{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Primal-Dual Proximal Splitting\n", "==============================\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" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This tour explores a primal-dual proximal splitting algorithm,\n", "with application to imaging problems." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "library(imager)\n", "library(pracma)\n", "library(plot3D)\n", "\n", "options(warn=-1) # turns off warnings, to turn on: \"options(warn=0)\"\n", "\n", "# Importing the libraries\n", "for (f in list.files(path=\"nt_toolbox/toolbox_general/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_general/\", f, sep=\"\"))\n", "}\n", "for (f in list.files(path=\"nt_toolbox/toolbox_signal/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_signal/\", f, sep=\"\"))\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Convex Optimization with a Primal-Dual Scheme\n", "---------------------------------------------\n", "In this tour we use the\n", "primal-dual algorithm detailed in:\n", "\n", "\n", "Antonin Chambolle and Thomas Pock\n", "_A First-order primal-dual algorithm for convex problems with application to imaging,_\n", "Journal of Mathematical Imaging and Vision,\n", "Volume 40, Number 1 (2011), 120-145\n", "\n", "\n", "One should note that there exist many other primal-dual schemes.\n", "\n", "\n", "We consider general optimization problems of the form\n", "$$ \\umin{f} F(K(f)) + G(f) $$\n", "where $F$ and $G$ are convex functions and $K : f \\mapsto K(f)$\n", "is a linear operator.\n", "\n", "\n", "For the primal-dual algorithm to be applicable, one should be able to\n", "compute the proximal mapping of $F$ and $G$, defined as:\n", "$$ \\text{Prox}_{\\gamma F}(x) = \\uargmin{y} \\frac{1}{2}\\norm{x-y}^2 + \\ga F(y) $$\n", "(the same definition applies also for $G$).\n", "\n", "\n", "The algorithm reads:\n", "$$ g_{k+1} = \\text{Prox}_{\\sigma F^*}( g_k + \\sigma K(\\tilde f_k)) $$\n", "$$ f_{k+1} = \\text{Prox}_{\\tau G}( f_k-\\tau K^*(g_k) ) $$\n", "$$ \\tilde f_{k+1} = f_{k+1} + \\theta (f_{k+1} - f_k) $$\n", "\n", "\n", "The dual functional is defined as\n", "$$ F^*(y) = \\umax{x} \\dotp{x}{y}-F(x). $$\n", "Note that being able to compute the proximal mapping of $F$ is\n", "equivalent to being able to compute the proximal mapping of $F^*$,\n", "thanks to Moreau's identity:\n", "$$ x = \\text{Prox}_{\\tau F^*}(x) + \\tau \\text{Prox}_{F/\\tau}(x/\\tau) $$\n", "\n", "\n", "It can be shown that in the case $\\theta=1$, if\n", "$\\sigma \\tau \\norm{K}^2<1$, then $f_k$ converges to a minimizer of\n", "the original minimization of $F(K(f)) + G(f)$.\n", "\n", "\n", "More general primal-dual schemes have been developped, see for instance\n", "\n", "\n", "L. Condat,\n", "_A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms,_\n", "J. Optimization Theory and Applications, 2013, in press.\n", "\n", "\n", "Inpainting Problem\n", "------------------\n", "We consider a linear imaging operator $\\Phi : f \\mapsto \\Phi(f)$\n", "that maps high resolution images to low dimensional observations.\n", "Here we consider a pixel masking operator, that is diagonal over the\n", "spacial domain.\n", "\n", "\n", "Load an image." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "name = \"nt_toolbox/data/lena.png\"\n", "n = 256\n", "f0 = load_image(name, n)\n", "f0 = rescale(crop(f0, n / 2))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display it." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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xW0tBLqNPswXuKryWn1E9Vx/pwKNsgsMJu9Ml6gEjx0HkJERQ1mkVhsCiUeKGpQ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"text/plain": [ "Plot with title \"\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=5, repr.plot.height=5)\n", "f0 = f0[,]\n", "imageplot(f0)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We consider here the inpainting problem. This simply corresponds to a\n", "masking operator.\n", "\n", "\n", "Load a random mask $\\La$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "rho = .8\n", "Lambda = rand(n / 2, n / 2) > rho" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Masking operator $ \\Phi $." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Phi = function(f){f * Lambda}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the observations $y=\\Phi f_0$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "y = Phi(f0)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display it." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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haoglFtOU855RQL4vQ+jdg4n4lSmkonqt+s0p6SY0J17ty5FiRqOqqq0UzTl1SB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"text/plain": [ "Plot with title \"\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imageplot(y)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Total Variation Regularization under Constraints\n", "------------------------------------------------\n", "We want to solve the noiseless inverse problem $y=\\Phi f$ using a total\n", "variation regularization:\n", "$$ \\umin{ y=\\Phi f } \\norm{\\nabla f}_1 $$\n", "\n", "\n", "This can be recasted as the minimization of $F(K(f)) + G(f)$ by\n", "introducing\n", "$$ G(f)=i_H(f), \\quad F(u)=\\norm{u}_1 \\qandq K=\\nabla, $$\n", "where $H = \\enscond{x}{\\Phi(x)=y}$ is an affine space, and $i_H$ is the indicator\n", "function\n", "$$ i_H(x) = \\choice{ 0 \\qifq x \\in H, \\\\ +\\infty \\qifq x \\notin H. } $$\n", "\n", "\n", "Shorcut for the operators." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "K = function(f){grad_3(f)}\n", "KS = function(u){-div_2(u)}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Shortcut for the TV norm." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Amplitude = function(u){sqrt(u[,,1]^2 + u[,,2]^2)}\n", "F = function(u){sum(sum(Amplitude(u)))}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The proximal operator of the vectorial $\\ell^1$ norm reads\n", "$$ \\text{Prox}_{\\lambda F}(u) = \\max\\pa{0,1-\\frac{\\la}{\\norm{u_k}}} u_k $$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ProxF = function(u,lambda)\n", " {\n", " return(pmax(0,1 - lambda / array(c(Amplitude(u), Amplitude(u)), dim=c(dim(u)[1],dim(u)[2],2))) * u)\n", " }" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the thresholding on the vertical component of the vector." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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wCuK6Jo88CBSqnbbrst7k/QUlERtk733XffiBEj0un0pEmTKioqunXrFneiVqKw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\n5XLOQMK58zz3hDO4ShV6Cm6MR3feeefR8dZaM52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KVUzCY4wf0mazvbTbxk3EMZ/N1//mwdP9SQZ+0+QAACAASURBVNbsMIsH2yKZGPGC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\nAElFTkSuQmCC", "text/plain": [ "Plot with title \"\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = -linspace(-2,2, 201)\n", "Y = meshgrid(t,t)$Y\n", "X = meshgrid(t,t)$X\n", "U = array(c(X,Y), dim=c(201, 201, 2))\n", "V = ProxF(U,1.)\n", "\n", "persp3D(X, Y, V[,,1], theta=30, phi=50, ticktype=\"detailed\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "For any 1-homogeneous convex\n", "functional, the dual function is the indicator of a convex set. For\n", "the $\\ell^1$ norm, it is the indicator of the $\\ell^\\infty$ ball\n", "$$ F^* = i_{\\norm{\\cdot}_\\infty \\leq 1}\n", " \\qwhereq \\norm{u}_\\infty = \\umax{i} \\norm{u_i}. $$\n", "\n", "\n", "The proximal operator of the dual function is hence a projector (and it\n", "does not depend on $\\sigma$ )\n", "$$ \\text{Prox}_{\\sigma F^*}(u) = \\text{Proj}_{\\norm{\\cdot}_\\infty \\leq 1}(u). $$\n", "\n", "\n", "A simple way to compute the proximal operator of the dual function $F^*$, we\n", "make use of Moreau's identity:\n", " $$ x = \\text{Prox}_{\\tau F^*}(x) + \\tau \\text{Prox}_{F/\\tau}(x/\\tau) $$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ProxFS = function(y,sigma){y - sigma * ProxF(y / sigma, 1. / sigma)}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display this dual proximal on the vertical component of the vector." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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zU3Nz/yyCP//u///s1vfvPPHvX6669774cOHfperfIchL3W/ffff8cddzQ2Ni5c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8/Pyspq7ruYNm2acfVdNE8Qnjx58v79+76+vlKp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\ngg==", "text/plain": [ "Plot with title \"\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "V = ProxFS(U,1)\n", "persp3D(X, Y, V[,,1], theta=20, phi=50, ticktype=\"detailed\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The proximal operator of $G = i_H$ is the projector on $H$. In our\n", "case, since $\\Phi$ is a diagonal so that the projection is simple to\n", "compute\n", "$$ \\text{Prox}_{\\tau G}(f) = \\text{Proj}_{H}(f) = f + \\Phi(y - \\Phi(f)) $$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ProxG = function(f,tau){f + Phi(y - Phi(f))}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Primal-dual Total Variation Regularization Algorithm\n", "----------------------------------------------------\n", "Now we can apply the primal dual scheme to the TV regularization problem.\n", "\n", "\n", "We set parameters for the algorithm.\n", "Note that in our case, $L=\\norm{K}^2=8$.\n", "One should has $L \\sigma \\tau < 1$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "L = 8\n", "sigma = 10\n", "tau = .9/(L * sigma)\n", "theta = 1" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Initialization, here |f| stands for the current iterate $f_k$,\n", "|g| for $g_k$ and |f1| for $\\tilde f_k$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "f = y\n", "g = K(y) * 0\n", "f1 = f" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Example of one iterations." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "fold = f\n", "g = ProxFS(g + sigma * K(f1), sigma)\n", "f = ProxG(f - tau * KS(g), tau)\n", "f1 = f + theta * (f - fold)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Implement the primal-dual algorithm.\n", "Monitor the evolution of the TV energy $F(K(f_k))$\n", "during the iterations.\n", "Note that one always has $ f_k \\in H $ so that the iterates\n", "satisfies the constraints." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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fzxx0VFReHh4bNmzfrnn39yc3P/+OOPyZMnP//88/fv3xedVB5atsQXXyApCWPG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\ncDLNZs5EcTLNx/thbm5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"text/plain": [ "Plot with title \"Decay of the Energy\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/optim_5_primal_dual/exo1.R\")" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert code here" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display inpainted image." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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YVOXnTRRRFx1llnRWd9ZDjoQrxJuR2crxGQoEY1TQ06dvi1woo1hudQNT2fOOX+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\nGSkB9YYOUIUxXAgilwlUytVrUgZJw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"text/plain": [ "Plot with title \"\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imageplot(f)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Use the primal dual scheme to perform regularization in the presence of\n", "noise\n", "$$ \\umin{\\norm{y-\\Phi(f)} \\leq \\epsilon} \\norm{\\nabla f}_1. $$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "source(\"nt_solutions/optim_5_primal_dual/exo2.R\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Solution not available" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Inpainting Large Missing Regions\n", "--------------------------------\n", "It is possible to consider a more challening problem of inpainting large\n", "missing regions.\n", "\n", "\n", "To emphasis the effect of the TV functional, we use a simple geometric\n", "image." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n = 64\n", "radius = 0.6\n", "t = linspace(-1,1,n)\n", "Y = meshgrid(t,t)$Y\n", "X = meshgrid(t,t)$X\n", "f0 = (pmax(abs(X),abs(Y) ) < radius) * 1.0" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We remove the central part of the image." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "a = 4\n", "Lambda = matrix(1, n, n)\n", "Lambda[((n/2) - a):((n/2) + a),] = 0" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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9Z6Fhwle3AQGLB7UAirsmbNmqVLl9Z6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\nCE0IAQhNCAEI7T88yIgzkeJxzQAAAABJRU5ErkJggg==", "text/plain": [ "Plot with title \"Damaged\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imageplot(f0, 'Original', c(1,2,1))\n", "imageplot(Phi(f0), 'Damaged', c(1,2,2))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "Display the evolution of the inpainting process." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Plot with title \"\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/optim_5_primal_dual/exo3.R\")" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert code here" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.4.2" } }, "nbformat": 4, "nbformat_minor": 0 }