{ "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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yAU1BNMk7NOm4WYkmGjfR8hkM9XBTEO9DU6qb/WkmounKzVWULGhy8muZKtZN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\ne1Lv9X7hnKIfhpN2Sku7s0njvOEzZrq8w3HxPqLuybns/ZvmNZ9PHwd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"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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zzjnH+XbrvJLyxbzIsj0fkgbOIolcCRMnToztLNvkSWV89rv/008/ubGVVvL/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VAAAF\nmUlEQVTPP/+82WPZpg534N8br80x/l50KWYWvFNAREREIsKLAiIiIirgRQERERGJSBnlFCBsFay9\n9dZbZn/NNdfEPhZL7Dy6/GXFihXm2L59+1K/DtJ5BEmjk9PmESTlEOgxrUkjZvG4J2kMc5xicgh0\n6Z4u6UuCcU8v3wDjkyFtj712yZgP4+UfzJ492+zvvffeaK3jkWfixT7Hjx8fe2zs2LHu62bljQLG\nY3r8dTH5BhinzSppdHIp2hN7OQQIY8yY/6I/gyH5WF5ZH5blenRJn4gIlsWH5OBkzScLaZ/swe8d\n5uDo70///v0zvQfCn1feuRO8U0BEREQiwosCIiIiKiibjobjxo2LPVEs1znXYSmKnnxYKk2bNjX7\ngwcPxj4WJ8Z99NFH0Xr79u2Zz0F3OMyzu6G+jY7wlnsIXQ6FtwmnT58e+zy8Fam/YyFhhySPP/54\ntMZS0XHjxpn9woULozWWLGHpmVZVVWX2Y8aMSX1++lZqSBjC67johR2QV4Io4pcOrlq1yuxHjBgR\n+z5o7dq10Xro0KGpn1cM/TnXpYIi/u8Xj+kSbSwzxL9b+nOOIQFdtofn531fk+jPvIj/bwuhQ4lZ\np+omefHFF82+X79+JXkfXdb8xRdfmGONGjViR0MiIiJKhxcFREREJCK8KCAiIqKCsilJ/NrX7PXL\nE088EfvYn/70p2avY2wY6wqhS7dC2luimsghQF4OAbZBxTapWfXs2dPsvTyCyspKs1+5cmXsYzGO\nWEzegIZlSnm1as2rZGju3Llmr38O8+bNc5+r26Tefffdqd8Tcwh0vD+pXbLOIwjJTcDX1fH9pNi+\nzhPwWh6L+KWD559v/zTqzyN+VnGqo9d6N2sL5CRenF6XUovYfBhsq63zQCZPnmyOhZTtzZo1K/X5\nhfDabHvTIL1y46Tj+P+J/r8IJ6J6QnII9uzZY/a6vb1uiy9iS3ZFqk+o1NLkEPJOAREREYkILwqI\niIiogBcFREREJCJllFPQpEmT2GP33Xef2T/00EO5vCfGaX/3u9/l8rp5wdhS0thl7Yc//GHep1MN\nxlZ1+2SMbXk5BAhrlbVi2peGPHbatGnRGuvC8RwwJpkV5gLMnz8/Wk+YMMEcCxmfq3+eSXXfXh6B\n1+I1pL/BsmXLzF7nEWD/APyM6Th9Uq8BL1cB8xHwteLeM0kpWiCL+H0AvJwW/J1NnDgxWs+ZM8cc\n83IT8PuMf5P1a+H5YA8Qnc+hW5if6X007NWh8xrwfELg+eX1fcaW8HrsfOvWrc2xQ4cORWvMIcgb\n7xQQERGRiPCigIiIiArKps1xrVq1zInqW4x4+xZvBW7bti1ad+nSJfM5dOrUKVq/88477mP1rSxs\nK4tatWoVrZOmLdavXz9aHz16NNXjkh6LsHWsbi3brVs3c2zLli2pX/dswFt9uhw062Q0kbC2qN77\nhEyEw9u5Gt5SxHCBF2oIodslYyvlYloi51Wqp8NQOBXxzjvvzPy6ce8h4pco4i1t/bcAQx94viE/\nPx3q1CGAM8k6VTQEflaxvLGcYBk7tnTW9PdDpPp3JKv9+/dHayw5rFOnjtnrzxX+P/Df//6XbY6J\niIgoHV4UEBERkYjwooCIiIgKyiangIiIiEqLdwqIiIhIRHhRQERERAW8KCAiIiIR4UUBERERFfCi\ngIiIiESEFwVERERUwIsCIiIiEhFeFBAREVEBLwqIiIhIRHhRQERERAW8KCAiIiIR4UUBERERFfCi\ngIiIiESEFwVERERUwIsCIiIiEhFeFBAREVEBLwqIiIhIRHhRQERERAW8KCAiIiIR4UUBERERFfCi\ngIiIiESEFwVERERUwIsCIiIiEhFeFBAREVEBLwqIiIhIRHhRQERERAW8KCAiIiIR4UUBERERFfCi\ngIiIiERE5P8AzprKX12TLEcAAAAASUVORK5CYII=\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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Ghp0OLElSvdqwAfr0KZ6snD0bDjggd6La0NjYSGNj45u2rVu3ruLvE8WwrnJExGJgSUrp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\ndlXqZ0dND+pvaqBjU0rv3Il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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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9DB52qOmTvfKhvtPeGk/yy6Zpofca76Ypked8272wNGVEapgqH/TuMTIGZU6q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\na5ke3qbhg56OOIXNaariqrb8q4ckemlYDdVz/dT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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": 31, "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))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Choose a value of the regularization parameter." ] }, { "cell_type": "code", "execution_count": 32, "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": 33, "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": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0074218749999999997" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tau = 1.9*np.min(u)\n", "tau" ] }, { "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 [default]", "language": "python", "name": "python3" }, "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 }