{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Inpainting using Sparse Regularization\n", "======================================\n", "\n*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) 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", "$\\newcommand{\\Om}{\\Omega}$\n"], "metadata": {}, "cell_type": "markdown"}, {"source": ["This numerical tour explores the use of\n", "sparse energies to regularize the image inpaiting problem."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 2, "cell_type": "code", "language": "python", "metadata": {}, "input": ["addpath('toolbox_signal')\n", "addpath('toolbox_general')\n", "addpath('solutions/inverse_5_inpainting_sparsity')"]}, {"source": ["Here we consider inpainting of damaged observation without noise."], "metadata": {}, "cell_type": "markdown"}, {"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 focussed 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 used 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."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 128;\n", "name = 'lena';\n", "f0 = load_image(name);\n", "f0 = rescale(crop(f0,n));"]}, {"source": ["Display it."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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E2hFmh6kcmq1sXkCd5qdskcNGqHMsIk+OhkOXUA5BM5ZOxGbZm87UFlKLmnlyzHgy01Sa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\n9gyxAAAAAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(f0, 'Image f_0');"]}, {"source": ["Amount of removed pixels."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["rho = .7;"]}, {"source": ["Then we construct a mask $\\Omega$ made of random pixel locations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Omega = zeros(n,n);\n", "sel = randperm(n^2); \n", "Omega(sel(1:round(rho*n^2))) = 1;"]}, {"source": ["The damaging operator put to zeros the pixel locations $x$ for which $\\Omega(x)=1$\n", "\n", "\n", "*Important:* Scilab users have to create a file |Phi.m| to implement this\n", "function."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["if using_matlab()\n", " Phi = @(f,Omega)f.*(1-Omega);\n", "end"]}, {"source": ["The damaged observations reads $y = \\Phi f_0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["y = Phi(f0,Omega);"]}, {"source": ["Display the observations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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HQCvjmMeYi4/+Rga91wBG4HMCJOyIzH/KT8ym+OSTT6Jo3759xTuOHDkSBYVf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\nmWeiuOyyyyoeipoqsvatTlSkckh5JzPpfOTIkSiOOuqo5O0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"output_type": "display_data"}], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(y, 'Observations y');"]}, {"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.\n", "\n", "\n", "\n", "*Important:* Scilab users have to create a file |SoftThresh.m| to implement this\n", "function."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["if using_matlab()\n", " SoftThresh = @(x,T)x.*max( 0, 1-T./max(abs(x),1e-10) );\n", "end"]}, {"source": ["Display a curve of the 1D soft thresholding."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "T = linspace(-1,1,1000);\n", "plot( T, SoftThresh(T,.5) );\n", "axis('equal');"]}, {"source": ["Note that the function |SoftThresh| can also be applied to vector\n", "(because of Matlab/Scilab vectorialized computation), 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."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Jmax = log2(n)-1;\n", "Jmin = Jmax-3;"]}, {"source": ["Shortcut for $\\Psi$ and $\\Psi^*$ in the orthogonal case.\n", "\n", "\n", "\n", "*Important:* Scilab users have to create files |Psi.m| and |PsiS.m| to implement this\n", "function."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.ti = 0; % use orthogonality.\n", "if using_matlab()\n", " Psi = @(a)perform_wavelet_transf(a, Jmin, -1,options);\n", " PsiS = @(f)perform_wavelet_transf(f, Jmin, +1,options);\n", "end"]}, {"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", "$$ S_T^\\Psi(f) = \\Psi \\circ S_T \\circ \\Psi^*$$\n", "\n", "\n", "\n", "*Important:* Scilab users have to create a file |SoftThreshPsi.m| to implement this\n", "function."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["if using_matlab()\n", " SoftThreshPsi = @(f,T)Psi(SoftThresh(PsiS(f),T));\n", "end"]}, {"source": ["This soft thresholding corresponds to a denoising operator."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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GGFV2IQ46AFfqfgnuEQ0uM+iTufq+DugaHfNVVBJi5UrNl5Nva1hltNK3s0JY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\niopaHQ3kI9fpfnB8DI+OHNJt8KpsrpA0fsChQxo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"output_type": "display_data"}], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot( clamp(SoftThreshPsi(f0,.1)) );"]}, {"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."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lambda = .03;"]}, {"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.\n", "\n", "\n", "\n", "*Important:* Scilab users have to create a file |ProjC.m| to implement this\n", "function."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["if using_matlab()\n", " ProjC = @(f,Omega)Omega.*f + (1-Omega).*y;\n", "end"]}, {"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."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fSpars = y;"]}, {"source": ["First step: gradient descent."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fSpars = ProjC(fSpars,Omega);"]}, {"source": ["Second step: denoise the solution by thresholding."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fSpars = SoftThreshPsi( fSpars, lambda );"]}, {"source": ["__Exercise 1__\n", "\n", "Perform the iterative soft thresholding.\n", "Monitor the decay of the energy $E$ you are minimizing."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display the result."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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15mylU7Sy+mj0WAcHFcJWEbK5rYP2HB4pHIEZY4yZJH6BGWOMmSSWEBdKdb6N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\nwIUyJj9enWyQ4kPKU06WqlgyH8aSvvGpT31Ki+e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MMcZMEr/AjDHGTBK/wIwx\nxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkwSv8CMMcZMEr/AjDHG\nTBK/wIwxxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkwSv8CMMcZM\nEr/AjDHGTBK/wIwxxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkwS\nv8CMMcZMEr/AjDHGTBK/wIwxxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkwSv8CMMcZMEr/AjDHGTBK/\nwIwxxkwSv8CMMcZMEr/AjDHGTBK/wIwxxkyS/w/Af8VHnt+TZwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 23, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(clamp(fSpars));"]}, {"source": ["__Exercise 2__\n", "\n", "Since there is no noise, one should in theory takes $\\lambda\n", "\\rightarrow 0$.\n", "To do this, decay the value of $\\lambda$ through the iterations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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sZVR6PRjnTP8IqhJ2zn0eoJR6GkHNTCkPoQbOBypRofmJZNRaOmFJFlpH0wkM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\nSPULrKqqqlqkihDXqgQ7EvgO5gZbUFwXaZwOPfRQFUCIBH5ZzVQlPpO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"output_type": "display_data"}], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 25, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"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 wavele 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)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 26, "cell_type": "code", "language": "python", "metadata": {}, "input": ["J = Jmax-Jmin+1;\n", "u = [4^(-J) 4.^(-floor(J+2/3:-1/3:1)) ];\n", "U = repmat( reshape(u,[1 1 length(u)]), [n n 1] );"]}, {"source": ["Value of the regularization parameter."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 27, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lambda = .01;"]}, {"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."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 28, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.ti = 1; % use translation invariance\n", "if using_matlab()\n", " Xi = @(a)perform_wavelet_transf(a, Jmin, -1,options);\n", " PsiS = @(f)perform_wavelet_transf(f, Jmin, +1,options);\n", " Psi = @(a)Xi(a./U);\n", "end"]}, {"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", "$$\\tau < \\frac{2}{\\|\\Psi\\Phi \\|} \\leq 2 \\min( u ). $$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 29, "cell_type": "code", "language": "python", "metadata": {}, "input": ["tau = 1.9*min(u);"]}, {"source": ["Initialize the wavelet coefficients with those of the previous reconstruction."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 30, "cell_type": "code", "language": "python", "metadata": {}, "input": ["a = U.*PsiS(fSpars);"]}, {"source": ["Gradient descent."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 31, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fTI = Psi(a); \n", "a = a + tau*PsiS( Phi( y-Phi(fTI,Omega),Omega ) );"]}, {"source": ["Soft threshold."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 32, "cell_type": "code", "language": "python", "metadata": {}, "input": ["a = SoftThresh( a, lambda*tau );"]}, {"source": ["__Exercise 3__\n", "\n", "Perform the iterative soft thresholding. Monitor the decay of the\n", "energy $E$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 33, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "prompt_number": 34, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Perform the reconstruction."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 35, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fTI = Psi(a);"]}, {"source": ["Display the result."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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PnEFHHkXfynXN5AsuOYt94lVsUF7w2VvYhMzAQgghrJK8wEIIIaySSIhbBdEJCUgqDZse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\n4+pT0kKXeXmYw2IxBmtzh1E3BXevSsn2S9P8ifEHHvZEZmAhhBBWSV5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"output_type": "display_data"}], "prompt_number": 36, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(clamp(fTI));"]}, {"source": ["__Exercise 4__\n", "\n", "Perform the iteration with a decaying value of $\\lambda$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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ieIE+8zHR0qa3ILyV3bzUmfQ0weDQvZk6axYoNovWSpPUFuGK24td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\nC5xoMGFuSEW1AAAAAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 37, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "prompt_number": 38, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"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."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 39, "cell_type": "code", "language": "python", "metadata": {}, "input": ["if using_matlab()\n", " HardThresh = @(x,t)x.*(abs(x)>t);\n", "end"]}, {"source": ["Display a curve of the 1-D Hard thresholding."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 40, "cell_type": "code", "language": "python", "metadata": {}, "input": ["t = linspace(-1,1,1000);\n", "plot( t, HardThresh(t,.5) );\n", "axis('equal');"]}, {"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."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 41, "cell_type": "code", "language": "python", "metadata": {}, "input": ["niter = 500;"]}, {"source": ["List of thresholds. One must start by a large enough initial threshold."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 42, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lambda_list = linspace(1,0,niter);"]}, {"source": ["Initialization."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 43, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fHard = y;"]}, {"source": ["Gradient descent."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 44, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fHard = ProjC(fHard,Omega);"]}, {"source": ["Hard threshold (here $\\lambda=\\lambda_0$) is used)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 45, "cell_type": "code", "language": "python", "metadata": {}, "input": ["fHard = Xi( HardThresh( PsiS(fHard), tau*lambda_list(1) ) );"]}, {"source": ["__Exercise 5__\n", "\n", "Perform the iteration with a decaying value of $\\lambda$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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lPhNdZ6n0R6xt/lurhHg6aoGVUkrZJH2BlVJK2SSVEA8K4pt5JaUXljmPITGh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\n3e/q8NVXX1WBHcUknqQ4CTqDqpM/++9MwmQVZhmSsuWZm8D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"output_type": "display_data"}], "prompt_number": 46, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo5()"]}, {"collapsed": false, "outputs": [], "prompt_number": 47, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}], "metadata": {}}], "nbformat": 3, "metadata": {"kernelspec": {"name": "matlab_kernel", "language": "matlab", "display_name": "Matlab"}, "language_info": {"mimetype": "text/x-matlab", "name": "matlab", "file_extension": ".m", "help_links": [{"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md", "text": "MetaKernel Magics"}]}}}