{ "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": [], "source": [ "from __future__ import division\n", "\n", "import numpy as np\n", "import scipy as scp\n", "import pylab as pyl\n", "import matplotlib.pyplot as plt\n", "\n", "from nt_toolbox.general import *\n", "from nt_toolbox.signal import *\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "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": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n = 128\n", "f0 = load_image(\"nt_toolbox/data/lena.bmp\")\n", "f0 = rescale(f0[256-n//2:256+n//2,256-n//2:256+n//2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display it." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DjWBe6IPBYLARvCCcolFTqEpGZbGirjzPa4zEiSaEOCw6Iq2oY6lcdPh7QFNG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\n3bOvvEnzPJdjGy/b6jIGLZPUnErm5DPHHe9v2adGQcz7r0nYa9ml5lz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TGgDeh6pa2uTY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\nv1YmGdtbzjxCAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (6,6))\n", "imageplot(f0, 'Image f_0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Amount of removed pixels." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rho = .7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we construct a mask $\\Omega$ made of random pixel locations." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from numpy import random\n", "\n", "Omega = np.zeros([n, n])\n", "sel = random.permutation(n**2)\n", "np.ravel(Omega)[sel[np.arange(int(rho*n**2))]] = 1" ] }, { "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": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Phi = lambda f, Omega: f*(1-Omega)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The damaged observations reads $y = \\Phi f_0$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "y = Phi(f0, Omega)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the observations." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0KqOJlGV/mxoqnEILdiy06Q7Sinx196DmXanOyDzUrtqysbaKjbHz4GdS5fPQ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\nK0UVv3Og2RlsRcuxyTXWaw4bNqztvla0nEIfo7sX7SAtitV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hYtOLisLfov6dKPTMV29z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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.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": 9, "metadata": { "collapsed": false }, "outputs": [], "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)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display a curve of the 1D soft thresholding." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1, 1, 1000)\n", "\n", "plt.figure(figsize=(7,5))\n", "plt.plot(x, SoftThresh(x,.5))\n", "plt.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": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Jmax = np.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": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from nt_toolbox.perform_wavelet_transf import *\n", "\n", "Psi = lambda a: perform_wavelet_transf(a, Jmin, -1, ti=0)\n", "PsiS = lambda f: perform_wavelet_transf(f, Jmin, +1, ti=0)" ] }, { "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": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "SoftThreshPsi = lambda 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": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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adh1fnKfB46ica9XBumTDZlnemr25BGch0cp1wVnHqPG0jknLVwFKWuVPPvnk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\n2NJ8Odx8WSJc5Mt6Xvf6uxALPYQQdsLZLHQ2f1apXFrgSkd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "imageplot(clamp(SoftThreshPsi(f0, 0.1)))" ] }, { "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": 15, "metadata": { "collapsed": false }, "outputs": [], "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": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ProjC = lambda 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": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fSpars = y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First step: gradient descent." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fSpars = ProjC(fSpars, Omega)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Second step: denoise the solution by thresholding." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fSpars = SoftThreshPsi(fSpars, lambd)" ] }, { "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": [ "" ] }, "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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\n6eMf//jQxzl9+9vflrT86+uxklQuLSRzSuj83Nclf/pewqQ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"text/plain": [ "" ] }, "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": [ "" ] }, "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": 25, "metadata": { "collapsed": false }, "outputs": [], "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))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Choose a value of the regularization parameter." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "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": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Xi = lambda a: perform_wavelet_transf(a, Jmin, -1, ti=1)\n", "PsiS = lambda f: perform_wavelet_transf(f, Jmin, + 1, ti=1)\n", "Psi = lambda 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": 28, "metadata": { "collapsed": false }, "outputs": [], "source": [ "tau = 1.9*np.min(u)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialize the wavelet coefficients with those of the previous reconstruction." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a = U*PsiS(fSpars)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gradient descent." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [], "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": { "image/png": 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"text/plain": [ "" ] }, "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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\nWeAVFW1FyUs42uOqmpN7zsrpyXeUtOdsXceKbleFzadI/y2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MV/Oo9iCjkXB1HlzgBN8X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\nQmCC\n", "text/plain": [ "" ] }, "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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"text/plain": [ "" ] }, "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": 38, "metadata": { "collapsed": false }, "outputs": [], "source": [ "HardThresh = lambda 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": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1, 1, 1000)\n", "\n", "plt.figure(figsize=(7,5))\n", "plt.plot(x, HardThresh(x, .5))\n", "plt.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": 40, "metadata": { "collapsed": false }, "outputs": [], "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": 41, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lambda_list = np.linspace(1, 0, niter)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialization." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fHard = y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gradient descent." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fHard = ProjC(fHard, Omega)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hard threshold (here $\\lambda=\\lambda_0$) is used)." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fHard = Xi(HardThresh(PsiS(fHard), tau*lambda_list[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": { "image/png": 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82+TJxjFxbvQE9H3JHp5t0tvSganIjpOdt8iFIgQr1Ngm45RbYdcKDOV5cN+8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TAAAG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\n", "text/plain": [ "" ] }, "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": "Python [Root]", "language": "python", "name": "Python [Root]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }