOL6srExlZWVV14uKihogOfCdKR9v0ktLt9mOAcBDRvTvQgGDNR4tYYcPH5bL5VJ8fPXP2ePj45Wbm1vjPnl5eTWOLyoq0smTJxUREVHttkmTJmnixIkNGxyQlL3tiF7+z3cF7Pz4ZgriG1OAX+nfraUevLKz7RgIYB4tYY1h3LhxGjVqVNX1oqIiJSUlWUwEf1B4skKjZ+XIGCnzoiRNvrWX7UgAAD/j0RLWokULOZ1O5efnV9uen5+vhISEGvdJSEiocXxUVNQp74JJUlhYmMLCwhouNCDpyfnfan9hqdo1b6Lx13e3HQcA4Ic8+u3I0NBQ9e7dW4sWLara5na7tWjRIvXt27fGffr27VttvCR98sknpx0PNLR3c/bpvTX75QxyaHpmmpqG+fwbxgAAL+TxJSpGjRql//3f/9Vbb72ljRs36te//rWOHz+ue+65R9J3HyfeddddVeMfeOABbd++XY899phyc3P10ksvadasWRo5cqSnowLae/SEfjfvu2/m/vaqLrqg7XmWEwEA/JXH/xc/MzNThw4d0vjx45WXl6e0tDQtWLCg6uT7AwcOaPfu3VXjO3TooA8++EAjR47UjBkz1KZNG7322msaOHCgp6MiwLncRqOy1qi4rFIXto3Rg1d2sh0JAODHPL5OWGNjnTDU10tLt+pPCzapaahTHw7/qdo1b2o7EgDAB9S3e/C3IwFJ6/YWaurHmyVJE27oQQEDAHgcJQwB72S5S8OzVqvSbfSzngm6rXcb25EAAAGAEoaA98yHG7T90HHFR4XpjzelyMGirACARkAJQ0BbnJuvf3z13RdDptyWqvOahlpOBAAIFJQwBKzDJWV6bM5aSdIvftJBP+0SZzkRACCQUMIQkIwxGjNnrQ6XlCs5PlKPDUq2HQkAEGAoYQhIb3+9W4tyDyrUGaTpQ9MUHuK0HQkAEGAoYQg42w6V6A8fbJAkPTYoWd1asZ4cAKDxUcIQUMor3RoxM0elFW5d1rmFfvGTDrYjAQACFCUMAWX6p5u1bl+hYpqEaMptqQoKYjkKAIAdlDAEjOU7CvTyf7ZJkv54U4oSosMtJwIABDJKGAJCUWmFRmblyBjp1t5tdE1KK9uRAAABjhKGgDDh3fXad+yk2sY20VM39LAdBwAAShj833tr9mve6n0KckjTMlPVLCzYdiQAAChh8G/7jp3UE/PWSZIeuqqLereLtZwIAIDvUMLgt1xuo9GzclRcWqnUpBg9fFVn25EAAKhCCYPfeu2z7fpqe4GahDo1PTNNIU5+3QEA3oNXJfilb/cVasrHmyRJ46/rrg4tmlpOBABAdZQw+J3SCpdGZOWowmV0dfd4ZV6cZDsSAACnoITB70z6cKO2HixRXGSYnr2llxwOVsUHAHgfShj8ypJNB/VW9i5J0pTbUhXbNNRyIgAAakYJg984UlKmR2evlSTdfWl7XXF+nOVEAACcHiUMfsEYozH/WqfDJWU6P76Zxv6sq+1IAACcESUMfmHmN3v06cZ8hTqDND3zAoWHOG1HAgDgjChh8HnbD5Xo6X9vkCQ9MvB8dU+MspwIAICzo4TBp1W43BqZlaOTFS717dhcv7yso+1IAADUCiUMPu3Pi7Zozd5CRYUH6/khqQoKYjkKAIBvoITBZ63YWaAXl2yVJP3x5hQlxkRYTgQAQO1RwuCTiksrNCIrR24j3XxBa13XK9F2JAAA6oQSBp/01HsbtPfoSbU5L0ITB/ewHQcAgDqjhMHnfLD2gP61aq+CHNK0zDRFhofYjgQAQJ1RwuBTDhSe1OPz1kmSftOvsy5uH2s5EQAA9UMJg89wu41Gz1qjwpMV6tUmWsMzutiOBABAvVHC4DP+9vkOfbntiCJCnJqemaYQJ7++AADfxasYfMKG/UV6buEmSdKT13VXx7hmlhMBAHBuKGHweqUVLo3IWq1yl1sZ3eJ1e58k25EAADhnlDB4vckLcrU5v0QtmoVp8i0pcjhYFR8A4PsoYfBqyzYf0htf7JQkPXdrLzVvFmY3EAAADYQSBq9VcLxco2evkSTd1bedruza0nIiAAAaDiUMXskYo3Fz1+pQcZk6xTXVuJ91sx0JAIAGRQmDV5q9Yq8Wrs9XiNOhGUMvUESo03YkAAAaFCUMXmfn4eN66t/rJUmjBiSrZ+toy4kAAGh4lDB4lQqXWyOycnSi3KX0DrG6//KOtiMBAOARlDB4lb8s3qqcPccUGR6sqZlpcgaxHAUAwD9RwuA1Vu46qhcWb5Ek/eHGnmodE2E5EQAAnkMJg1coKavUyKwcuY10Y1qiBqe1th0JAACPooTBK0x8b712F5xQ65gITRzc03YcAAA8jhIG6z5ad0CzV+6VwyFNHZKq6IgQ25EAAPA4Shisyiss1bh56yRJD1zRSekdm1tOBABA46CEwRq32+jROWt07ESFeraO0siM821HAgCg0VDCYM0bX+7UZ1sOKzwkSNMzL1BoML+OAIDAwaserMjNK9LkBbmSpCeu7a7OLZtZTgQAQOOihKHRlVa4NGJmjsor3bq5izvMAAAeS0lEQVSqa0v9T3pb25EAAGh0lDA0uucWblJuXrGaNw3V5Ft6yeFgVXwAQOChhKFRfb7lsP72+Q5J0p9u7aW4yDDLiQAAsIMShkZz9Hi5Rs/OkSTdkd5W/bvFW04EAIA9lDA0CmOMHp+3TvlFZeoY11S/u7a77UgAAFhFCUOjmLNyrz76Nk/BQQ7NyLxAEaFO25EAALCKEgaP233khJ56b70kaeSA85XSJtpyIgAA7PNYCSsoKNAdd9yhqKgoxcTE6N5771VJSclpx1dUVGjMmDFKSUlR06ZNlZiYqLvuukv79+/3VEQ0gkqXWyOyVut4uUt92sfqgSs62Y4EAIBX8FgJu+OOO7R+/Xp98sknev/997Vs2TLdf//9px1/4sQJrVq1Sk8++aRWrVqluXPnatOmTbrhhhs8FRGN4KWl27Rq9zFFhgXr+SGpcgaxHAUAAJLkMMaYhr7TjRs3qnv37vrmm2900UUXSZIWLFiga665Rnv37lViYmKt7uebb75Rnz59tGvXLrVtW7sFPYuKihQdHa3CwkJFRUXVew44d6t3H9Wtr2TL5Taalpmqmy5oYzsSAAANrr7dwyPvhGVnZysmJqaqgElSRkaGgoKC9PXXX9f6fgoLC+VwOBQTE3PaMWVlZSoqKqp2gX3Hyyo1MitHLrfR9amJujGtte1IAAB4FY+UsLy8PLVs2bLatuDgYMXGxiovL69W91FaWqoxY8bo9ttvP2OrnDRpkqKjo6suSUlJ55QdDeP372/QziMnlBgdrj8M7smq+AAA/EidStjYsWPlcDjOeMnNzT3nUBUVFRoyZIiMMXr55ZfPOHbcuHEqLCysuuzZs+ecHx/nZuH6PM38Zo8cDmnKkFRFNwmxHQkAAK8TXJfBo0eP1t13333GMR07dlRCQoIOHjxYbXtlZaUKCgqUkJBwxv2/L2C7du3S4sWLz/rZalhYmMLC+NM33uJgUanG/mutJOn+n3bUpZ1aWE4EAIB3qlMJi4uLU1xc3FnH9e3bV8eOHdPKlSvVu3dvSdLixYvldruVnp5+2v2+L2BbtmzRkiVL1Lx587rEg2Vut9Ejc9bq6IkKdW8VpVFXn287EgAAXssj54R169ZNgwYN0n333afly5friy++0EMPPaShQ4dW+2Zk165dNW/ePEnfFbBbb71VK1as0Ntvvy2Xy6W8vDzl5eWpvLzcEzHRwP6evVPLNh9SWHCQZgxNU1gwq+IDAHA6dXonrC7efvttPfTQQ+rfv7+CgoJ0yy236M9//nO1MZs2bVJhYaEkad++fXrvvfckSWlpadXGLVmyRP369fNUVDSAzfnF+uNH350P+Pg13dQlPtJyIgAAvJvHSlhsbKzeeeedM4754RJl7du3lweWLEMjKKt0afjMHJVXunXF+XG6q28725EAAPB6/O1InLPnP96sjQeKFNs0VM/d1ovlKAAAqAVKGM7Jl1sP638/2y5JevbmFLWMDLecCAAA30AJQ70VnqjQ6NlrZIx0e58kXd3jzMuPAACA/6KEoV6MMXp8/jodKCxVhxZN9eR13W1HAgDAp1DCUC/zVu/TB2sPyBnk0LTMNDUJ9dh3PAAA8EuUMNTZnoITGv/ueknSiP5dlJZ0+j+wDgAAakYJQ5243EajZuWopKxSvdudp1/362Q7EgAAPokShjp5eelWfbPzqJqFBWt6ZpqCnfwKAQBQH7yCotbW7Dmm6Z9ukSRNvKGHkmKbWE4EAIDvooShVk6UV2pkVo4q3UbXprTSzRe2th0JAACfRglDrfzhg43afvi4EqLC9cxNPVkVHwCAc0QJw1l9siFf73y9W5L0/JBUxTQJtZwIAADfRwnDGR0sLtWYf62VJN330w76SecWlhMBAOAfKGE4LWOMxsxZq4Lj5eqaEKlHBibbjgQAgN+ghOG0/vHVLi3ZdEihwUGaMfQChQU7bUcCAMBvUMJQo60Hi/WHDzZKksYO6qrkhEjLiQAA8C+UMJyivNKt4TNzVFbp1k+7tNDdl7a3HQkAAL9DCcMppn6yWev3F+m8JiGacluqgoJYjgIAgIZGCUM12duO6K/LtkmSJt2coviocMuJAADwT5QwVCk8WaHRs3JkjDTkojYa1LOV7UgAAPgtShiqPDn/W+0vLFW75k004foetuMAAODXKGGQJL2bs0/vrdkvZ5BD0zLT1DQs2HYkAAD8GiUM2nv0hH4371tJ0sNXddaFbc+znAgAAP9HCQtwLrfRqFlrVFxWqQvaxuihKzvbjgQAQECghAW4vy7bpuU7CtQ01KnpmWkKdvIrAQBAY+AVN4B9u69QUz/eLEmacEMPtWve1HIiAAACByUsQJ0sd+m3M1er0m00qEeCbuvdxnYkAAACCiUsQP3xw43afui4WkaGadLNKXI4WBUfAIDGRAkLQItz8/V/X+2SJD0/JFXnNQ21nAgAgMBDCQswh0vK9NictZKkX/ykg37aJc5yIgAAAhMlLIAYYzRmzlodLilXcnykHhuUbDsSAAABixIWQN7+ercW5R5UqDNI04emKTzEaTsSAAABixIWILYdKtEfPtggSXpsULK6tYqynAgAgMBGCQsA5ZVujZiZo9IKty7r3EK/+EkH25EAAAh4lLAAMGPRZq3bV6joiBBNuS1VQUEsRwEAgG2UMD+3fEeBXlq6TZI06eYUJUSHW04EAAAkSphfKyqt0MisHBkj3dq7ja5JaWU7EgAA+P8oYX5swrvrte/YSSXFRmjC9d1txwEAAD9ACfNT763Zr3mr9ynIIU3PTFNkeIjtSAAA4AcoYX5o/7GT+t28dZKkh67srN7tYi0nAgAAP0YJ8zMut9GoWTkqKq1UalKMHu7fxXYkAABQA0qYn3nts+36anuBmoQ6NT0zTSFODjEAAN6IV2g/8u2+Qk35eJMkafx13dWhRVPLiQAAwOlQwvxEaYVLI7JyVOEyurp7vDIvTrIdCQAAnAElzE9M+nCjth4sUVxkmJ69pZccDlbFBwDAm1HC/MCSTQf1VvYuSdKU21IV2zTUciIAAHA2lDAfd6SkTI/OXitJuvvS9rri/DjLiQAAQG1QwnyYMUZj567T4ZIydWnZTGN/1tV2JAAAUEuUMB8285s9+mRDvkKcDk0fmqbwEKftSAAAoJYoYT5qx+HjevrfGyRJjw5MVo/EaMuJAABAXVDCfFCFy60RM1frZIVLfTs21y8v62g7EgAAqCNKmA/686ItWrO3UFHhwXp+SKqCgliOAgAAX0MJ8zErdhboxSVbJUnP3JSixJgIy4kAAEB9UMJ8SHFphUZk5chtpJsvaK3rUxNtRwIAAPVECfMhT723QXuPnlTrmAg9NbiH7TgAAOAcUMJ8xAdrD+hfq/YqyCFNH5qmqPAQ25EAAMA5oIT5gAOFJ/X4vHWSpN/066yL28daTgQAAM4VJczLud1Gj8xeo8KTFerVJlrDM7rYjgQAABoAJczLvf7FDn2x9YgiQpyanpmmECeHDAAAf+CxV/SCggLdcccdioqKUkxMjO69916VlJTUev8HHnhADodD06dP91REr7dhf5H+tGCTJOl313VTx7hmlhMBAICG4rESdscdd2j9+vX65JNP9P7772vZsmW6//77a7XvvHnz9NVXXykxMXCXYCitcGlE1mqVu9zK6NZSP+/T1nYkAADQgDxSwjZu3KgFCxbotddeU3p6ui677DK98MILmjlzpvbv33/Gffft26eHH35Yb7/9tkJCAvcbgJMX5GpzfolaNAvVs7f0ksPBqvgAAPgTj5Sw7OxsxcTE6KKLLqralpGRoaCgIH399den3c/tduvOO+/Uo48+qh49arcOVllZmYqKiqpdfN2yzYf0xhc7JUnP3ZqqFs3C7AYCAAANziMlLC8vTy1btqy2LTg4WLGxscrLyzvtfpMnT1ZwcLB++9vf1vqxJk2apOjo6KpLUlJSvXN7g4Lj5Ro9e40k6c5L2unKri3PsgcAAPBFdSphY8eOlcPhOOMlNze3XkFWrlypGTNm6M0336zTR2/jxo1TYWFh1WXPnj31enxvYIzRuLlrdai4TJ3imurxa7rZjgQAADwkuC6DR48erbvvvvuMYzp27KiEhAQdPHiw2vbKykoVFBQoISGhxv0+++wzHTx4UG3b/vcEdJfLpdGjR2v69OnauXNnjfuFhYUpLMw/Pq6bvWKvFq7PV4jToRlDL1BEqNN2JAAA4CF1KmFxcXGKi4s767i+ffvq2LFjWrlypXr37i1JWrx4sdxut9LT02vc584771RGRka1bQMHDtSdd96pe+65py4xfdLOw8f11L/XS5JGDUhWz9bRlhMBAABPqlMJq61u3bpp0KBBuu+++/TKK6+ooqJCDz30kIYOHVpt2YmuXbtq0qRJuummm9S8eXM1b9682v2EhIQoISFBycnJnojpNSpdbo3IytGJcpfSO8Tq/ss72o4EAAA8zGPrhL399tvq2rWr+vfvr2uuuUaXXXaZXn311WpjNm3apMLCQk9F8BkvLN6qnD3HFBkerKmZaXIGsRwFAAD+ziPvhElSbGys3nnnnTOOMcac8fbTnQfmT1buOqq/LNkqSfrDjT3VOibCciIAANAY+EOEFpWUVWpkVo5cbqPBaYkanNbadiQAANBIKGEWPf3v9dpdcEKtYyL09OCetuMAAIBGRAmzZMG3BzRrxV45HNLzQ1IVHRG4f6IJAIBARAmzIL+oVGPnrpMkPXBFJ13SsflZ9gAAAP6GEtbI3G6jR2av0bETFerZOkojM863HQkAAFhACWtkb3y5U59tOazwkCBNz7xAocEcAgAAAhENoBHl5hVp8oLv/rbmE9d0U+eWzSwnAgAAtlDCGklphUsjZuaovNKtK5Pj9D+XtLMdCQAAWEQJayRTFm5Sbl6xmjcN1Z9uTZXDwar4AAAEMkpYI/h8y2G99vkOSdKfbu2luMgwy4kAAIBtlDAPO3aiXKNn50iS7khvq/7d4i0nAgAA3oAS5kHGGD0+b53yi8rUsUVTPXFtN9uRAACAl6CEedC/Vu3Th+vyFBzk0PShaWoS6rG/lw4AAHwMJcxDdh85oQnvfitJGjngfPVqE2M5EQAA8CaUMA+odLk1claOjpe7dHH78/TAFZ1sRwIAAF6GEuYBLy3dppW7jioyLFhTh6TJGcRyFAAAoDpKWANbvfuoZizaIkl6+sYeSoptYjkRAADwRpSwBnS8rFIjs3Lkchtd16uVbkxrbTsSAADwUpSwBvT79zdo55ETahUdrmduTGFVfAAAcFqUsAaycH2eZn6zRw6H9PyQVEU3CbEdCQAAeDFKWAM4WFSqsf9aK0m6/6cddWmnFpYTAQAAb0cJO0fGGD0yZ62OnqhQ91ZRGnX1+bYjAQAAH0AJO0dvfblTyzYfUlhwkGYMTVNYsNN2JAAA4AMoYedgc36xJn2UK0l6/Jpu6hIfaTkRAADwFZSweiqrdGn4zByVVbp1xflxuqtvO9uRAACAD6GE1dPUjzdr44EixTYN1XO39WI5CgAAUCeUsHr4ctthvfrZdknSszenqGVkuOVEAADA11DC6qjwRIVGz1ojY6Tb+yTp6h4JtiMBAAAfRAmro2CnQ5d3iVOHFk31u2u7244DAAB8VLDtAL6maViwJt/aS0WlFWoaxo8PAADUD++E1VNUOH+WCAAA1B8lDAAAwAJKGAAAgAWUMAAAAAsoYQAAABZQwgAAACyghAEAAFhACQMAALCAEgYAAGABJQwAAMACShgAAIAFlDAAAAALKGEAAAAWUMIAAAAsCLYdoKEZYyRJRUVFlpMAAIBA8H3n+L6D1JbflbDi4mJJUlJSkuUkAAAgkBQXFys6OrrW4x2mrrXNy7ndbu3fv1+RkZFyOBweeYyioiIlJSVpz549ioqK8shjeKNAnHcgzlli3oE070Ccs8S8A2nejTFnY4yKi4uVmJiooKDan+nld++EBQUFqU2bNo3yWFFRUQHzS/xDgTjvQJyzxLwDSSDOWWLegcTTc67LO2Df48R8AAAACyhhAAAAFjifeuqpp2yH8EVOp1P9+vVTcLDffaJ7RoE470Ccs8S8A2negThniXkH0ry9dc5+d2I+AACAL+DjSAAAAAsoYQAAABZQwgAAACyghAEAAFhACavBM888o0svvVRNmjRRTExMrfYxxmj8+PFq1aqVIiIilJGRoS1btlQbU1paqgcffFDNmzdXs2bNdMsttyg/P98TU6iXgoIC3XHHHYqKilJMTIzuvfdelZSUnHEfh8NR4+W5556rGtOvX79Tbn/ggQc8PZ1aq8+877777lPmNGjQoGpjvPl413XOFRUVGjNmjFJSUtS0aVMlJibqrrvu0v79+6uN87Zj/eKLL6p9+/YKDw9Xenq6li9ffsbxS5cu1YUXXqiwsDB17txZb7755iljZs+era5duyo8PFwpKSn68MMPPZS+/uoy77lz52rAgAGKi4tTVFSU+vbtq4ULF1Yb8+abb55yXMPDwz09jTqpy5yXLl1a479beXl51cb527Gu6d8th8OhHj16VI3x9mO9bNkyXX/99UpMTJTD4dD8+fPPuo9XP68NTjF+/HgzdepUM2rUKBMdHV2rfZ599lkTHR1t5s+fb9asWWNuuOEG06FDB3Py5MmqMQ888IBJSkoyixYtMitWrDCXXHKJufTSSz01jTobNGiQSU1NNV999ZX57LPPTOfOnc3tt99+xn0OHDhQ7fL6668bh8Nhtm3bVjXmiiuuMPfdd1+1cYWFhZ6eTq3VZ97Dhg0zgwYNqjangoKCamO8+XjXdc7Hjh0zGRkZJisry+Tm5prs7GzTp08f07t372rjvOlYz5w504SGhprXX3/drF+/3tx3330mJibG5Ofn1zh++/btpkmTJmbUqFFmw4YN5oUXXjBOp9MsWLCgaswXX3xhnE6n+dOf/mQ2bNhgfve735mQkBCzbt26xprWWdV13sOHDzeTJ082y5cvN5s3bzbjxo0zISEhZtWqVVVj3njjDRMVFVXtuObl5TXWlM6qrnNesmSJkWQ2bdpUbU4ul6tqjD8e62PHjlWb7549e0xsbKyZMGFC1RhvP9YffviheeKJJ8zcuXONJDNv3rwzjvf25zUl7AzeeOONWpUwt9ttEhISzHPPPVe17dixYyYsLMz885//rLoeEhJiZs+eXTVm48aNRpLJzs5u+PB1tGHDBiPJfPPNN1XbPvroI+NwOMy+fftqfT+DBw82V111VbVtV1xxhRk+fHiDZW1I9Z33sGHDzODBg097uzcf74Y61suXLzeSzK5du6q2edOx7tOnj3nwwQerrrtcLpOYmGgmTZpU4/jHHnvM9OjRo9q2zMxMM3DgwKrrQ4YMMddee221Menp6eZXv/pVAyY/N3Wdd026d+9uJk6cWHW9tv8W2lLXOX9fwo4ePXra+wyEYz1v3jzjcDjMzp07q7Z5+7H+odqUMG9/XvNxZAPYsWOH8vLylJGRUbUtOjpa6enpys7OliStXLlSFRUV1cZ07dpVbdu2rRpjU3Z2tmJiYnTRRRdVbcvIyFBQUJC+/vrrWt1Hfn6+PvjgA917772n3Pb222+rRYsW6tmzp8aNG6cTJ040WPZzcS7zXrp0qVq2bKnk5GT9+te/1pEjR6pu8+bj3RDHWpIKCwvlcDhO+cjeG451eXm5Vq5cWe3nHxQUpIyMjNP+/LOzs6uNl6SBAwdWG1+bMTbVZ94/5na7VVxcrNjY2GrbS0pK1K5dOyUlJWnw4MFav359g2avr3OZc1pamlq1aqUBAwboiy++qHZbIBzrv/3tb8rIyFC7du2qbffWY10f3v689q6lY33U9+cRxMfHV9seHx9fdVteXp5CQ0NPecH64Rib8vLy1LJly2rbgoODFRsbW+t8b731liIjI3XzzTdX2/7zn/9c7dq1U2JiotauXasxY8Zo06ZNmjt3boPlr6/6znvQoEG6+eab1aFDB23btk2PP/64fvaznyk7O1tOp9Orj3dDHOvS0lKNGTNGt99+e7U/iOstx/rw4cNyuVw1Pidzc3Nr3CcvL6/G8UVFRTp58qQiIiJOO8b2Mf1efeb9Y1OmTFFJSYmGDBlStS05OVmvv/66evXqpcLCQk2ZMkWXXnqp1q9frzZt2jToHOqqPnNu1aqVXnnlFV100UUqKyvTa6+9pn79+unrr7/WhRdeKOn0vw/+cqz379+vjz76SO+880617d58rOvD25/XAVPCxo4dq8mTJ59xzMaNG9W1a9dGStQ4ajvvhvD666/rjjvuOOUkzvvvv7/qv1NSUpSYmKirrrpK27ZtU6dOnRrksX/M0/MeOnRo1X+npKSoV69e6tSpk5YuXar+/fvX+37PRWMd64qKCg0ZMkTGGL388svVbrNxrNFw3nnnHU2cOFHvvvtutaLet29f9e3bt+r6pZdeqm7duumvf/2rfv/739uIek6Sk5OVnJxcdf3SSy/Vtm3bNG3aNP3f//2fxWSN56233lJMTIxuvPHGatv97Vh7u4ApYaNHj9bdd999xjEdO3as130nJCRI+u7juFatWlVtz8/PV1paWtWY8vJyHTt2rNq7I/n5+VX7e0Jt552QkKCDBw9W215ZWamCgoJa5fvss8+0adMmZWVlnXVsnz59JElbt2712AtzY837h/fVokULbd26Vf3797dyvBtjzt8XsF27dmnx4sXV3gWrSWMc65q0aNFCTqfzlG+jnunnn5CQUOP4qKgoRUREnHGMJ5/DdVGfeX9v5syZ+uUvf6nZs2ef8tHMj4WEhOiCCy7Q1q1bzznzuTqXOf9Qnz599Pnnn1dd9+djbYzR66+/rjvvvFOhoaFnHOtNx7o+vP557fGzznxYXU/MnzJlStW2wsLCGk/MnzNnTtWY3NxcrzhR25j/nqy9YsWKqm0LFy6s9cnaw4YNO+Wbcqfz+eefG0lmzZo19c7bUM513t/bs2ePcTgc5t133zXGePfxru+cy8vLzY033mh69OhhDh48WKvHsnms+/TpYx566KGq6y6Xy7Ru3fqMJ+b37Nmz2rbbb7/9lBN4r7vuumpj+vbt63Una9dl3sYY884775jw8HAzf/78Wj1GZWWlSU5ONiNHjjznvA2hPnP+sYyMDHPTTTdVXffXY23Mf7+YUJtv/3nbsf4h1fLEfG9+XlPCarBr1y6zevVqM3HiRNOsWTOzevVqs3r1alNcXFw1Jjk52cydO7fq+rPPPmtiYmLMu+++a9auXWsGDx5c4xIVbdu2NYsXLzYrVqwwffv2NX379m3UuZ3JoEGDzAUXXGC+/vpr8/nnn5suXbqcsmzBj+dtzHeFs0mTJubll18+5T63bt1qnn76abNixQqzY8cO8+6775qOHTuayy+/3KNzqYu6zru4uNg88sgjJjs72+zYscN8+umn5sILLzRdunQxpaWlVft48/Gu65zLy8vNDTfcYNq0aWNycnKqfX29rKzMGON9x3rmzJkmLCzMvPnmm2bDhg3m/vvvNzExMVVftx87dqy58847q8Z//1X2Rx991GzcuNG8+OKLNX6VPTg42EyZMsVs3LjRTJgwwSuXLajLvN9++20THBxsXnzxxWrH9dixY1VjJk6caBYuXGi2bdtmVq5caYYOHWrCw8PN+vXrG31+NanrnKdNm2bmz59vtmzZYtatW2eGDx9ugoKCzKefflo1xh+P9ff+53/+x6Snp9d4n95+rIuLi6tekyWZqVOnmtWrV1d9S9vXnteUsBoMGzbMSDrlsmTJkqoxkswbb7xRdd3tdpsnn3zSxMfHm7CwMNO/f3+zadOmavd78uRJ85vf/Macd955pkmTJuamm24yBw4caKRZnd2RI0fM7bffbpo1a2aioqLMPffcU614GnPqvI0x5q9//auJiIio9o/293bv3m0uv/xyExsba8LCwkznzp3No48+6lXrhNV13idOnDBXX321iYuLMyEhIaZdu3bmvvvuO2UtHW8+3nWd844dO2p8TvzweeGNx/qFF14wbdu2NaGhoaZPnz7mq6++qrpt2LBh5oorrqg2fsmSJSYtLc2Ehoaajh07nvK7bowxs2bNMueff74JDQ01PXr0MB988IGHZ1F3dZn3FVdcUeNxHTZsWNWYESNGVN1ffHy8ueaaa6qtI+YN6jLnyZMnm06dOpnw8HATGxtr+vXrZxYvXnzKffrbsTbmu3fpIyIizKuvvlrj/Xn7sf7+XbzT/b762vPaYYwxHv7EEwAAAD/COmEAAAAWUMIAAAAsoIQBAABYQAkDAACwgBIGAABgASUMAADAAkoYAACABZQwAAAACyhhAAAAFlDCAAAALKCEAQAAWEAJAwAAsOD/AY237sHGPs0DAAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000001F1DBE10>)"
      ]
     },
     "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": {},
   "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": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Jmax = log2(n) - 1\n",
    "Jmin = (Jmax - 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shortcut for $\\Psi$ and $\\Psi^*$ in the orthogonal case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#19) (generic function with 1 method)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Psi = a -> NtToolBox.perform_wavelet_transf(a, Jmin, -1, ti=0)\n",
    "PsiS = f -> NtToolBox.perform_wavelet_transf(f, Jmin, +1, ti=0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#21) (generic function with 1 method)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SoftThreshPsi = (f, T) -> Psi(SoftThresh(PsiS(f), T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This soft thresholding corresponds to a denoising operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "BoundsError: attempt to access 16×16 Array{Float64,2} at index [1:128,Colon()]",
     "output_type": "error",
     "traceback": [
      "BoundsError: attempt to access 16×16 Array{Float64,2} at index [1:128,Colon()]",
      "",
      " in throw_boundserror(::Array{Float64,2}, ::Tuple{UnitRange{Int64},Colon}) at .\\abstractarray.jl:355",
      " in checkbounds at .\\abstractarray.jl:284 [inlined]",
      " in _getindex at .\\multidimensional.jl:270 [inlined]",
      " in getindex at .\\abstractarray.jl:752 [inlined]",
      " in lifting_step(::Array{Float64,2}, ::Array{Float64,1}, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:179",
      " in #perform_wavelet_transf#31(::String, ::Int64, ::Int64, ::Function, ::Array{Float64,2}, ::Float64, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:90",
      " in (::NtToolBox.#kw##perform_wavelet_transf)(::Array{Any,1}, ::NtToolBox.#perform_wavelet_transf, ::Array{Float64,2}, ::Float64, ::Int64) at .\\<missing>:0",
      " in (::##17#18)(::Array{Float64,2}) at .\\In[32]:1",
      " in (::##21#22)(::Array{Float32,2}, ::Float64) at .\\In[33]:1"
     ]
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(clamP(SoftThreshPsi(f0, 0.1))) #There is still a problem with perform_wavelet_transf especially for dir=-1\n",
    "# SoftThreshPsi(f0, 0.1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambd = .03"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#23) (generic function with 1 method)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ProjC = (f, Omega) -> Omega.*f + (1 - Omega).*y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.0       0.802956  0.802956\n",
       " 0.571429  0.0       0.0       0.0          0.807882  0.0       0.0     \n",
       " 0.0       0.0       0.581281  0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.566503  0.0          0.827586  0.0       0.0     \n",
       " 0.0       0.0       0.0       0.551724     0.0       0.79803   0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.418719  0.0          0.82266   0.812808  0.0     \n",
       " 0.546798  0.0       0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.349754  0.0       0.182266     0.0       0.0       0.82266 \n",
       " 0.413793  0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.0       0.374384  0.0       0.0          0.812808  0.812808  0.837439\n",
       " 0.0       0.0       0.0       0.369458     0.0       0.0       0.0     \n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.689655  0.482759  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.463054  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.472906  0.0       0.507389     0.977012  0.0       0.0     \n",
       " 0.492611  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.522168  0.0          0.0       0.0       0.91133 \n",
       " 0.551724  0.0       0.0       0.689655     0.0       0.960591  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.458128  0.458128  0.0       0.0          1.0       0.0       0.916256\n",
       " 0.0       0.418719  0.0       0.566503  …  0.0       0.97537   0.0     \n",
       " 0.0       0.0       0.0       0.0          0.97537   0.0       0.916256\n",
       " 0.0       0.0       0.694581  0.0          0.0       0.0       0.0     "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fSpars = y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First step: gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.0       0.802956  0.802956\n",
       " 0.571429  0.0       0.0       0.0          0.807882  0.0       0.0     \n",
       " 0.0       0.0       0.581281  0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.566503  0.0          0.827586  0.0       0.0     \n",
       " 0.0       0.0       0.0       0.551724     0.0       0.79803   0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.418719  0.0          0.82266   0.812808  0.0     \n",
       " 0.546798  0.0       0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.349754  0.0       0.182266     0.0       0.0       0.82266 \n",
       " 0.413793  0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.0       0.374384  0.0       0.0          0.812808  0.812808  0.837439\n",
       " 0.0       0.0       0.0       0.369458     0.0       0.0       0.0     \n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.689655  0.482759  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.463054  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.472906  0.0       0.507389     0.977012  0.0       0.0     \n",
       " 0.492611  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.522168  0.0          0.0       0.0       0.91133 \n",
       " 0.551724  0.0       0.0       0.689655     0.0       0.960591  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.458128  0.458128  0.0       0.0          1.0       0.0       0.916256\n",
       " 0.0       0.418719  0.0       0.566503  …  0.0       0.97537   0.0     \n",
       " 0.0       0.0       0.0       0.0          0.97537   0.0       0.916256\n",
       " 0.0       0.0       0.694581  0.0          0.0       0.0       0.0     "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fSpars = ProjC(fSpars, Omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second step: denoise the solution by thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "BoundsError: attempt to access 16×16 Array{Float64,2} at index [1:128,Colon()]",
     "output_type": "error",
     "traceback": [
      "BoundsError: attempt to access 16×16 Array{Float64,2} at index [1:128,Colon()]",
      "",
      " in throw_boundserror(::Array{Float64,2}, ::Tuple{UnitRange{Int64},Colon}) at .\\abstractarray.jl:355",
      " in checkbounds at .\\abstractarray.jl:284 [inlined]",
      " in _getindex at .\\multidimensional.jl:270 [inlined]",
      " in getindex at .\\abstractarray.jl:752 [inlined]",
      " in lifting_step(::Array{Float64,2}, ::Array{Float64,1}, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:179",
      " in #perform_wavelet_transf#31(::String, ::Int64, ::Int64, ::Function, ::Array{Float64,2}, ::Float64, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:90",
      " in (::NtToolBox.#kw##perform_wavelet_transf)(::Array{Any,1}, ::NtToolBox.#perform_wavelet_transf, ::Array{Float64,2}, ::Float64, ::Int64) at .\\<missing>:0",
      " in (::##17#18)(::Array{Float64,2}) at .\\In[32]:1",
      " in (::##21#22)(::Array{Float64,2}, ::Float64) at .\\In[33]:1"
     ]
    }
   ],
   "source": [
    "fSpars = SoftThreshPsi(fSpars, lambd) #Problem: perform_wavelet_transf especially for dir=-1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YjpIkVRiOkiRVGI6SJFUYjpIkVRiOkiRVGI6SJFX8f5v8Q6y1k/L8AAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cc95334f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run -i nt_solutions/inverse_5_inpainting_sparsity/exo1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jt3qfj3UpTu1U3FtaaCqs/OV94r5zj+yc0NIe1qmU1ZO203PvRfOOdWHcTamc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cc95354a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6))\n",
    "imageplot(clamp(fSpars))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2yTjlVti1AkN5Htw3rxd/x/vdZov99PgY1OoZz3iGJOmMM87o69inxXtUEFLB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\nPPOvNNhd0wb0pJNO6ss777yzpFl2Pmn8qdU2O5VS2UkDS55EES2YBaO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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cc953fff60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run -i nt_solutions/inverse_5_inpainting_sparsity/exo2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13×128×128 Array{Float64,3}:\n",
       "[:, :, 1] =\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",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625    …  0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 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      \n",
       " 0.25        0.25        0.25           0.25        0.25        0.25      \n",
       "\n",
       "[:, :, 2] =\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",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625    …  0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 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      \n",
       " 0.25        0.25        0.25           0.25        0.25        0.25      \n",
       "\n",
       "[:, :, 3] =\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",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625    …  0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 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      \n",
       " 0.25        0.25        0.25           0.25        0.25        0.25      \n",
       "\n",
       "...\n",
       "\n",
       "[:, :, 126] =\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",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625    …  0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 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      \n",
       " 0.25        0.25        0.25           0.25        0.25        0.25      \n",
       "\n",
       "[:, :, 127] =\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",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625    …  0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 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      \n",
       " 0.25        0.25        0.25           0.25        0.25        0.25      \n",
       "\n",
       "[:, :, 128] =\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",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625    …  0.015625    0.015625    0.015625  \n",
       " 0.015625    0.015625    0.015625       0.015625    0.015625    0.015625  \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 0.0625      0.0625      0.0625         0.0625      0.0625      0.0625    \n",
       " 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      \n",
       " 0.25        0.25        0.25           0.25        0.25        0.25      "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# J = Jmax - Jmin + 1\n",
    "# u = np.hstack(([4**(-J)], 4**(-np.floor(np.arange(J + 2./3,1,-1./3)))))\n",
    "# U = np.transpose(np.tile(u, (n,n,1)),(2,0,1))\n",
    "\n",
    "# U = repmat( reshape(u,[1 1 length(u)]), [n n 1] );\n",
    "\n",
    "J = Jmax - Jmin + 1;\n",
    "\n",
    "\n",
    "u = vcat([4^(-J)], 4.^(-floor(J+2/3:-1/3:1)))\n",
    "\n",
    "\n",
    "U = repeat(u, inner = [1, n, n])\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Choose a value of the regularization parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambd = .01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#35) (generic function with 1 method)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xi = a -> NtToolBox.perform_wavelet_transf(a, Jmin, -1, ti = 1)\n",
    "PsiS = f -> NtToolBox.perform_wavelet_transf(f, Jmin, + 1, ti = 1)\n",
    "Psi = a -> Xi(a/U)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007421875"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tau = 1.9*minimum(u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the wavelet coefficients with those of the previous reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "BoundsError: attempt to access 128×13×1 Array{Float64,3} at index [Colon(),[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,127],Colon()]",
     "output_type": "error",
     "traceback": [
      "BoundsError: attempt to access 128×13×1 Array{Float64,3} at index [Colon(),[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,127],Colon()]",
      "",
      " in throw_boundserror(::Array{Float64,3}, ::Tuple{Colon,Array{Int64,1},Colon}) at .\\abstractarray.jl:355",
      " in checkbounds at .\\abstractarray.jl:284 [inlined]",
      " in _getindex at .\\multidimensional.jl:270 [inlined]",
      " in getindex(::Array{Float64,3}, ::Colon, ::Array{Int64,1}, ::Colon) at .\\abstractarray.jl:752",
      " in lifting_step_ti(::Array{Float64,2}, ::Array{Float64,1}, ::Int64, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:227",
      " in #perform_wavelet_transf#31(::String, ::Int64, ::Int64, ::Function, ::Array{Float64,2}, ::Float64, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:118",
      " in (::NtToolBox.#kw##perform_wavelet_transf)(::Array{Any,1}, ::NtToolBox.#perform_wavelet_transf, ::Array{Float64,2}, ::Float64, ::Int64) at .\\<missing>:0",
      " in (::##33#34)(::Array{Float64,2}) at .\\In[67]:2"
     ]
    }
   ],
   "source": [
    "a = U.*PsiS(fSpars) #Problem: perform_wavelet_transf especially for ti=-1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: a not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: a not defined",
      ""
     ]
    }
   ],
   "source": [
    "fTI = Psi(a)\n",
    "a = a + tau*PsiS(Phi(y-Phi(fTI, Omega), Omega))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Soft threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = SoftThresh(a, lambd*tau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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
   },
   "outputs": [
    {
     "data": {
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eCEccUfnfqNRpxvcDT6WUFrfzWZ1NlK0u/o/UM7Zbz9huPWO7VYdKBd7HgZ91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\nkyQ1BANPktQQDDxJUkP4//uKBmalgYaPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cc9545f160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run -i nt_solutions/inverse_5_inpainting_sparsity/exo3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform the reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fTI = Psi(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SkPulo4NTEjo/l2PIkWsRlJAooetX1/W5Is9sZ+RdLltSn3M9XvnKVw7ta6+9dsc8nBTC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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cc95680da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6))\n",
    "imageplot(clamp(fTI))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Exercise 4__\n",
    "\n",
    "Perform the iteration with a decaying value of $\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cc4ey2TXaC1MckGyg3WdLrJCCCiXlFtkp/zZ5snFMnBs9AX1fsodnm/S2dGAq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\nIAiClSAf9CAIgpUgH/QgCIKV4H8Bdyw43n36IWsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cc956ee2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run -i nt_solutions/inverse_5_inpainting_sparsity/exo4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#37) (generic function with 1 method)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HardThresh = (x, t) -> x.*(abs(x) .> t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display a curve of the 1-D Hard thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000255BB978>)"
      ]
     },
     "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": {},
   "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": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "niter = 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List of thresholds. One must start by a large enough initial threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "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": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_list = linspace(1, 0, niter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.0       0.802956  0.802956\n",
       " 0.571429  0.0       0.0       0.0          0.807882  0.0       0.0     \n",
       " 0.0       0.0       0.581281  0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.566503  0.0          0.827586  0.0       0.0     \n",
       " 0.0       0.0       0.0       0.551724     0.0       0.79803   0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.418719  0.0          0.82266   0.812808  0.0     \n",
       " 0.546798  0.0       0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.349754  0.0       0.182266     0.0       0.0       0.82266 \n",
       " 0.413793  0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.0       0.374384  0.0       0.0          0.812808  0.812808  0.837439\n",
       " 0.0       0.0       0.0       0.369458     0.0       0.0       0.0     \n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.689655  0.482759  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.463054  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.472906  0.0       0.507389     0.977012  0.0       0.0     \n",
       " 0.492611  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.522168  0.0          0.0       0.0       0.91133 \n",
       " 0.551724  0.0       0.0       0.689655     0.0       0.960591  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.458128  0.458128  0.0       0.0          1.0       0.0       0.916256\n",
       " 0.0       0.418719  0.0       0.566503  …  0.0       0.97537   0.0     \n",
       " 0.0       0.0       0.0       0.0          0.97537   0.0       0.916256\n",
       " 0.0       0.0       0.694581  0.0          0.0       0.0       0.0     "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fHard = y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.596059  …  0.0       0.802956  0.802956\n",
       " 0.571429  0.0       0.0       0.0          0.807882  0.0       0.0     \n",
       " 0.0       0.0       0.581281  0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.566503  0.0          0.827586  0.0       0.0     \n",
       " 0.0       0.0       0.0       0.551724     0.0       0.79803   0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.418719  0.0          0.82266   0.812808  0.0     \n",
       " 0.546798  0.0       0.0       0.0          0.0       0.82266   0.0     \n",
       " 0.0       0.0       0.0       0.394089     0.0       0.0       0.0     \n",
       " 0.0       0.349754  0.0       0.182266     0.0       0.0       0.82266 \n",
       " 0.413793  0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.0       0.374384  0.0       0.0          0.812808  0.812808  0.837439\n",
       " 0.0       0.0       0.0       0.369458     0.0       0.0       0.0     \n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.689655  0.482759  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.463054  0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.472906  0.0       0.507389     0.977012  0.0       0.0     \n",
       " 0.492611  0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.0       0.507389  0.0       0.546798  …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.522168  0.0          0.0       0.0       0.91133 \n",
       " 0.551724  0.0       0.0       0.689655     0.0       0.960591  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.0       0.0     \n",
       " 0.458128  0.458128  0.0       0.0          1.0       0.0       0.916256\n",
       " 0.0       0.418719  0.0       0.566503  …  0.0       0.97537   0.0     \n",
       " 0.0       0.0       0.0       0.0          0.97537   0.0       0.916256\n",
       " 0.0       0.0       0.694581  0.0          0.0       0.0       0.0     "
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fHard = ProjC(fHard, Omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hard threshold (here $\\lambda=\\lambda_0$) is used)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "BoundsError: attempt to access 128×13×1 Array{Float64,3} at index [Colon(),[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,127],Colon()]",
     "output_type": "error",
     "traceback": [
      "BoundsError: attempt to access 128×13×1 Array{Float64,3} at index [Colon(),[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,127],Colon()]",
      "",
      " in throw_boundserror(::Array{Float64,3}, ::Tuple{Colon,Array{Int64,1},Colon}) at .\\abstractarray.jl:355",
      " in checkbounds at .\\abstractarray.jl:284 [inlined]",
      " in _getindex at .\\multidimensional.jl:270 [inlined]",
      " in getindex(::Array{Float64,3}, ::Colon, ::Array{Int64,1}, ::Colon) at .\\abstractarray.jl:752",
      " in lifting_step_ti(::Array{Float64,2}, ::Array{Float64,1}, ::Int64, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:227",
      " in #perform_wavelet_transf#31(::String, ::Int64, ::Int64, ::Function, ::Array{Float64,2}, ::Float64, ::Int64) at C:\\Users\\Ayman\\.julia\\v0.5\\NtToolBox\\src\\perform_wavelet_transf.jl:118",
      " in (::NtToolBox.#kw##perform_wavelet_transf)(::Array{Any,1}, ::NtToolBox.#perform_wavelet_transf, ::Array{Float64,2}, ::Float64, ::Int64) at .\\<missing>:0",
      " in (::##33#34)(::Array{Float64,2}) at .\\In[67]:2"
     ]
    }
   ],
   "source": [
    "fHard = Xi(HardThresh(PsiS(fHard), tau*lambda_list[1])) #Problem: perform_wavelet_transf especially for ti=-1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Exercise 5__\n",
    "\n",
    "Perform the iteration with a decaying value of $\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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/+KQwfA/7JrXDtUt13i9SYl4nUpSbbz6EYDF3w/WmXPWd73znijrLlL/yla/0dZRdm2Lk\nvpByMcXL9bRcnfty221D7DGP07J2zk0a1ozn09cpI6cMPZ1PrrfbJKW/885LYcu32GIIT2KdgTSc\nAcrI9923D0Pe6wIOPniIx2XOzlwKfycNHFE6P9Jwxrje1huQs+I8/UyQMuVz4rmzn8Sxk6vwWeYa\nJmo9UdisG6PAx+o8Zo6d5y9xwGmerPPzwfnw/eizRG6uhaLQC4VCYUFQL/RCoVBYENwllKJmP6hI\ncB3ZjIc//OF9mezJam2SFTT7SRbpCU94Ql++6KKLJE0rzwiLAagwM1vZYrvMXm6//ZD31v1wHpz7\n17/+dUnTogqynxZrUGFLsYXZYyoL3T5ZfI7T46BYgfD1ZNZF8cif/Mmf9OW3ve1tkqYVvhYnSYMC\nleylx05FKsUBZn/JBlPxaLGJxSzSoKSjaSiViTxXBkVcXkeK2nzWuO8UMXhMj3jEENab/Vx66aWS\nptfbZ5V7SZPNW25ZCuFOU0e26XNLE0WvPcVWNHV0maI49u/2KTK0yIXityT65Jll2evEPo2W2aDv\nbykq/awks8SkXGV9q03/NilSx5SvfHa5Nj5LPF9uK4mYpOGZaCnYp/od/UWhUCgU7haoF3qhUCgs\nCOYmciF7aiRPupa9sTXsFMlQ5GL2JWmY2Q/tnc3m0EKC7VvjT3vkpH0nK7rNNkvJzi+55JK+jt6F\nZpM5dosgaGVisQHH5LalaRFCYgc9PvZDts9sIdeL/VtUw+sWPfF3r3nNkETngAMOkDRtMWJxkjSw\npbzfa0uWk6x5sjjhetvqhGfFlhwUO/C694PrxnPnPaIozmKgZEnEOdFDkvtuS5WrrhpyK9tKht6h\nFDd5D/jscB28H7z/gguW8iNbXCNNs/Z+jug7wXXy+DkPP5vJE1kazkhLHOU95PXkB8FxJssY9kkR\nxyzYDjFmBePyam3Pjsngc8Y2k02561pz8xlI3rqzKAq9UCgUFgRzo9D51bRihja9VvxQAUSllinK\nRNlK2VM0fUlpk2tKj9QulUEGlRMeB6ldKsLcFq+T6krUg7/YpPr5RTe1QsqWMWncJtfLFGlSNLXa\nZJ+myqiE8xo/5znP6es+//nP92XvK/uhgsj1YzbIKZ5Py544KZk9N3JWVLq6nvtKqsz1jNfjMfPM\n0i/A919xxZCc6Oyzz+7LPg/cY5812sMn70D6VpDj2WmnnSRN26577FQSJ8qY8yU1zrLhM5JiAUnD\nM9dSRvp+PhO+h2eBnFmiTtP5TRR2Kz5R8p7mdZ+1O9s7NXmP8jn0uduQ2DJFoRcKhcKCoF7ohUKh\nsCC4S7j+m6Wg/atBpSQDVJm9JYvG37p9Kr+sQCLL+dWvfrUv2+WartW02TXbR9Y6BewiG2xxAcUG\nZJnNzpGdMptMFoxiGs+JYoVNNtmkL7stKnet0GObSaGXQgBIgziKduy+5/jjj+/ruIeeMxV37NMs\nM1lrj52KTp4Vrw3Xm9c9fvbp9eL5WLt2bV+2iIJjT6GYqWxMIqjLLrusL9v+m2F8OSaLw6677rq+\nzmIRiuwIK8apSKXYwgpQigh8D89KEktstdVWfR3PgM88z2yym2afXm+KL1KYiSTeawWHS0pRtp9E\nRx4Hx5mMCziOJF5piY5SXbJdH7NjT21yHt5jGhe0UBR6oVAoLAjmRqGTYjBIQfmrRcqAlJyVma2v\nZ/JGS4HiSTm7/3/8x39ccQ/7SgGXSAUwkFFS1pAKcJ9U0qUAQBxz4mjYvr/kSQnMcSYlTPK0kwYK\nn9yJqdyDDjqor7MHpDSsI6l6UkhJ2ej14Hx43eeBlC8DglkJTe7EivW99tqrr3v729/el5/3vOdJ\nmg6fS6p/l112kTQki5Ckc845R5J07rnn9nWvfvWr+/IrXvGKFfOlstOJPg4//PC+zmaHPB+k1q1w\nftWrXtXXMZmKPUR5lhw4jd7NpOptosizxOcweVz7XHBf2WcKNpWCWfHZTGbGyRSyBd+fvC1bnO7s\n7zg2ziNR0GPepUSLK55FUthKgxSixT1PtTH6i0KhUCjcLVAv9EKhUFgQzE3kkvIBss4KjVagLMez\nTpln2BbbNIvY8jL0dbZJ+1eLCFLewpatq1m4lLFFGtjfxOqRxUrsJ8UCvJ4UTEay2Z7ty6Bdttlw\nrodzXNIWmyICs7dcY8JrQhbf60ExC+3H3T8VzyynXLKOBU4xzJFHHtmXrRTlOOif4Djl9PRMAb2S\nWIBiCSpAPT+3LQ2iMooibFvO8f3Zn/1ZX8dAXBZHcY+8HvSnSPHpOXfuoc8Qn5l0pnmuLH5p5fL0\n/Hh/Cv5GjHl1puBdSUHJZ8bnsuWV7HrW+TnjGm5o7tHZvgzPuRWMz3uTfAJmURR6oVAoLAjqhV4o\nFAoLgrmJXOienOxFzY6R5Uxp2MjCkG1MWm+zuXTtT+IR9kPtvS0FKNoxm0x79+S+zLGlcVIskWzC\naRtvm+HPfvazfR3Z7GTh4z5ZR5GKWWrOnWvrtGann356X2cLiTVr1vR1dP13OIJkQ88+GbbA4pFW\nrG3fQ0situn9onjE9uFMlcdgVBZbcG2OOeaYvmy775NPPrmvs8/CEUcc0ddxDyyS4VmgxZRt2vkc\nPPvZz5YknXbaaX0dRSVm7RlbP9mCUzzidaC12H777deXk3iP47SIIVlHtdLrjVlMua2xoFcpvEPL\njT4lRk/27sl6pIUkBvKz2bLgSfbwKYVdsqFPvg/ScK6YgH3dunVxzEWhFwqFwoJgbhT6Nddc05ft\n5Ug7XyvcSPXQU8pUX6LapZwFyUqxVljaFGgrKWmoXKPCzuAX2dQOqdREsXIc7p/cAakJU1v0TDz6\n6KP7sueebPAJUjimiEktJ+owBRmjN20KmUpqm9SjuQZSj6ZsqUwkZe2QvAwHS47L1B/Pim3WDznk\nkL6O5+LCCy+UNE3187cnnXTSin68H8997nP7OipS9957b0nTa8N52LadZ+XUU0+VNG2vzvDOfhZa\nAev8HNFr2O3Tf4BKZHMqrWw5yQba18nhpSBzLR+R5B3tM9sKdXtHMgUZKcgcx9cK85u4F59Zzo3P\nROJOEhLV3rrHZ5lJzlsoCr1QKBQWBPVCLxQKhQXB3EQuFK8kO2UrqpiYl6yR2TaynGQrDbJwZvfJ\nbpNNtp0nlWyEWZ+Wks9ISk8GdmJGGLN1dJm32IH2wCm0ABV7FBckttXseut3ngfbJLvvPaIYxsGk\nHBRKmlbsrOaOLWUFksVE3COy9t5vzoP7bvENxQ5un6zxCSec0JcPPPBASUPGIEk65ZRT+rLnTJGL\nFdMUezFZtvfOylNJ2nXXXfvyZz7zGUnSn/7pn/Z1n/vc5yRNny+GobBIkGJIhkDw+aUNv+2u+exQ\nbOH14j3J1juJOlpJoL2HFG/Q/jspAZNoJ8W0b2XcSn4UqyWO5piSEpjjS/buVAiPBd9Kvh8pPnwK\ncMb6sfAHUlHohUKhsDCoF3qhUCgsCLqNcVv9WeL5z3/+io7JtlkUQlaKbJtZrxabYjadlh5mzVnH\n9s3OkwVj++4zRWBsafST+zBhFpCWCxbPMAIe2XmLP1IiY2mwvEkp12ihQ9bdfVJEQLGFrUoYk36f\nffaRNIgP2A9ByxZe9zqlxMDJGkEa1j4lgZYGVjiFPSC7zvW22ITnj3toixdGa3S0xC996Ut9HS1a\nnvzkJ0uaFr8RtoLhvnoetsWXpvfDUSUpsqOIwJZSFItZZMmzwDNvsQVFbUlElt4TnFuy0GiJOlYT\n44ylraOojaJaP1+8f+zZo8jGSJER2abXOyW0Z5utPA3pvZSiOlKk42eb4Sb23HPPKH8pCr1QKBQW\nBHNTipJqs7KJXzIr3JhRiPBXraVwMyVKCicpzEj12wabVA+ppRT0arWsOxxnS9mTFLX+bSuY1Ikn\nnihper0SZZzabHlgmqJgHSlOt09Ky221fAFMjYwFLuM4U2Le5KnHNaYS0dc5D7fPfmin7rlxD0lh\nmcrlense5HKo6Hdf22yzTV9H23rPk4pvB5xjXcobkNZYGp4Zrof3qJUsPQWHS4pH7oHn0fIqHsvq\nM2ajne5xOa0Hx5cyBdHHg3NzeYyTSGNq/c5tpSTjUn4HJQ6C59PvpQ1Zt6LQC4VCYUFQL/RCoVBY\nEMxN5EIRhFkO1pndT0ldpYFl5T1kc8zSkP1MbsFUcDr4Fu9JSjzCyrmkjJGy7WhKAMt5WOnFuTvl\nmTS4AJ911ll9HRWDq60NFStpHAwWxf69nqw744wzJE2nN6OYhmIPY0x55vZTXGqWWyn/UvueM/eC\n4QYs9uJ6MQSCxX50ybeIgv4FVEZaNMD1pq23FV0UIXgeVL4SSdzAfXebPLO+h2eaa5dEdSlwFEUV\nFiGwrqVQTnUpTvmGimnSe4PjTDbfnPuYLXfKS5DEK2mNpByXnWWfh5YIzEiJ1VthEYii0AuFQmFB\nMDcKnd6FpuQY8tRUQMs0yl/fZJ4mZUWYKUmGeLXpnSRdfvnlktpUQPJ8NFqKwWSalyhnfpFn+5Om\nlZmmOFIYX2mgnJIClH3TdM9rS6qLwaQc0Inz8D3MWMQwv6bWuTakZrw3ifPiXpNaNpXL7D/JY5H3\nuM2WIsr30OuYCumXv/zlkqR3vvOdfZ2paIYOZrLqsYxaXmdSaqbe6B3NMXvv6B2aAtIl0zs+B+Qa\n3H+L+ksKO9e1FINuK9VJObF6UiaOUcbJkzSFoWY/5Mi9ni2qPa2n+2wlfk6hhRMnw+cwvVfo/ezz\nUEmiC4VC4R6EeqEXCoXCgmBuIhcqspKdpdklKjSI1TKpsC2KMuzlSDb5oosu6stm12gvTHFAsoF2\nny2xQgoqlJRbZKf82+TJxjFxbvQE9H3JHp5t0tvSganIjpOdt8iFIgQr1Ngm45RbYdcKDOV5cN+8\nXvwd73ebLfbT42NQq2c84xmSpLPPPruvY58W71FBSAXnK1/5SknTmX689mynlXzc4LmwSIdK6Cc9\n6UmSphXPti2XhrXh+aSY0mNJMb1pC819T/dwj5OSOQVQaykBE3x/EnW07k125smnIQXGayVGdz3P\nb4rbnpSeLVGaRVit90EaRxLTUIyZlLMtFIVeKBQKC4J6oRcKhcKCYG4iF2rvbaFBNiSleiJLa7EE\nWTDeb1ENRTZ2zSbr4rjrknTTTTdJalvOJKT0UcmmljbIFL+YzeLc/FuKFSgCuOGGGyRNs97Jhppr\nbFEFxQpk8dxWy9rB9cm1uhVP2vNkn2SJPeYU6IgiuR133HFF+1xPWqfYhp/puv78z/9ckvT85z+/\nr2Osd9/PsdP6ZP369ZKkPfbYo6+zCIP7zkBdKexBOqu//Mu/3Nc57SLTCXJtvM4pITjbTOIPzo17\n3HKln+0/nemWr0AaWzo3vCedhSSGTO2wzDGlpO/JzpyB7WhdkhKrW5TGfeX9Xs/W+8DlMbt9Ppu+\nTsutFopCLxQKhQXB3MLnHnrooX3H/qqRKjL4RaXCzsq35OkmDRQePQKt1KINc1KuUWlEStFj4dc3\nhe0k1ePxcRz07jO1RaWVqQDWUenpPjmPpKBincstz1evQ1Iqsc10Xlp2vP4t943UTAoMZSUfzwIz\nCaXk35yT58GxW9l4/vnn93Up5C73aMxG2pwdg28x+bKpeZ4vBnqzbfG6dev6OnMVX/ziF/s6Kj19\nLuiZmwKGcZzJa5jUZbKL3tBQuKRcWU6ZfhJlnIwYWmFpk7KcSOfCz3Er2XpSRqZMQWMBu7h2nifv\nScHpkmEFwTEl44jddtutwucWCoXCIqNe6IVCobAgmJtSlCycWd0UZInsxlVXXdWX99xzT0nTLu+p\n/d13372v+9CHPiRJ+rVf+7UVfbP/lmLGbB/Z8RQUiGUrZcniJ/twsoKuI5tKltYKTAZx4tqYXSPb\nZnY9JcnlOGkDTff31djklpLN8yQbS0WZ15t77P1gm4xp73AEHAfbTK7/7mfnnXde0Y+URX2ExWJU\nXNu1n8pq9unxce7czxR7/7zzzpM0HUIgBaBK4guC1y1uSKIuaTjfSVEv5aw9HlMamzSsZyumvcVE\nFCmm54jKX4uzOHa26bOWxEVJES/lXAZJvJKMJFq2+mkeSbzCubuupUBP82ihKPRCoVBYENQLvVAo\nFBYEcxPoB7KrAAAgAElEQVS5kM01W0rWx2wf2ZDddtutL9vKJSW8lbJlgm1MGc0uJYxupdbyb8ci\n3JGd8jzYDrXuFhekcAEtt3JbOTAa4tq1a/tyiuRn9pIu8WQF3ScjMLJ9jyWx+GwniY5oL8/7vQ5c\nT/822bNLQ3o2itooqvM6cQ8d8oG26057KA3iD4qbUlQ/igAscuHcmNTbkSYpvuAeej3tUyAN4hta\nNDEdndeZZ5brlOzQkzgppUtkOynFYhL/cY24B177lhjS15Oog/tGqyHvDdtJYT+SXX4rkbz7GovL\nTnjMyU6caCVGT/D4+N6g/4znNBbLXSoKvVAoFBYGc6PQ6ZHlLxwVN+mrR0XWaoGIJOmaa66RJO26\n6659nT0n+cUmFWAqg9QKgyz5C0rKwm21PPFMIZG6I1eRPCNTNpvkWUYvV65DUijbM5JUAPtMXnPJ\njp3UchpbUjqRskj2zkmRlQIi8X5SPSx7/Gm9OfdUTl6ZbJ9Ul9eefZPzs3cr15jUYTqLKfF0UpSl\n2OJsP3lL8hy3AlwleN95ljwnzodjdj3HSQo/cd+Ju0iULc9fCpCV7OFb65UU12PUtPshh8e5m5No\nKU1TtiefWbbJZ8/tpwxgsygKvVAoFBYE9UIvFAqFBcHcRC4UdZC9NZKNM0UuvoesM1nmo446SpJ0\n6aWX9nVmXchmUhHmMsUCyQV3LHhXcp9vsXK2T98YkYvHR7dwsmsGFYfuh78jq2kRWEqeLA3rTVYy\nhUJIduqttGLJ3dt1LRv8pLhm2YpJ3u995V6y7LVp2aP7jHE9rMBkUmz6BXiduEdcJ/fP85eCSfEs\nem1bduheR+5RSm1IeEytoFdJvJIU5Gnt2A7nlO5PitYxcRPbtHI6heBozS3FdU+KWp4Vi9WYMHzM\nLyWJxbivDo3RMgRwW+k9OYui0AuFQmFBMDcKPVFlKdlvogykrEQh5eJQplQGmUq+5JJLVrQjDdQS\nqf6kzEmBjji2REFRYeYwvtJAWTBwk+dE6i1R+OQE+EWnksawmR3Xk/Pw159UQlKepT1qKWs8D14f\n87pzm63Qq75O7oNUlb0s6ZlrMMyuA3ZJ0mWXXSZp2lyQa++15Tx8vvbff/8VY5OmA2jNtiMN68w2\nbVaZPD1ZToHDeH0sqFXimLjeyawxKflayZdNOSeFr5SDdyVPZJa9dmPelFwP38O9TGvX4jC9DlxP\nP1stRWsyA03BtcbCEfN+P+eVsahQKBTuQagXeqFQKCwI5iZySYrDJIZpJY2lWMQgS2vvP7KvVvDQ\nNp2iDrLkqR+zVi3v1AR7fG255ZZ9XQpmRRbd4hF6EToTD9tiYCgGdLLC+atf/WpfZ5HPxtggkwX0\nmJPIJWVkkYb1arGSyQsxJfZNYPLkzTbbrC8nEYLFGvS6vPjii/vydtttJ2n6LJDNtiiEcd233357\nSdOet4yN7nVu2cv7DCVxVCtpcRI7sOw5J7Ea/T64Nv4t92DMLyAF50r+B0lZyN/ynjEPZI+5tTaz\nY5MGhXDLuzTFJk/z5PUU5C5lXkrK7Nn7jBR3ne8ytzX2TEhFoRcKhcLCoF7ohUKhsCCYm8glJSNO\nNswpYJc0sIhjNqZJvME434m1YRAnJlp2myltXWK7iCS+kAY2KwXSoniCVhsWr7z+9a/v64477ri+\n7GBUjhkvSVdccYWkadb69ttv78u0BjJSHGeKyiyOog094bmlGOnSsPbJMoHsJ21+XSbrzXPhdaYI\ny3UtnwWHRWA7KTwDz4LRSticUhMyeJfXhPtB8UkaZ7LfTkHEkqUSx8Y+3X4rQFXaj5Q4Op3pVjCp\n1axLeA/3w+NP9tlSfnY9Jj5bydY7BYyTsst9svbiuUp2/WMpK1PIhpSSslz/C4VC4R6EuVHoDA+Z\ngvWsZqsqDVRGS0FkkDKxPSrDwvKr5y8y76HSy190Uof+UpNy4FfeipkWtWLbZ87N9ySFF8e/Zs2a\nvo4KP1OcpAhtt90KFmXKhvMgxWBwTPZoJTWbFKQtpan7StQh6+i96rUnx2KlJn/Luds7llwI2/Qe\n77TTTn0dFefJizHNnXvkubGOnEZSuCUqNSnCWh6YPouJgm9RtomiJDzOMWVk2uMW95wSKSclMtfO\nFCs9nckt2miAHJP3iO0w3LGfmZZxgPc2BePjerT8BgyujTkEPkc24Ej+GNKwd+l5nEVR6IVCobAg\nqBd6oVAoLAjmJnJh0CCz/mMsWHKpJ/uYkqjS/tasNd21nflIGpSESWlEkB1KilLbkUsDm01Wj7DI\nh+IA28O3wh54fBwnbdY9PyYtdhCpyy+/vK8je5qyzJDFs2iIbtSz45E2ToTgvaXSyuvYCkzmPWT4\nBLrsH3jggZKkc845p69LCkjCWZqo9GT/jn1+/fXX93VeG4qweAbMJtNGnuEfvI7Jbp9I9sxJ6S4N\nzxTPTRJ7EUlBSfFMEiluiD10qx9pOGtJ5EdQrOHfJgUlx8l4/u6T75qk/CdScLAUwqAV4z+JgsdE\naBtyTRr3eZGKQi8UCoWFQb3QC4VCYUEwN5FLsp9NUcvIhiQrF4oVkliC7Ljtt88666y+juy83clb\nERzNWrHO1hLUpCcbaEYHJGytQVZwq622kjTN4nNuZj8pIqCYZ4sttpAkve997+vr7Jb+vOc9L87t\nwgsvXDEPsnhmuen+7vtTdD6OuWU3naIYej94Fhg2wfNISbMl6fOf/7ykaSsXi6PYN+fh3/Ierq3P\nEO8xa899oQjL4+O+87rjpNPaJsWH5zxTusNkCZXqWhEFk5s++/cZSH4jLeulJGqjWMKi0RRbn/NN\n4r8U6ZRt0nrOzxTFhBTzpNAARDq/yU0/rUPL+s7jTDblrbR1rk97MIui0AuFQmFBMDcKncoLU9lU\nHCaFBOEvJL+4rd8aprRIhe6zzz592R6k/KInu1dSrjvssMOKfqictSIsBf1hPZW/yS42JVfmF5vK\nOZc5Ntvc8ndU0iXPXAarOvbYYyVJH/zgB/s6UzBUaCUui+Pk2iQb6aT4Y9A0c1FUijpQljTYK9tb\nVhoUk1SAkwLfdtttJU0HOLvuuuv6sik9jsnUHe3/OU5zXokTkAaOiAG9vE6kUklxmqofo4wTxZls\nz9lnCpDG9lMc8ZZ3abqePLbHEjbzuteeHE9S0CefCJ457offB3yeyf24rTTOZMAxW54dhzRQ5inW\nezIO4D1j7zepKPRCoVBYGNQLvVAoFBYEcxO5UMRgtpKspllAsmopBV0rLnGC2yK7zSTSZpMp+knx\n0Fn3la98RVKOwywNijAqb8kCJkWYWSwq0chees4Un5A1N9t65JFH9nWek5WGknT11VevGAeTGnNM\nFrVQQek2kzs/61s20F6HFCecc2ebZo8pUqEoxS7gti3nbylS4TxcbomwPH7uYWLHrYyWppWdaR57\n7LGHpGmRnveAYgeKdHzGWsqzZEiQ7Mwpckwil7HwDav9bravVOe95b77LFDswOfMv6Xyn/e7/SQy\nYR3FjB5HK+yBsTGp8sZ8L5LYxPNMdvVsi+enhaLQC4VCYUEwNwo9KQZT6ExSK4S/YKSakoccYSog\neUhKA5VCk6KUcSZld2kldHb7LaWox0Rlj/tnVh5+nd0WlZ40e3z3u98tSfrQhz6kWTzlKU/py6T+\nbrrpJknTZp4pdDHHYUqPfXMPPbdWUCGvE5WqpqKZbeltb3tbX/7ABz4wda80TQFZ2U4uyJ6epPi4\nx6TajJRcnPD99ESmot9z5rlgn6ZEN4Y6TCaEaW2T0rN1T6KmScEnpATtfI5SNibOw8HlqES2spIc\nojNvScM6kcLlc+w5JW9gzj0pTVmXsiilbEstE8KkNE2m14mjSYpjzm3srEhFoRcKhcLCoF7ohUKh\nsCC4S2QsMhtCdsmsbMooJA2sF9lcsilJGWSWO8U3nu0/jdNsIdn5lNiXSlHfTxae93ssFHWY7SRL\nybkZF1xwQV+muOlXf/VXJUnr1q3r6xwjncG5KGrwOKjMo6jBoi0qrTynlkIs2UWTFfX9TIBtZSHF\nMBSVrF+/XtL0et16660rxrn11lv3dW6fynDGube9Pc8C+09sssUJnE/yWeCZSgHHEmvesu9OOQLS\nmU2ezi07dM+DhgDJDp1jSkHAUkauFK9cGvaG8eHdP5X7tBn32rEfnlWfkeRp2jp/Y0j3J+VrEoW0\nbMaTKDhlQeLaJeVuC0WhFwqFwoKgXuiFQqGwIJibyCXFgSZLfM0110iath1O7GVLm2xNfbIu4e+Y\nyiy59lPjb3aQ40g2tclWltYQZOdTKjJbeJAlpd20befJ1tGawiIEimS8trvvvntfRxbOseBbrHmy\nbPB6tVLQmRUlG8z9MOtN8YnTwFEEcNppp/Xlj3/845IGd31J2nHHHfuyzwv3LaUSY0Avi6O4R8mO\nmG0m6xC69nvfucYUUZi95nq5fYonWrHPjXT+k9iLZ5ZizHTmkwUR2/R+cb1o0eLnJAU4k7LlWhJB\npXSIXM+UHJz75raS5QrLLeuRZOWSxIgpRAFFJkkEOyamSfve8ueYGvPoLwqFQqFwt8DcKPQk4Kct\n9i677LKijl+wZH/LOlMcY8FyUkYkUitU0th7MNmmU1nIL7ptbnkPKTlfp82tPQ4ZIIr2uf7Kk0JJ\n9t/kFGjza1ChbE6DlFyi6rh2ydMzUYdU7lLB6aBazqYkSZ/73OckSXvttVdfx6Tehx56qKQ2x+My\n20xZZEhB+Z5WuNdkr+z9JtXOeaaE4+zTylueFVOxKWSulG2fk9do4h64l8k+nOPgmU/Pj8+iuTpp\nWunv9aSSmHD7iZrmOLh2ScmYqPXkTT5GoROJw0wZizi25OGZvN6lrFQd88KdHc9qKAq9UCgUFgT1\nQi8UCoUFwdxELhRrmD1NsbpbbuNmbVISXZbJfo7Zc5ptJLueRB1JEUV2mOyWxSucmwN6SYN4Zbfd\nduvrrDTadNNN+7o1a9b0ZSdApqiBYo+0ZklJl1hFimkoHiEbbiS76ORmzfEwdrlDFHzkIx/p66wQ\npqgtiUdae2jlMeOlW0mc2HEp+ydQLOH+k0gm2XRLwzpQFMeyWXYq5a0kpigsZctJogqOiXV+jngm\nKS6wKI1tjilFUwJ3tpmChKXgX0n80VJ6pkxARLKXH8uclDD2DvE8OfckCkvrIQ1nLcV9byWWTu20\nUBR6oVAoLAjqhV4oFAoLgrmJXFLCXLpjJ5flMa002TqzRCnWNtkuikJ8P0UdvO62OI7k4s0IkLYP\nJwtFdsz29hajSNIznvEMSdL555/f15177rl92WIcsmhk4cy2Uqw1ltbO+0GxA9nf5AOQEt1yP9y+\nLZYk6bDDDuvLJ510kqQh9Z+Ubf1pl23rlpabtEU2rPM60XY9pUfjWeE8LALhmU0sPuF50PrDqfCk\nwW2dZ8X90KeA8/S5aSVK9nXuodtqWa6k8ad9Z58poTPXO1lEpec4ifxayZdTlMMUp3wsXVxqM/nE\nsJ5z8xkYi3FO8LrXJlnObEwquxaKQi8UCoUFwdwodFOmLNPjzzauVMwlDzNSI4mKHAtokyj8lnIs\neYGZKmLfpOpNJbMdUuiOec77k+KG1J09SLmGHJM99KhYTMoc3jM7XmlaOWeQKktKo6QQpiL0sssu\n68umvGmvnJSJpGJN8SZPUGng9nhWTBVxbmNBrzgnr1lSHHK+V1xxRV/2fpNCT5Ri4ohIhfLcmKpL\ngbDYF/c9Kci570khTA9Nj4nnM2XQ4dq6/xYnkc5N4iqJxGEmD06uV7onBT5rKXc9/sS5jQX5Ssps\naVh7npuE1YJ4rdrv6C8KhUKhcLdAvdALhUJhQTA3kQsVZWa3HCRJGpRfZNvIRidb2JROjhgLspTS\ndSU3f8YRTyKXZLPLQEVUenlOe+65Z1933nnnSZoOIMU2b7jhBknT7vxkJc162/6a4BpyvbfbbrsV\nY6PLvdc22Sizb6a18x7uvPPOfd2b3vSmvnzIIYdImo5nbjEM0+9R5OJxkCXl2nofOA8njOa+kg12\nmXuYRBkpdRvPklPdSUNwMa4NA45ZNJAU+a0AVR5nSySTFPTeb7bTUroaKbxDEm8k0Y2UA+Px2dyY\n+OGz9yRlIvtMfhYtMU6aRxLLJWXlmIKyFeQupbH0O25j4uC3UBR6oVAoLAjmRqEnz8MUsIZfN3tV\nSgNV11K8JLNHf335FWaAoRRuk6ZqplgZGCqZ2ZEasoKo5YnnOSXFYFK+sq8jjzyyr6NCzutAT9KD\nDjpoxThJBf/xH/+xpHY2J5dJ4Xtt6O144IEH9mWv4+/+7u/2dS972cv6spWuVL56v7gH3EOPj56g\nNHtMSnDva8skM4UGTsHOqOD0+WQ7HIcV41R+pYBfSfHMvrm2PiMM7kZT32SmlwLOsU+Pj2vDs+br\npA7dJ+tY9jqNeXW2gsvN9s3xJc9vKe+75zxm+twKwZ3GP2ZO6HKLi0pK1UR5p0CEpRQtFAqFexDq\nhV4oFAoLgrmJXMjWJS8xs1Nku1J85RabbHaL/di2mTbOqS2yQBQxWERB1tpjbgXrsfiF46AC6frr\nr5eUvS4pcuHaeBz0HmX/V155paRptu2SSy6RNC1iok344YcfLkm68MIL+7qxDDsW6VAsQFHIe9/7\nXknS8573vL6ONvoWV1FJ5/1uxbB2X1T4UmmaYmCnrDxjSX65XykZtveLIjkqdy3q4D3sMymZPWaK\nxRLrzfPF859s2z3OFAxKGvaAY+OYvDbMOOR+UrYvzmMMYz4iSWHbshn3PJNHa0t8l5C8RseUkSk4\nXSuLl6/zLI7Fr9+QOOhGUeiFQqGwIKgXeqFQKCwI5iZyITuVWKvE0lLkkrTJCcnyJcXslrJdNdlC\nB1RKgZ3YJq97Hq3UWmaFafWTLHS22WabFffzOtfGYguKcW655RZJ02nt3vrWt/bl3/md35E0bUFB\n8YjFIrTwsUv/fvvt19e95CUv6ctveMMbJLWtUJJrdbK1th25lO2NU6JlsqwWcVHUNZZwPIkdeFY8\nJ4ZfOOKII/rypz/9aUnT4g/G1ndfHIfnxL7pa+B6ijfSc5QsVlqpBd1ny27av+XaWYyYbOhZP5b0\nOFmUtGLWe71az67nnMIRtCzMvDYpvMfsfbNjbonS3Bb3gGX3n95bydafffG90UJR6IVCobAgmBuF\nTqQwllZckhrh15XUo9GiMgx/SflFZTv+urYoC3uIUhnkry+9R6nINWXTUoLYJjhlNaEHJL02fZ3K\nQMLtp7CfpKZNlbP+qquu6utop24FKCl4K8pOPPHEvu6YY47py1wTg+vpdeR+JE6AFL7vSaFTpWGd\n0x62fAUSJcdx+lyk0KtU6NIj9sMf/vCK64lKTcovnnMqWq1wTnb7Ug6faw4wKU+l4SyRQzQnKg0K\nYY5ptj9p+ixa8c4znzxFk/K3pUxM2YcI35/8C3gPlcPJQzNx9GmPWrbrYwpMnztyBb6f+5YMRBJX\nOYui0AuFQmFBUC/0QqFQWBDMTeRCsYTZIAZ2YiAjIyWapXs7RQxmvZJygQoJsjlU/BhkAck+G26f\n80mu10lEJA1iDdr5ms1tuYCbPSb7mGJgk300G801fPjDH96XLdJxrPXZ33ruXI999tlH0pDcWJoW\nEVjkwn1lm84MRdbdrH0KO8D7WxmgVssk1ArOlcRzSSGXXMhbNsoWGXI9k8ItuY3z/NAowGeoFRLC\n9bzuNlsiKq8JRVA8y76P+5Z8LyiySaKOVE6+AEnMMlu/WptJfNJKqm20RLVJGT7muj+m7Ez9pHZS\necxuXyoKvVAoFBYG9UIvFAqFBcHcRC7JtZvRFO2qTpaTbJ1ZFmrkqUlP4QRcR/aR7c/+TpoWlZgF\no823rUPOPPPMOI5kcUKW1hYcFOdYjMTf0eLk0ksvXTHOxMIlEQGtZSgKscjmCU94Ql93+eWX92XH\n+qbliuOy33jjjX0dbca9tq2wB1tttdWK+5PFyZh4JPkAJCsB3pusDFqWC0Zqc8zSiPvWsl02LELj\nfLleFuNwPZO9c4rb3gp14GeqlSIxhRPwHrWSiI+tXRKFJJFKiqzYEnGlfR+LsZ58SJJYLiWObolc\nxuae7klIvgAbElKhKPRCoVBYEMyNQqcSz4GW7M0oSTvssIOk6aw6pFj91SKFRMpita8iv3QMVmXl\nHqmiq6++ui8n6jHFm06BulqepB4nOQUGyErw+Fq2xUkhaKVXUjBK0qGHHipJet/73tfXvfnNb+7L\nZ5xxhqRpRar3w1mGpGmbcdusc9/oLfnJT35SknTAAQesmEeL+vM8Wtlwkvef16mlQF9N6ckxJe9T\nnj8GDNt3330lSRdffHFf95SnPKUvW+nPcZiav+mmm+Lc0llKNtJj96Tzl4JSteD7SbWnNrmGiXIe\n8/ImPM+xNomUIHtMQTo2prF7fIZamZV8rrnvKRtTar8o9EKhULgHoV7ohUKhsCDoNiTx6J3Scdf1\nHVshSJtds510NU/BaVqpntDPqvezzq7VHMfpp5/ely1KoQjB95P1JjuVYrBT0Wr3frLJDsRFUQaT\nSL/rXe+SNK0QprLSLB7FFhZVUKzAJNTu/xnPeEZfd/755/flZz7zmZKk97///X3d7rvvLmkQj0nT\nIoZ169ZJmp4713vbbbeVNK1kHksgnFjeFEyN7GmKsT6WviyJXxJr3UpB5/Wmop+Btnzm01lqufYn\nF/GkAE2Jz1sKYZc5t6QUJVKAqST24tx43WvfEtkYY6Ifwu0ne/mWmCalnExnLYlpWqIb35/2RRrW\njtdTCILkK8Ox7bzzzjHGQFHohUKhsCC4S3iK+gvHhLemYEjNkvI1BURlYqK0Wl51BqlUU8SkfBO1\nTWrDHpzJo08a5kmFHCkCmxHSU9RzY1JiKoxN0fIrzrl7PflFNyWWsrxIg0KO1OH69etXjDN5B1JR\nSo7K8+Q8qHBO3sBGizpLIY6Tp14KpNWiyt1Wi0r1WBJ110pa7Dm3PDANni9Tl60gTcmbMlHwSQHK\nfUvmma15pKBZNq/kvo555qZnL3FBycx4tv+E1cwFW9R0SkTf8m6d7WcsoFcaB6/z/jGv0bSHLRSF\nXigUCguCeqEXCoXCgmBuIpfNN9+8L5t1Jwtu8QftxJOtdys5c4ptbjaGbC49NP1bKq+S0optJjYo\nXafCjCKdFIzKCs7bbrutr/vKV77Sl70OFONQfOL5MXiX+6HylmN3ebPNNuvryFJ/+ctfXlFncQLF\nKFQoJ5ty7mHygEtBlpKCKXltStlD2GvLcdLr2GeN4pExhVwSbyQRRMs7NGXYSXXJo7plh56Upj6/\nrWxNPtMpATbb5Jh8VpJYimNuZf9Zzda7JfJIHprpevIRaWVWGvPgTGdtDEl8kkQ3YwG9Ujz+ylhU\nKBQK9yDUC71QKBQWBHMTuVx77bV92Swv2ZCkDU7x0BlCIKWGS/fTIoVt2tKDYh6yr6vFJT733HP7\nMlO72WacfZI1T6yi6yieSCnTOA6ug1k0WpzYgsiJnaVpcZLXjmKeNWvWrBgT2UOniWulGrMNNq1+\nKAYye5qCmbGflLCZ7OeGxinnXiexQis5eBqTz0Wye+ackvu5NKwDWesUKI7ivyTGYf/eQ66N154i\nP+67y+w72UhzvVKIAWLMPT5ZDaU1TiEMWnHdV9tDjp33p71ppcAzkkgwWVQRreBfs2224qFvTIiE\notALhUJhQTA3Cp1ekFbE3XzzzX2dKYuWl6DLVPaQijVIvVkhyDapbDTouZhsevkVvvLKK1fcz+tW\nUHKciSLl3PxbUonJy5F1pKxNdTkjkDSsjcPgStPepUnpRNt3U+OksK0ApYJxyy237MumLltBlBIF\nlRSDLJsibdkOJ9vjxF2QS0pZezjORB0m++2xJL78rc8Y2/SYmPWJZ9HnItmzSzl4nCnvFjXtudH/\ngO2nM+89aiU+T+ud7KpTWOQWNTqWfDldTwpfPlMub0zY5MRRp3PTUu6uxr0kA47Z8hiKQi8UCoUF\nQb3QC4VCYUEwN5ELFV2OI03WO7FerBuLYZ1sds0aUdTw5Cc/uS+fdNJJkqaVibSrtrKUduyO5c1E\nyWRPzSa3gvXYbZ6xtK2M/PrXv97XMdNQYu25dhaBMBPQLrvsImkIiCVNB9W67rrrJLXDHnh8a9eu\n7ev8Wwbxoh27xS9cjzE35xS2gGXvIc8Pg38lN+mkyKLi0GWKxSiCsGiBbaYAU5yn20w28tLg/8Az\n6zj4DnomSVdccUVf3nXXXSVNi73GlPb27UgJ0Nk/z08SN7FP/5br3lJWJvj8JmViy709iSXGzlIa\nD+/xOrVCLaRAW54713hMPDJmT59+l0RYGyJ6KQq9UCgUFgT1Qi8UCoUFwdxELrRNNmtDNsN1Y6mx\n0j1SFtmYzWV0wE984hN92ZEXyW6TrTTbSvbUyazPPvvsvo5jtoiCYQ0o8jHrltipJNqRBosWikdY\ntmUD0705NjnFNeecc05fTgmwCVrHGJ4bxVIUEyXrEFpGeB0plkju2kn7z3a4Xykeusst1tv1tOVP\nEQeTGChZ6Mz2ZSQrG67NeeedJ2mIhy9Je+21V1+22KsVR3w10RHFiESKNJlEelxvn8sxP4mWdVPy\nMfF6p6ihvL+VSs/XU0q+1jvEbbXEZum95Hmyn1Y8dWMsAbbnPGYltSH26EWhFwqFwoJgbhR6Uhwm\nJQspoOTF1aLQk72oKQt+6ehd6nHwS8my76edrql+2nzTJtz3s0/abW+33XaSpBtuuKGvM/dCBdFV\nV13Vl90W14tzd+Yl2oSb2qEXbIqXzvWkr4B/y+BeplaosOU8zSm07HDd51jscq5Dy/PSSEl43U9K\n8ixlyjYpM9lmosQY0/6rX/2qpGnK9VOf+lRf9t5stdVWfZ2DrfH88KzYrj9l/5ntyzCXRk/RZCPd\n8vY1kv02z4q9rAnuWxpzUhZS+ZpioyebcCknB08UbYof37L/NlfNAH7Jz2EsrnsKKJao/pbxgOfR\nUrfCvFAAACAASURBVGwTRaEXCoXCgqBe6IVCobAgmJvIhSyLRQwUZSSWltfNhlC5msQvZFMsouDv\neP0Rj3jEij5bsdENiyAoniDMMqck0NKgCKN9twNpkf2k3bRFB2RpOfYdd9xR0iB64TyY5o/sqdlK\n2pGPpcEyi8jfUSSTlJGE+082+tx/srwWe1C8wHm4L7r2e9+4nomN5v5SxOAzls5aS0RgkQtFaWzT\nCk4qoT0m+wRI02vjtaeojf37jPFMW3zD85fCZXANk3iE4gCPk/NhsD2L2loil+QXkO5h2Qpr9sln\nwvenYGkt+233T7FWEgXzrLl/zmcsrV3qPz1brTj47osivxaKQi8UCoUFwdwo9JaHp5GUoolabpkk\n+atLE0FTNuzv6KOPXnGdJoCkgPwlZZ1NIO3lJ01T4Fa6chykpr0OpP5sakZKjJSv504q1MGzpEFB\nRQrGlF7ykJQGjodUPbkGz5MUvsfZSvacgqElBRT3wxQQqeVLL720L3t8PAucu+/n2vi3j370o/s6\nUr6+h2Pj2iQKydd5VnimPf7E9UmDcprKxJRli23yjBhU/LlPUno+qxwn27GpLk02uR8pRLLvb2W/\n4rk1UljZ1CZNbXnW/BxxHim87lgQr0Q5t0J0ex3HkoMn88lEgROprpUlK4UCb6Eo9EKhUFgQ1Au9\nUCgUFgR3CZGLWafE8pJ1IftqNiTZa0qDQiPZFvMeK68kae+995Y0batNUHli2I6c7CFFFWY/v/a1\nr/V1VMj5Ou9Pc+fcHAiMNvQsW8Rgdloaz4piVpIsLe3LV7OBJpuc7HO5rxSFJFh8Qxae7Se2NCUK\np1jMCckpGiIbnTJmJRtpiiq8R7Q9T0HXuNcc5/XXXy9pWjx3+eWXS8o+CdIg4uA5pJLQwbuYPNxK\nV8a25z0ef8tL0c8P18YJw+m9zDElX4GWXbZhkQ/9OShK87lMWaOIFDQrxbFnW61nwmtCsW+qS+Lj\nVkaj1cQvrUBubr+CcxUKhcI9CPVCLxQKhQXB3EQuTFZstpIscUokSyuD5FKfAuaklGctltVsOsU0\nTJ5r1ohstK1X2Ldty6XB5Xr9+vV9HcU8KThSCvzkhMvSwHpTBMWAYylWt1lvWo9YFCENYiKOg5Ye\nHhPvTynPkv1ssl2Xhv1kcC2LZJga8KijjurLJ598sqScqJv1HLtFRxw7xVG+zrNGkY1Zf6ZItFiO\ndvu0FPHcW5YgZqOvvvrqvs5hACjy22mnnfryTTfdJGkItDZ7/1lnnSVJuuaaa/o6i6v233//vo5r\n474o3uD5d8gJBgnzPbRmSeIPPs+cu9ckxfDns8lUfF5nPnsUR7l9nouUyDulxRsTZSSRCttM+9pK\nQbdakukUloBzKpFLoVAo3IMwNwo9hWnll84UYctu2l/fVhCnRP2Z8mhR/abUGNSKCiYrsjbZZJO+\nzh5ytP0lNf3EJz5R0nQyaSoGrQwlteFwtPwdqRW3yXGQ2jFlRIWd50GqilmWTAkyyxGDRHmdSXGm\n4FocRwqPS5jK4X44/K4VfNJ0UCvbbZMaTrbYpKCs9KRimhS6KU5Sf6T0zj33XEnTSmKvA5XIpGwT\nt8c2PWZya/vss4+k4ZyxThrOMjNNkZP5vd/7PUnTZ9EeqQxrzHF4vfjskENwX7zf3CbPSgqi1/IQ\nNtfLs+h95Tmnx6yfKe47x5w4dpfHvDZb1HRKXJ2U8slruRVELCk4xzxJW89PQlHohUKhsCCoF3qh\nUCgsCOYmcqESxuzFWBCcZPPbsp81y0OW1+wU2SYqbswuMfb4QQcd1Jdd/+IXv7ivM3tK1puxp80m\nk5XjmJLdqllZKgMp+jGrSZEM2/T8UsJnihpo3+0+qTgkG22lVMqWQxae7GFK+JzYR7aZYljzrFhU\nx7FRROA589zY5Z9hDd773vf25Wc/+9mSBjtwaVqU4fFxHsmemKy9x0dRGsdpsRnFDl4bhgOwIlSS\nDj/88BXjOOKII/qyM1AdeuihfZ33ncrGVg4Bg6JNi44omvScWEclsueRRGHSkPiahhE2LuB68Nn2\nsz8WEzzZb3M+RIpdvqF+DmM+Czx/XBuDz8GYS7/H3woNQBSFXigUCguCeqEXCoXCgmBuIpfE2lNE\nYBaR7EpiXcZYn6RNJjtEl3tr8hmVj5p8g7HPLbaguzb7tIiArvkp9jRZxT322GNFHRMxmy1ds2ZN\nX0cxj930ybLuvvvukqYtcGjlYksSijf4W48lxTvneo4lyU1WCLzHZ4B1XDuz0YxemSLkUXxn93pG\nxDzuuOP6sq1YKNKjeCRFHPRZayVs9m9bVhmut+hFGljrNHaC54f7bhHdRRdd1NfZYov38PxabMd2\nkiiFIr8U/Y+iJYvgKD6hVZvXwRY4UhYr8Dn0/QwNQPFLskhJSaBTZMSWSNBz5/3Juo5IouCUnHws\nhnpKLVjRFguFQuEehLlR6KQOHTiI3o6mlvjl53VTEWMU+phdKj1B/UVO3o7EO97xjr5sSmtDvLgM\nZnfxF5+UrxWpVBrRNt724bSL5jg9J3qSmsqldygVwqb2SVmQMvGaUAFqyobrRUowJRNOXntU2Jl6\nJIVMpVYKZETO7cADD5wamyS94hWvkCS99KUv7evoF/ClL31pxXyTzTgpTlOZPF9JcUguhxTpapwM\n23QgLI6JFDap2L/6q7+SJL3gBS/o604//fQVvzv77LP7steBHCA5v0RNm0rms/nIRz6yL1uRyzpy\nVD4jVOr7jKTnTRqoVK5xUijzfKX1TLHmue/pfcL7k8I3jZlnnkj7nrxHk3J3LEG6VBR6oVAoLAzq\nhV4oFAoLgrmJXMhGm91Lqd+SXTLvJxtCdj8hpZwii2XFDxVAiXWie7JZqKc//el9HdlTB0oie8r2\nLVqgyMVsJUUmZJnN0jJYFG2sLZpim14ninuopPN1so8UO6Q0bV7vFINaGthkXqfCz3vLOo+dLHqK\nc09FaRKVvOlNb+rrrAB18Cppeo+8N1wPKu0tAuP5skiQIgDa+Pt6Kw65lZBjij0qK/1MUPzGoG9W\n7vIsep0YToChA6yAp0I4hQngmKygpMKW87Qohfb03COLBLnGFpXwzBJeG4pZkjKz5cZvpPdJyw3f\nc09B/4ik4GQ/vJ4Sq6f3EpGS07dQFHqhUCgsCOZGoZPasWKRlK+/SgyulbzISMWSCk4emKaGWp6J\nbpPUG+938KYUFpSJjDnOZIqWkvRSsXfwwQdLmqaAGMTJZnTkaM4///y+bKptl112WdEn7yGVYKoq\nmVhJw9xTQueWCZfnnoKqScPakjL22pIydVhZjpltPu5xj1sxJlKHKaws5+b15HpwP/xbJqZOXoj2\ngJQGz1qeL1Kf3gcqtpN5Gs39TJHyOs34DJ5fc2RcT1Lj3tdkdsh5kKt0/2yTnB2DnBkpkFzyKk5c\noZQV0ymEbcqoxX4SVd9S2qck5r6f9/BM+7ctw4qU8cj3tziFpDRtoSj0QqFQWBDUC71QKBQWBHMT\nuZB1MjtH8YkVM2Q5KbYwW0fWmDblKWhXUnCStTH7TJEKYYXdjjvuuKJNiotoV508QclKWvlHsYFt\nxWlvzLFfcsklK+po82vb5+TdlxQ0HOcYUiCuVvYg7xfFEhyzWUgqBu252/LmtRiKojhmDXJQLSoO\nuTdGitXNM8n98rnivlqsQYUVWeLLLrtM0vQacx187nhOrWBt2Rt7nSjeO/PMM/vy0572NEnS6173\nuhVj57NBsZvr+RzwLNlGn+th8Ql9GpIHMZ9XPtvJFjsFckvGC2wziUeSqCIln2eZ11l2+6nNlExa\nGhfjpGdltcTRRAXnKhQKhXsQ6oVeKBQKC4K7hMjFbBTZFFtdpAA90sCekjVJSY0Ti0arCsJsXysV\nWdKk067bIPtpO3Oy3hSlWGS033779XWOy23RijTNsrp/imlS0u0UD71lq58S0SaLliSqaLlBJzf9\nZEnCPTI7z/PB/bANPq/TuuSDH/ygpGlLDp+F5MItDeKbluWCxWK06rAVDdOkpbVtnU+PJQUWY990\nj/d17gHbt18C98BnkVYmFFN6nVqu6rai4Zn1ejI8QxKPcD34zPm3SfzWOisu83lk+8lNP6V749rQ\nhyDB7XPf3H8KgcH6Vgq62bFx7C0berfViutOFIVeKBQKC4K5UegMK+qvVQpOs/fee/d1zCJjRVfL\nptyUB7+kViqRIkxUaCuprCkS3m/FIxWpVJ4l22Eq9J70pCdJmk7I/JznPEfStCcoKU7bQ1MhRwrK\nylsqE1Oo2kThcO6Jk0kUOu9J2XBanrkpuJf75HxIVX3hC1+QNL3eDLRlipIUqRXsKTwzx5zCpM6O\n33DQLIYbTspf3st5Jq9Qr21L0ep67hs9Zr3fDHznc0PPW1Km7p/PCSlvP6c8C54z50Ou1BwV941l\nnwGOw/enZ4dIXI40rB3H4evsJ53Fln2394hzT5wM7/c6JgqbY0rK31ZSbWMsW5NUFHqhUCgsDOqF\nXigUCguCuYlc6GqclFZWCFKBQ1Zy2223lTQtlmAAIosdUmColqu6x9Gyq7YCi2yXx0cWivMwO5WS\nFvM+BlR65zvfKWk6mw3FNLb/bcVLT+KoxL5yHmZlmTg6BUJKgbio2Etu/klZLWUlYkoOnlzRTzrp\npL6O623xClleiw1abuOz85Gm18binSSiGmuTIEudfmuRCsdB8YtZf64H2/EZ4Xo7EBdDR3C9UjAp\niiiSrbb73HXXXfs6Ps8WDTAEAeF1TCK9Vvag9I5IYRWSeIX7xvXyHreSZq+W46D1uxSQjvvusYwF\n/EpioFKKFgqFwj0I9UIvFAqFBcFdQuSS7EEPOeQQSdLatWv7OrK37373uyVNW5yQDaJViJG0xGR3\nkngk2REnti1Zakg5zjhZpwMOOEDStLhot912kyR98pOf7OtsDSMN8eO5bldddVVf9jpQXOX+uQYc\nk1lB7gvtv1dzO26JEsbsv5NFgNeObXJt7ItAu3xGmnT7dHVfbd9YTqwzx8n19NxaVhdJlEHW3/Nj\nn77OsVHk4r1jXTp33GNb9jBiJW3nU9RIrr3PCEUI/q3DG0jTa+u+uF4Mz+DnmGvsObXyH3icLZGd\nrWO4NikcQIqM2IpyuJoVzJhFSgteT+5xigw7lk6zhaLQC4VCYUEwNwqdX+eU8NmKPdoTn3DCCX3Z\nCX/pqUkFqb/YVCaaikh2uFIOvDOWVNZfXLaZsp7QXpgZY8455xxJA0ciDXG7GfyI7ZsSa3nimYIa\ny96SAgi1vGiTN5spC1Jn6Tr3mvbjXhMGEfN+kIqkQu/GG2+UNG23zz5TTHGvHbmPRO1wPZJSK3Ef\n5BoJnwFS0Imb5DjdFu/hvruee0S76+22207SdNx2e5ryHq6Df9ui/mzbTr8A98nzR27P2YuYRSuN\nifvufeWZT8mbW4rKlFHL5ZTsfPa3CYmCN3hWkgK/RcEnjt5ngGcucZAtY42pMY/+olAoFAp3C9QL\nvVAoFBYEcxO5jLlWW1Ry0UUX9XW//du/3ZfPPvtsSYOCUJL22muvvmyFjOM5SznOORU3Zqlbsctd\nn+yVW6xgUkbytw7yZFdyaRCZMO46lbxuM6XGYn1yLx5TALUCPyX2Myk9k5gnxWWXsiLM17lvN9xw\nQ1+2qIWitBRwiaKK5D+Q9otzT8qz5MZPMUpaz5SOrdW/RS5U6CZRG/d13bp1ffmLX/yipGn/BZ8r\nBvmimMjiFypFOc+kFLX4hfvGeXq9GXqCSlFfZygGi1oYgC+JFFthJAzucbIJT2gFZfM6p35SELAN\ngdeZylu3RTFMUuBvSM6CotALhUJhQTA3Cj0p5PhVMuXAL+HVV1+9oh0qx5iZxl90ej46/GmLGjEV\nTaqopew0/EWn0illD6Jyl3N30KRE/XHuL3zhC/vyKaecImna4zQld07UcotKdT0pXypyTR2kNkk5\nJI/ZliepKT0r0STpPe95jyRpzZo1fR3vd5ukpBjQyQo7Jl/2WUpUkZRDs7JsijZxAqQiuXaeJ/tJ\nZrMck5WIKfSvNHCT5ETJ2f3BH/yBJOnNb35zX/fMZz5TkvT5z3++r7OprCTtvPPOkqYD351xxhl9\n+a1vfask6TWveU1fZ47J5rXS9H6Y8ua+8az6WeF1U+ak9BMV3FL0p3eI17YVPG41BaU0PFMcRwqQ\nlrxGqawm3CbH4f5bCdp91kopWigUCvcg1Au9UCgUFgTdagFo7kxsuummfcdmOZJSoGUbbCUPlZpJ\ngUQWzmwwg1olkQ0z0yR2inUWS7SS23qcBx54YF/HMbvMeToIGb1DaZdt9rWlkEuBtFLs8cQ2chy0\nPbaijgq1ZJue7PbJslIRZlHIJz7xib7OLC0TIad41BSzMNY3y7P38HykOPgUf1CJaE9Viu+8b1xj\nKvRSICUqh32+KdZysCuKbjhOrwMDsf3Kr/xKX7a3MIPYOTAZRR7cA4u72OenP/3pvnzBBRdImp67\nxTTcA4pcfC4dQE+aVop6bbneyfeCbabAZDy/yQ49KfqTIUHLnt7XKSpLBgcUr/g5YR3t/t1XmgfH\nxvPjZ47X165dG4O4F4VeKBQKC4J6oRcKhcKCYG5WLsnCYsy2kyIGs0asS6nlyGab1aOYhVpxs0tM\nK0btv0ULZMcd85k244961KP6slkvBpAim2yXaLK8Dg1ASw2y6x4HxUnJfjwlqm0lgXaZ4o0kAkvx\n5bmGFMm4LbKfDKrlUA4MwObwDWRz2b5FHewniVLIsvp+zj0FteL5o/jk8MMPlySdddZZfZ3nRIsU\nik+8N/R9SOKqFLSNFlEUtbkvriHbtE/GLrvs0tddeOGFkqbDYnCc69evlzSIViTpoIMO6stO78cx\nWVRC8UgKtcA9TCE4koVZywItBbmjKMN7mNL3pUBYLKdAbFK2Q3cdn5MUQoDX07njs+vrHAfTAFpE\nxncRnxmiKPRCoVBYEMxNKbrJJpv0HftL2fJSTPCXrpXYN9l7OoFwshdmuZV5xkpC25ZL0rnnnitJ\nOuyww/o6Kou8vsxIRKWTbY/p8Wqqy8GWpGnFjedOToGUi6+n0K6t7Cxun22yT1OsKbwuuQcGYfIe\ncl/IdZgjstcv+2EScVK5nhP3kGMylZOUdK2wtKa2uYZUCJ933nmSptfLZ4k29OTSrBDkdYYB9vl0\nZi1pWA/amdP3wntIO3IqHn3W9ttvv77O1HJrHD6rDBjH626Te2yjAVKR6XxyD0ldmnptnV8jeT9T\nuZo48mSrnTxfOWaeFc7TIIfp+0mBkxPxHtLblxy/vWfTmFjHfTeXduqpp/Z1p5xySilFC4VCYZFR\nL/RCoVBYEMxNKUpxwGo2pBR/kB1KLvMpMwmVX2YvaQdOMY9ZWraZFCpUwlkBStaZLJbvp4s2FSJm\nIbfZZpu+bqeddpIk/d3f/d2K30nDOrTsgI1kp9uK9e7fcr34W4+Za2dRR8rkw3s++9nP9nW0kTbr\nTjbZ/XPsaW6tuO2+PwXn4nySizdFAFScv+hFL5I0rYD867/+a0nSnnvuGcdh0RPHSRGarzNchWPi\n88xTpHLaaadJms4URP8GJ85+3ete19fts88+kqbFNBQP+swz5nzKbkTxin/rhNzStG28z7ITvUvT\nIgiLuyjKSL4CCTzzyX2eSL4XKcl0CiEgZfFN8vFImagoBmQ5jTfNmevp/WA4jBaKQi8UCoUFQb3Q\nC4VCYUEwN5HLmL2nQRaJGupkl0p2P0UstGUE2Z3kot2yW3VfFDFYhECWlKIhW0vQDtgx0KWB7WSE\nRrdFdj1FLEzRKaXBYoFu8B4T153tp8hyLNvShHOzDT5DJVBs4XFeccUVfR1FLm4zueFzX2lF4L3j\nXnMeZl9TSIgUkoFz4j1JNOXE5JJ07LHHSpoOUUARgsURFF/QbttzohjH/VvkJk2LqzxORjnkufvD\nP/xDSdJTn/rUvs7PCWOTf+xjH+vLDoNB23bvqzSs7U033dTX2R6eFk20GrLIkaJHztNry7rki0Ks\nlqhbymkCZ++dve4zliKE8jqxWq4BlrmeKWk8rY58FvneYcTL008/XdL0u8q+ESvGF2sLhUKhcLfD\n3Cj0VhJVw19xUlLJdpNfNV5Pdtf+UreSxibFCr+utqEmlWkKrJVBx/3zi81AR+6T97sfevQlioAU\nECn8ZOfr9ebYktccKRiuk9siNW7ugwpb2hubgmspG+0Bxz2y8ozrTkWYy6SGeT0lWnZbpIq4Xp4T\nldX09vX4qLi25yQTIVOx6Pup8GJQLFPoL3nJS/q6lK2Ja+fgXVxD2nrbXp5tOvky7eqtKJWGgF6k\n9HlW7ReQMm6RW0veki07c68Dr3u/SOmnhM4t/5QUL90g1Z1ijrOfViAvw3NvvXc8/paxhst8Zvzs\n89nimL0fG5IZqSj0QqFQWBDUC71QKBQWBHeJFHQpgbHZnVaqMbPRZGlTWrGk8KCSJLmIJ4WtNNiB\n8h677F977bUr5iMNioykCGX7DPJk1p8sOkUQSXRE9tAsHPvx3FuirqSQTgmyKaqwizgVZhQXOG42\n2Uv+1mNJoq6kvJKG9aJ4hOvkOfO6RRQUdXEeFsUwAFViiSmqsOKQ4gmWrQSneITKxhe/+MWSpIMP\nPrivs8LPKQal6ZAQVpYy+BZtk71HtA93mAqeYyozLTKigpKByaxsp621zzIVremZoZiGykyLClMY\niZaI1echiXaIJHJppa1LIozUfiuFXWrTIpdWwme/D1LwLb4D+DxaXJaek1kUhV4oFAoLgrlR6OlL\nOBYoLAVX4pc/BZ5iAJ+ULSSBihlSh/7SOjCTNJgGUmHGwDr+ItNkzcotaaCqSK14HVKSZs4jhR+V\nsmnVmFlYMgfkb80hkCswd0TKghSjKXiOM4XXTRQUPQtT0LZWkl6PiXU2jySHx/1waGOeH5qImbJP\nGXSomOY9pmK5b+l8c54ve9nLJA3JnmfnYQ6A3Br79Ph5bsxd8HdMGO2zSk6A3qk+VzyfKTgcnyn3\n1VI2+vniPd7XFHCrdT2Z3absWa0znZSiyfs07SHXk2cgcZ3J+5Rj95xItfN+c1mUArRQFHqhUCgs\nCOqFXigUCguCu0RwrpQkekz5kOymydKarUt26ClRLH9LZSJhpRaVa/baow0y+7SijSIRKqWSMshs\nYUsE5fG3gk1RHDF7vWWTm4KhpaBBVJhZBMGx09bb600be7LMXpM0d4q9uEdJXJYUcpynRWTcV4rF\njj76aEnT4iAqWj1nJlperW/OjcpVrrfPy/HHH9/XWeTCcXBtUqYfwmtL8YjPLBWY9ER1cC/Gqbft\neqtPn+/W3FNSY4ot0nPos5QMGwie7bF3xJhN+mrtSMM7KiXq5nwYr9/ilxRokOUkkuG+E26L+9ZC\nUeiFQqGwIKgXeqFQKCwI5iZySW69yb2d7ArZpWSXmmzKky1rKw2bY5rTBZdpxZ71rGdJkj73uc/1\ndWZPyebSysAWAxRfkHVP1jiJVUwWA2yT1j62nGCdWcUWe5lYa64908QZ3g9q7OliblaUbDJFOr6P\nYhyLRcjOU/ySfAWSO3dirckmJxEAWV5an3jtucceE9tJoSm4b7xusR3nYbEH7dmJZBlG0aXHz3Nh\nO3MG9KJIxWtPEVMKocGz5OBvXA+KHWz51YoZnoLxpX5SvH62mSzQiBQHn2clWXYRKXiXRWlJdCgN\n56/Vpt9RvN/WV7QWu+GGG/qywzu0AnIRRaEXCoXCguAuQaEnijR5NJK6NBXSCqbjLyC/nq7j15xK\nJ7fPbCH8kr7xjW+UJL385S/v62w7yq8rAzvZ5twhMKXpoEbJrjUFIkrcCynKpOwkx2Jqg9Ruyj7E\nfki1ec0uvPDCvs62y4973OP6OioevUfJy1UaqDqO3XNLCnBpWCdSXSlBdgryxDqWPXeOne37XHC9\n3Sd/x3l6/Dxf3A+fS1Ku9vDkHnBurSxNRgpIZ18ABvHi2lopz2eC/Xv8vM4k0gYV3+bSWs9m4oh8\nPWX/4Zg5jsRpJ69OrnvivFoemInL8nrw2Uge1VzjZOyRDA64v/STMJ72tKfFcRJFoRcKhcKCoF7o\nhUKhsCDoxtzt7yxsu+22fcdmo5IbM8dH9tXsGsUGdO22YpLso93z6eZMZc4111wjaVqxR/byL/7i\nLyRNKwgdhIm26QcddNCK9o844oi+Lik8KKZJrDPFEmbXGGDKY5cGt3OycLaPbQUm89pdfvnlfR3F\nTV5vrleKPU5RhsdJNpqspu/jvlkUQVEZlcwG14P3G4ldTxmYpGEPkohKGhSHTASewi/QBdznlopD\nBmizXTgzGlmZyPlyHbi26XpSxNkOnXPn+ff5bil33SafTY+d6zUWyiP5i7BNX0/iN2nYz1b2IZ+l\n5Fsxlvg8JVMnOCbvF99FfF/Y74B9sn3vMe3+HcCNvgJ8r3kdmPXsta99bXRGKAq9UCgUFgT1Qi8U\nCoUFwdysXMhSGMltt+Wqbja55fJuNpxs8MUXXyxpOmY3LTTMJjHuNVOM/dEf/ZEk6QlPeEJfZ4sY\nWkhceeWVffkFL3iBJOncc8/t6yhKMbuWUtgl6w3O82tf+9qKdqRBREB7ZrdFNpfiJIuBGImPc3ef\nZPu9xskGWBrY21ZUyGQJ4nu472RFXd+yBDHLPJZakO1bdMAzyf30elIU4nEyjANFMl5bxlinJZQj\n53Hf3Cbt8hnX3WIiriFFWBax8bp9KtauXdvX8dy4/WQXLQ3WFhTF2VKEPhrvete7+vJhhx22Yh48\nd2mP01kZ88egyCeJjlPic74jvN8pqqg0WKPRKs1nlaKZZLHCNpOFWrKxTxFT2SdFLi0UhV4oFAoL\ngrtEPHR/zZJ3H7/SVDAlu9OUOYQUpb+qVESRWrcy04oLaZpyPuqooyRNZ6FJlO+LXvSivnzRRRdJ\nmqYgyDX465w8Z1NQIM4jeQlKAzXWiu9tkBNxkCZSoUz4bHt7erkmb96kqGp59yXlb/IaTsGNk2XV\ntwAAIABJREFUiGTv3LJjnx0b26Rim2fNFBrn4eu0ayaFb2qrZd/tdU7x/FNMbmk4y2yHczPlTaX7\nC1/4QknTfhCJS2p5U3qeKbgcMzDxuinn5MErDRRt8vZteVimfedZWu0enoWUH6GlwDRSxqGWp7Kv\nsx2+1xK36Do+4zxXqc8WikIvFAqFBUG90AuFQmFBcJewQzcbRPYziRWSXXYrHroVghRvWJSy3Xbb\n9XVUSlmsQCXImCu77U55D9n1vfbaa6ptaZq1NxIbnRQn0sBqkpWkgujWW2+VNL12ZsPJtpE1d3xu\nhj2g3bTXNu1BS3HtcXK9WvbOs/20Yn67nuNI4oJ0rluiDCvYef7SOJOii+eP91s80krk7X1IoiH+\njvue0t7xtxYF0i3d4QSe+9zn9nUUKXruVOxx7hblcZxJ8cz1tjKU60FRR7rH7afgWVIWQ6YY7a0U\ni7NjZ5tpjaVBjETFtNeeIiZed5miS4p9U0JoK64ZniEF/6KI6zd/8zfLDr1QKBQWGXNTitJkzgqA\npDDjFzd5kfHryi+6Td1o8vbUpz5V0rSn5/r16/uy22Kb/BKbWmGdzdL23nvvvo7hd61UbYWlXS10\nML/S5ABMjaRMP6yn96gpi1NPPXXFfKRB2UlKzdSdNFAZpEbGlI0p5GmiuhKllqgvllNAJF5PlFrL\nzM3nLimr+Vvua8oqxbXx3qU1Wq1+NbgvehkmipPmkz4LTDDMcdpEkeNJZ4l7kMI3p7Xl2BLHNCYd\nGFN2p6w/SUHfevbcZjpfbD8pdPmu4nNojr6lFE2B9/xbcgdcT1P1LfNgoij0QqFQWBDUC71QKBQW\nBHMTuaR4vwyYZJajZYOclGPJDp1ii5NOOknSYHMtSbvvvntfPuuss1a0kxIUJ7tWsrRknTxmimmS\n6CjFeaZSkyyYy4nFl4agXRy7RS0Us6RY8QwSRsWO2U/a5bt9sr7Ja7NlN+37kghqzPY8ZT6SBpZ4\nTCnaimNu8CwmO/QkKuN+JcVhsjlP9swt8YfXPgVVkwbxHxX9bp++EzQK8HmgSC9lLEpiB46NZym1\n04rHbqRgfMlrNGXuYjmJhlr7PqaAd1/Jo5V985lIxgPJhySNnWeBYjOv7VVXXRXHSRSFXigUCguC\neqEXCoXCgmBuIpexpMiJZU5212SHKE445phjpv6VBrtr2oCedtppfXmXXXaRNM3OJ40/tdpmp1Iq\nO2lgyZMoogWzYHSzJ0ubghuR9f/MZz4zNTZp0L6TPeR6eUxk57kOtq2nmOeOsMkpnjXX5o4EaeI4\nE/uaxBsse51aIgTXp7qWW7freS5o+ZBc7pO4KbHuHActc5J/gveL9zDcxU477SRpWhyU+k/+BZwv\nbd/tA8LnjGNKIhu3mdaohZTwfOzc8B6fG56f5BewMcmqk0gl9Z8C77XCXfhdmfICzKIo9EKhUFgQ\nzI1CT4oGIik9k3KNX3R6dVoB6pC50pCxaIsttujrHN5Wkj7+8Y9LmqZ6aGvLgDmz42gpx0wZtSj0\nNHcHWSKFTU7CGWd22223vu6MM87oy1aOXXbZZX2dqQDOIWUFSkmc+Vt6wabgRokqatkB+/6kJB7b\n90RpcfykkHy9xSl4HKRSea421MY5BZxjnzwXHl9S8rWCWvkMkYtKVGriFLhG5kSlIdBWyqbEPjk3\nc3acD0M1e3ytPUpzT/20zs3s3NjXxlD1Y/d4bfg+SOFzk2K71ab7TOGdW74XnieV3S0UhV4oFAoL\ngnqhFwqFwoJgbiIXihMs9Kei1Ncp8kg2pLzO+/fdd19J0xlldt55Z0nTmVY+8pGP9GUncmbWHool\nHGfcbUvSLbfcIqnNeru+JXJxICMGyjr88MMlSe95z3v6OsZYf8Mb3iBpOkk0lVIeE9k6s4qt+NxJ\n1JHEFsmOPClsWW4p+VZzEU/sNMdJsH+LAbjeLreCc3kdGERpQxWx7CcpMCkeIeue2P1k48y18W/5\n7CQX8pShhyIkjtMiOIpPUjgN7qFFehS/8TlMSd/T85HOXyuOvetTprONwVic/LEgZJ5TyjAmDWvX\n8qNIiu8kbkqoeOiFQqFwD0K90AuFQmFBMLd46JtttlnfsdkYsm3W6LZchl0mG0KbX5dpCbLffvtJ\nmtbi2/JFGqxCNt10077upptu6steK7LmTqTMeygCMBuV3MalQeTCeTqq3/bbb9/XOSyBNCS2dtxz\naToZ8Uc/+lFJ0iGHHNLXOQZ2S4SV1pOsZIpHbasiihVSyjTuG61sVrMjHrNwSKm8OL5kHz7Gzrfm\nkWzOvY5jbHJy8W7B7bdSqyURQLLrT32m0BLSsLYMIcDz699SzONxsm9GgLRYhGctxcxvWbTM/o7j\n5FngmNP59Jxb/hpex1Yydtvw0/fC55fnOEW3pMVdsq2niNTiG4qTxqwA161bV/HQC4VCYZExN6Vo\nooboCeUvPrP7pOBG/Lryq+nMO6agJenkk0+WJB177LF9Hb/ozj505ZVX9nUMIuYyKXxToSmjENsn\n1UPKxmPmF9sK0i9+8Yt9Hefu684yJA2265J0wgknSJJ+67d+q68zJ0Jb1uR526Iik9dnUmpyX8di\nmyeKNNlvp2BRRKJIU9YdUk2JOyD1xnJK3mywnzT3pPyXhjVLilR68CZ75RZX4PtJuVoRyzrC46SC\nnYYEpjjJQfqstzgen4vE5bTg3/KeFJAu3TM7ltm6FrfntW8ZCqSY92Nx9lPmpTEjCZd5PhJHM7aG\nUlHohUKhsDCoF3qhUCgsCOYmckn2zmRtLH6hLWuy52QcZyoGzRYyTvmTn/xkSdIVV1zR1zEAll3d\naafOxKxbb721pGkWK6XPS8pEskuck0UgDEfg1HEpkbE0sOtU1lAB+qxnPUvSkHKP91NRRSTFYVrv\npIwke0nFtNcpKe7Y15hCjOs5Zofs8VHU4X1tjSOJCFKgJO6h20oBpohW3HX/lmchBQHbUEWqNJxF\n2oe7fY6DSn3Pk2EeUppB3uO5s58Erkfa9+TT0BK5pFALSfyXwkgkMQrbTDbh0rB2LZ+INM4x23a3\nlcSErZAPfpe1nl2iKPRCoVBYEMyNQk8edslUp2XuZ2qHX34qdnyd99t0j4GEvvCFL/RlZzJim1aU\nSsOXmGZKpmbGTLBI4XCe7v+Tn/xkX3f88cdLkrbddtu+jpyE+2R2ISrSbNbIDCem+qg4TuZvLYoz\nZVEyRZEy/rSQvBjHkt/efvvtfdlKvlYWmkTtJCVe8uRrKRtTwKWxjFkupyxGUlZwem1aXp1JScey\nz2dSFiZqlu2nLFu8n+M0ZZ4UodJwbqiIHQtC5vtboWy9JomjIZIitqXUTN6+KVw2+/Tzk5TVUlag\nJ7PDltJ0tm9pOP80EGmhKPRCoVBYENQLvVAoFBYEcxO5kK00C5c8ulqBimxTTNtNKkjNBvF+e2BS\n6cN7zFqR/aTdtllI3p8CIrWCQBlkK610pdLTHq0MAkaRikEFYVLKUsyTAlSN2YQTKUuN61rBt5Lo\nieyl1yHFO6eiKSXDbokl3Cf3w3ucFKHsM8VV53UiedYm1jplTpKyktnlVhzxMdv5FJgsiZOS4rAl\ndlhNcUiRShJrULmbbOuTkpr7njIFcQ342yReSUr3dCZbYjF7cPId4P6TT0GrzbEE2ukspQxQ9MZl\nom+iKPRCoVBYENQLvVAoFBYEd4kUdLY5t0hEypYFtNDw/RRL2LpDGthBW7ZIAxvENsnSWkRBkUsK\nVES2z6xkaof1ZMHISjoG+xOf+MS+zq77TvY8O2avV8uyxmMeC2qVLA8SW9+q9x7wWhJBtKwMkv9B\nShKd7iGStcRYKrzUThL9EMlSJAX5ao2D95tl53XXJft/lscCNyV7ZvZDCwrbNrfOZ9rDFAQsxRFP\n7vocUwqg1goWmOzQCd/P53BMzJiSnCdRXJo755bWsyVqMzbmrPkdVlYuhUKhcA/C3Ch0fmmtECRl\n7C8gvdFo/21QYXH99df3ZStRxjyy2Ke/qqlOGigoKnhI2Rj0WDVXwTbtCSpJl19+uaTpZNaXXnqp\npOkvO6mAFJI32TgnT7xWONfkvZeujyVKJpKCdSy4lufcsnEeC1ebkNpM/beCPSVqPI1tTPlGJGV6\nouqTnXmrn9UoPSqRUzCppKzm+FqK79S3r7NNnl+3yXEkpSfHkZSziRtMHugpQTXvT4HYiLTHPCvM\nXsRnP92fzlLi/Dk3v2Nuu+22vs7Z02ZRFHqhUCgsCOqFXigUCguCu0RwruRGnUDxi+N7UxHKQFxm\no3iP3cZpz/mYxzymL7stssG09bbIhyzazTffLGlajMJMQ6eccook6WlPe9qKfqQhpjnbtFKVY0+s\neRKpSINIiPHlzcKNBQBqiQoS652S/SaRDK+nWPHJxrmlFHVbYyKNZPNNUHFt1p/iM15PSGPn/Rax\nteaxWtzsltI+2f2znMIJeG4pl8Bs/7Nj4/UkAmNdsh9viY5SgKoU/iGNo5V9yGKPJDpq+UYkw4uk\nNOXYvI70jSB8nf4tDKq1WsLyFLRPGnI7VHCuQqFQuAehXuiFQqGwILhLiFyMFImPIMux1VZbSZIu\nuuiivo5xzG2HThddx3xmBEWKKr7zne9ImrY9p4jAqbmYgs6gjfxb3vKWvmwWjLHJn/KUp/Rls4hr\n1qzp6ywaIpucXO7JspJd8/3JVraVLi6JJVZL4ixlG+UkBuI9rTRvs2PifMnyJuuQJPJJYgX+jufC\n9SkRMseSxE2tOPduK4k/OCbCe5NsuqXxqJRun8+Jx0EREtcmxZfn2JKoLdl8JwuNlmgohRtI4hHC\n68h9Y/8WgSSxFtcj+V60REMpdIDPXzo/bJOu+xSf+Lfsx21xPRgKxOO/8cYb+zpGWiWKQi8UCoUF\nwdwo9PRVS8F8dthhh76OnlJWFFAByaTK/kJSeeE2+cXef//9+7Ip8JZ3n6loKjXTfEiJnXnmmZKk\nD3zgA30dv8S33nqrpOl456ZSSFWRekxKp6RsTHbgrWBnKajVmMdhojKTUqnlFefrY/bEyUNzTNmY\nxtSysU9eskmRxnGYA+SZ5X75t6TUeBY31L57zPs02VjzrDiWNs8kr5tz4xpuqCdqSynvebSSPDuw\nXho7+x6zl2/5KhjJozWhxUGa40p2+TyzDFJmajxl7mr1mTIS8R57iu61116rzkMqCr1QKBQWBvVC\nLxQKhQVB1wqGc2fjoQ99aN+x2RyyKXZtZbo4srS20T744IP7OiZ/NitMdsluubTPJh7/+MdLaisb\n3SdDDNj+lYpSKpp8nQoNsuGeM5UsyV3bik7eQ9bZbKw0iFp4v8uteOdGy6Y8iQPMdrYCfrktjqMl\n8pm93krRleLLEynZcOqHbY4p8dJ117Viaaf48imGdlJSp3ASUlbSJVEH185nlqIhPhPuK8XGZznF\n+2+JR9xmilfO/tO+cj0YYiP5qqQxJbFZEt2w3DprKRSInzPamTP1pdc55SKQciBCP898LySRn8Wz\nknTooYdGR4yi0AuFQmFBMDelKJGoP9eRmqbi0F9FUssM3kVFheGv69Zbb93X8ettiuB/t3fuqndV\nXRSf3yNYSLDQKDGiolh4iRcULOzES+Mr+ABaWWkjPoSFhSIWgiCCWilCFCuJYpDEJCaYNIqv8FVj\nn985GfPM/z/N8dvfGNVm7b32XnutfZnXMfn3ZYjje++9V1VVL7300tKm7FT+cSmJaRz8+1JC0v5J\nU3LVdhy1b5Un75qcnm6/k/6IfVS13dhdGN5E1+o0hY6gykmxWmNKSi6jsHOauutoTNQ+pqxOp/nx\nWXFjc88Fn1k60pw0rf5dGKj2dxW3nJPaXceNv8vAdGGgzkk8hU8elQyty47ePffuefZlJU/OW5cx\nzXYGeCjbnNYIhVBXbZyinWWBiIQeBEGwEuSDHgRBsBIczOQycXFLNadKy+yp69evV9U2/zB5iR13\ntJyVjpSqamMWYR9meX3//fdVVfX6668vbRcvXqyqbdWX49SYXAwzx0nHiyMFcqYQquYcp3McOlOE\niwPmfDj1dyJQ60wl7j52z83xdTHGGjPNJ061d+YPYirkTTiHnMvadMWZCce3PsW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TAAAG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cc9574c128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run -i nt_solutions/inverse_5_inpainting_sparsity/exo5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 0.5.0",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}