{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Forward-Backward Splitting\n", "===================================\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", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{\\arg\\min}\\;}$\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": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "using PyPlot" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This numerical tour presents the Forward-Backward (FB) algorithm to\n", "minimize the sum of a smooth and a simple function. It shows an\n", "application to sparse deconvolution." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Forward-Backward Algorithm\n", "--------------------------\n", "We consider the problem of minimizing the sum of two functions\n", "$$ E^\\star = \\umin{x \\in \\RR^N} E(x) = f(x) + g(x). $$\n", "\n", "So, we want to find a vector $x^\\star$ solution to the problem, i.e. a minimizer of $E=f+g$.\n", "\n", "\n", "We assume that $f$ is a $C^1$ function with $\\beta$-Lipschitz gradient.\n", "\n", "\n", "\n", "We also assume that $g$ is \"simple\", in the sense that one can compute exactly and quickly its proximity operator, which is defined as\n", "$$ \\text{prox}_{\\ga g}(x) = \\uargmin{y \\in \\RR^N} \\frac{1}{2}\\norm{x-y}^2 + \\ga g(y). $$\n", "for any $\\ga > 0$.\n", "\n", "\n", "The forward-backward algorithm reads, after initializing $x^{(0)} \\in \\RR^N$,\n", "$$ x^{(k+1)} = \\text{prox}_{\\ga g}\\pa{ x^{(k)} - \\ga \\nabla f( x^{(k)} ) }. $$\n", "\n", "\n", "If $0 < \\ga < 2/\\beta$, then this scheme converges to a minimizer of\n", "$f+g$.\n", "\n", "Sparse Regularization of Inverse Problems\n", "-----------------------------------------\n", "We consider a linear inverse problem\n", "$$ y = A x^\\sharp + w \\in \\RR^P$$\n", "where $x^\\sharp \\in \\RR^N$ is the (unknown) signal to recover, $w \\in\n", "\\RR^P$ is a noise vector, and $A \\in \\RR^{P \\times N}$ models the\n", "acquisition device.\n", "\n", "\n", "To recover an estimate of the signal $x^\\sharp$, we consider basis\n", "pursuit denoising, which makes use of the $\\ell^1$ norm as sparsity\n", "enforcing penalty:\n", "$$ \\umin{x \\in \\RR^N} \\frac{1}{2} \\norm{A x-y}^2 + \\la \\norm{x}_1, $$\n", "where the $\\ell^1$ norm is defined as\n", "$$ \\norm{x}_1 = \\sum_i \\abs{x_i}. $$\n", "\n", "\n", "The parameter $\\la$ should be set in accordance to the noise level\n", "$\\norm{w}$.\n", "\n", "\n", "This minimization problem can be cast in the form of minimizing $f+g$\n", "where\n", "$$ f(x) = \\frac{1}{2} \\norm{Ax-y}^2\n", "\\qandq g(x) = \\la \\norm{x}_1. $$\n", "\n", "\n", "$f$ is smooth; we have\n", "$$ \\nabla f(x) = A^* (A x - y), $$\n", "which is $\\beta$-Lipschitz continuous, with\n", "$$ \\beta = \\norm{ A^* A }. $$\n", "\n", "\n", "The $\\ell^1$-norm is \"simple\", because its proximal operator is soft\n", "thresholding:\n", "$$ \\big(\\text{prox}_{\\ga g}(x)\\big)_n = \\max\\pa{ 0, 1 - \\frac{\\la \\ga}{\\abs{x_n}} } x_n. $$\n", "\n", "Signal Deconvolution on Synthetic Sparse Data\n", "-----------------------------------------------------\n", "A simple linearized model of seismic acquisition considers a linear filtering\n", "operator (convolution):\n", "$$ A x = h \\ast x $$\n", "\n", "The filter $h$ is called the impulse response, or the poind spread function, of the acquisition process $x\\mapsto Ax$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1024" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N = 1024" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the width of the filter $h$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = 5" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define $h$ as the second derivative of a\n", "Gaussian." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "t = -N/2 : N/2 - 1\n", "h = (1-t.^2./s^2).*exp(-(t.^2)./(2*s^2));\n", "h = h - mean(h);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the operator $A$. For simplicity, here periodic boundary conditions are used, so that the convolution is efficiently implemented as a product in Fourier domain." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#1) (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h_tf = fft(fftshift(h))\n", "opA = u -> real(ifft(fft(u) .* h_tf))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We display the filter $h$ and its spectrum (amplitude of its Fourier transform)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(-100,100)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(t, h)\n", "xlim(-100, 100)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{Any,1}:\n", " PyObject " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(t, fftshift(abs(h_tf)))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We generate a synthetic sparse signal $x^\\sharp$, with only a small number of nonzero\n", "coefficients." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# random.seed(80) # we set the seed of the random number generator for reproducibility purpose.\n", "srand(80);" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "10-element Array{Float64,1}:\n", " 0.994844\n", " 0.852964\n", " 0.744861\n", " 0.893669\n", " -0.848174\n", " 0.766909\n", " 0.967159\n", " -0.876895\n", " -0.701886\n", " 0.943956" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = Int(round(N*.01)) # number of nonzero elements of xsharp\n", "sel = randperm(N)\n", "sel = sel[1 : s] # indices of the nonzero elements of xsharp\n", "xsharp = zeros(N)\n", "xsharp[sel] = sign(randn(s)) .* (1 - 0.3*rand(s))\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "0.2" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "noiselevel = 0.2" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the measurements $y=A x^\\sharp + w$ where $w$ is a realization\n", "of white Gaussian noise." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "y = opA(xsharp) + noiselevel * randn(N);" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject " ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig = figure(figsize = (14, 5))\n", "stem(sel, xsharp[sel])\n", "xlim(0, N - 1)\n", "title(L\"signal $x^\\sharp$\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig = figure(figsize = (14, 5))\n", "plot(0 : N - 1, y)\n", "xlim(0, N - 1)\n", "title(L\"signal $y$\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Deconvolution\n", "---------------------------\n", "We now implement the foward-backward algorithm to recover an estimate of the sparse signal\n", "\n", "\n", "We define the regularization parameter $\\la$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Lambda = 3" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the proximity operator of $\\ga g$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#3) (generic function with 1 method)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prox_gamma_g = (x, gamma, Lambda) -> x - x./max(abs(x)./(Lambda.*gamma), 1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the gradient operator of $f$. Note that $A^*=A$ because the filter $h$ is symmetric." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

\n", " \n", "__Exercise: write the code of the function grad_f.__

" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "ename": "LoadError", "evalue": "syntax: incomplete: premature end of input", "output_type": "error", "traceback": [ "syntax: incomplete: premature end of input", "" ] } ], "source": [ "grad_f = x -> # put your code here" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the Lipschitz constant $\\beta$ of $\\nabla f$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "85.03218404550671" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta = maximum(abs(fft(h)))^2\n", "beta" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the stepsize $\\ga$, which must be smaller than $2/\\beta$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "0.0223444807554652" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gamma = 1.9 / beta" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We compute the solution of $\\ell_1$ deconvolution (basis pursuit denoising).\n", "We keep track of the energy $E_k=f(x^{(k)})+g(x^{(k)})$." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

\n", " \n", "__Exercise: write the code of the forward-backward iteration.__

" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1024-element Array{Float64,1}:\n", " 0.0421011\n", " 0.0565931\n", " 0.0214569\n", " 0.342992 \n", " -0.0400405\n", " 0.224612 \n", " -0.0247864\n", " -0.216949 \n", " 0.0122498\n", " 0.411123 \n", " 0.372003 \n", " 0.288515 \n", " 0.244665 \n", " â‹® \n", " 0.410244 \n", " -0.219421 \n", " -0.0406528\n", " -0.260468 \n", " 0.0840309\n", " -0.209339 \n", " 0.184836 \n", " 0.0446881\n", " 0.396981 \n", " 0.147446 \n", " -0.280515 \n", " -0.381551 " ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nbiter = 2000\n", "x = y\n", "En_array = zeros(nbiter + 1)\n", "\n", "En_array[1] = vecnorm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1))\n", "for iter in 1 : nbiter # iter goes from 1 to nbiter\n", " # put your code here\n", " En_array[iter + 1] = vecnorm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1))\n", "end\n", "x_restored = x" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We display the result." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject " ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, (subfig1, subfig2) = subplots(1, 2, figsize = (16, 7)) # one figure with two horizontal subfigures\n", "subfig1[:stem](xsharp)\n", "subfig2[:stem](x_restored)\n", "subfig1[:set_title](L\"$x^\\sharp$\")\n", "subfig2[:set_title](L\"$x_\\mathrm{restored}$\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We plot the relative error $(E_k-E^\\star)/(E_0-E^\\star)$ in log-scale with respect to $k$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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AasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrORY71dXVmj59ujwejzIyMjRr1iydOnWqxWuMMVq+fLn69eun9PR0BYNBffDBBwn3OX/+fF1zzTVKT0/XgAED9MgjjygajTq1DQAA0MU5FjvTp0/X+++/r127dunll1/W66+/rjlz5rR4zZo1a7RhwwZt2rRJ5eXluvLKK5WXl6cvvvhCknTs2DEdO3ZMa9eu1YEDB1RUVKSSkhLNmjXLqW0AAIAuzmWMMW19p4cOHdKwYcP0zjvvaPTo0ZKkkpIS3Xnnnfr000+VmZnZ5BpjjDIzM7V48WI9+uijkqRoNCqfz6eioiJNnTq12cd66aWX9NOf/lR1dXVKSUlp1fpisZi8Xq+i0ag8Hs9l7hIAALSny/377cgzO6FQSBkZGfHQkaRgMKikpCSVl5c3e01lZaXC4bCCwWB8zOv1KicnR6FQ6KKPdWHDLYVOfX29YrFYwg0AAHQPjsROOBxW3759E8ZSUlLUq1cvhcPhi14jST6fL2Hc5/Nd9JqTJ0/qySef/MaXx1atWiWv1xu/BQKB1m4FAAB0cZcUO/n5+XK5XC3eDh8+7NRaE8RiMU2YMEHDhg3TypUrW5y7bNkyRaPR+K2qqqpd1ggAADpe697k8v8tXrxYM2bMaHHOoEGD5Pf7deLEiYTx8+fPq7q6Wn6/v9nrLoxHIhH169cvPh6JRJSdnZ0wt7a2VuPHj1ePHj20bds2XXHFFS2uye12y+12tzgHAADY6ZJip0+fPurTp883zsvNzVVNTY327t2rUaNGSZJ2796txsZG5eTkNHtNVlaW/H6/SktL43ETi8VUXl6uuXPnxufFYjHl5eXJ7XZrx44dSktLu5QtAACAbsaR9+xce+21Gj9+vB566CHt2bNHb731lubNm6epU6cmfBJr6NCh2rZtmyTJ5XJpwYIF+vWvf60dO3Zo//79uv/++5WZmalJkyZJ+jJ0br/9dtXV1enZZ59VLBZTOBxWOBxWQ0ODE1sBAABd3CU9s3MpXnjhBc2bN0+33XabkpKSNHnyZG3YsCFhzpEjRxK+EHDJkiWqq6vTnDlzVFNTo5tvvlklJSXxZ2/27dsX/zTX4MGDE+6rsrJSAwcOdGo7AACgi3Lke3Y6O75nBwCArqdTfc8OAABAZ0HsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALCaY7FTXV2t6dOny+PxKCMjQ7NmzdKpU6davMYYo+XLl6tfv35KT09XMBjUBx98cNG5d9xxh1wul7Zv3+7EFgAAgAUci53p06fr/fff165du/Tyyy/r9ddf15w5c1q8Zs2aNdqwYYM2bdqk8vJyXXnllcrLy9MXX3zRZO66devkcrmcWj4AALCEyxhj2vpODx06pGHDhumdd97R6NGjJUklJSW688479emnnyozM7PJNcYYZWZmavHixXr00UclSdFoVD6fT0VFRZo6dWp8bkVFhe666y69++676tevn7Zt26ZJkya1en2xWExer1fRaFQej+d/3C0AAGgPl/v325FndkKhkDIyMuKhI0nBYFBJSUkqLy9v9prKykqFw2EFg8H4mNfrVU5OjkKhUHzs9OnTuvfee1VQUCC/39+q9dTX1ysWiyXcAABA9+BI7ITDYfXt2zdhLCUlRb169VI4HL7oNZLk8/kSxn0+X8I1Cxcu1NixYzVx4sRWr2fVqlXyer3xWyAQaPW1AACga7uk2MnPz5fL5WrxdvjwYafWqh07dmj37t1at27dJV23bNkyRaPR+K2qqsqhFQIAgM4m5VImL168WDNmzGhxzqBBg+T3+3XixImE8fPnz6u6uvqiLz1dGI9EIurXr198PBKJKDs7W5K0e/duffTRR8rIyEi4dvLkyRo3bpzKysqavW+32y23293iugEAgJ0uKXb69OmjPn36fOO83Nxc1dTUaO/evRo1apSkL0OlsbFROTk5zV6TlZUlv9+v0tLSeNzEYjGVl5dr7ty5kr58Zmn27NkJ1w0fPly///3vdffdd1/KVgAAQDdxSbHTWtdee63Gjx+vhx56SJs2bdK5c+c0b948TZ06NeGTWEOHDtWqVav0wx/+UC6XSwsWLNCvf/1rDRkyRFlZWXr88ceVmZkZ/6SV3+9v9pmhAQMGKCsry4mtAACALs6R2JGkF154QfPmzdNtt92mpKQkTZ48WRs2bEiYc+TIEUWj0fjPS5YsUV1dnebMmaOamhrdfPPNKikpUVpamlPLBAAAlnPke3Y6O75nBwCArqdTfc8OAABAZ0HsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrETsAAMBqxA4AALAasQMAAKxG7AAAAKsROwAAwGrEDgAAsBqxAwAArEbsAAAAqxE7AADAasQOAACwGrEDAACsRuwAAACrpXT0AjqCMUaSFIvFOnglAACgtS783b7wd7y1umXs1NbWSpICgUAHrwQAAFyq2tpaeb3eVs93mUvNIws0Njbq2LFj6tGjh1wuV0cvp8PFYjEFAgFVVVXJ4/F09HKsxTm3D865/XDW7YNz/i9jjGpra5WZmamkpNa/E6dbPrOTlJSk/v37d/QyOh2Px9Pt/4fUHjjn9sE5tx/Oun1wzl+6lGd0LuANygAAwGrEDgAAsFryypUrV3b0ItDxkpOT9f3vf18pKd3ylc12wzm3D865/XDW7YNz/t90yzcoAwCA7oOXsQAAgNWIHQAAYDViBwAAWI3YAQAAViN2AACA1YidbqC6ulrTp0+Xx+NRRkaGZs2apVOnTrV4jTFGy5cvV79+/ZSenq5gMKgPPvjgonPvuOMOuVwubd++3YktdAlOnHN1dbXmz5+va665Runp6RowYIAeeeQRRaNRp7fTqRQUFGjgwIFKS0tTTk6O9uzZ0+L8srIyjRw5Um63W4MHD1ZRUVGTOS+99JKGDh2qtLQ0DR8+XK+88opDq+862vqcCwsLNW7cOPXs2VM9e/ZUMBj8xvvsDpz493zBli1b5HK5NGnSpDZedRdnYL3x48ebESNGmLffftu88cYbZvDgwWbatGktXrN69Wrj9XrN9u3bzb/+9S9zzz33mKysLHPmzJkmc3/3u9+ZO+64w0gy27Ztc2obnZ4T57x//37zox/9yOzYscN8+OGHprS01AwZMsRMnjy5PbbUKWzZssWkpqaa5557zrz//vvmoYceMhkZGSYSiTQ7/+jRo+Zb3/qWWbRokTl48KB5+umnTXJysikpKYnPeeutt0xycrJZs2aNOXjwoHnsscfMFVdcYfbv399e2+p0nDjne++91xQUFJj33nvPHDp0yMyYMcN4vV7z6aeftte2Oh0nzvmCyspKc9VVV5lx48aZiRMnOr2VLoXYsdzBgweNJPPOO+/Ex/7xj38Yl8tlPvvss2avaWxsNH6/3/zmN7+Jj9XU1Bi3223+8pe/JMx97733zFVXXWWOHz/erWPH6XP+qq1bt5rU1FRz7ty5tttAJzZmzBjz85//PP5zQ0ODyczMNKtWrWp2/pIlS8x1112XMDZlyhSTl5cX//knP/mJmTBhQsKcnJwc87Of/awNV961OHHOX3f+/HnTo0cP8/zzz7fNorsgp875/PnzZuzYsWbz5s3mgQceIHa+hpexLBcKhZSRkaHRo0fHx4LBoJKSklReXt7sNZWVlQqHwwoGg/Exr9ernJwchUKh+Njp06d17733qqCgQH6/37lNdAFOnvPXRaNReTyebvFNqmfPntXevXsTzigpKUnBYPCiZxQKhRLmS1JeXl7C/NbM6U6cOuevO336tM6dO6devXq1zcK7GCfP+YknnlDfvn01a9astl+4BYgdy4XDYfXt2zdhLCUlRb169VI4HL7oNZLk8/kSxn0+X8I1Cxcu1NixYzVx4sQ2XnXX4+Q5f9XJkyf15JNPas6cOW2w6s7v5MmTamhouKQzCofDzc6PxWI6c+ZMi3Mudp+2c+qcv27p0qXKzMxs8se7u3DqnN988009++yzKiwsdGbhFiB2uqj8/Hy5XK4Wb4cPH3bs8Xfs2KHdu3dr3bp1jj1GZ9DR5/xVsVhMEyZM0LBhw8T/pR26mtWrV2vLli3atm2b0tLSOno51qitrdV9992nwsJC9e7du6OX02nZ/zy4pRYvXqwZM2a0OGfQoEHy+/06ceJEwvj58+dVXV190ZeeLoxHIhH169cvPh6JRJSdnS1J2r17tz766CNlZGQkXDt58mSNGzdOZWVll7ijzqmjz/mC2tpajR8/Xj169NC2bdt0xRVXXMZuup7evXsrOTlZkUgkYTwSibR4rs3N93g8Sk9Pb3FOd3051qlzvmDt2rVavXq1Xn31Vd1www1tu/guxIlzrqio0Mcff6y77747/vvGxkZJXz67fOTIEV199dVtvJMuqKPfNARnXXjj7Lvvvhsf27lzZ6veOLt27dr4WDQaTXjj7PHjx83+/fsTbpLM+vXrzdGjR53dVCfk1DlfGLvpppvMLbfcYurq6pzbRCc1ZswYM2/evPjPDQ0N5qqrrmrxDZ3XX399wti0adOavEH5rrvuSpiTm5vb7d+g3NbnbIwxTz31lPF4PCYUCrX9orugtj7nM2fONPlv8cSJE80PfvADs3//flNfX+/cZroQYqcbGD9+vPnud79rysvLzZtvvmmGDBnS5CPR11xzjfnb3/4W/3n16tUmIyPD/P3vfzf//ve/zcSJEy/60fML1I0/jWWMM+ccjUZNTk6OGT58uPnwww/N8ePH47fz58+36/46ypYtW4zb7TZFRUXm4MGDZs6cOSYjI8OEw2FjjDH5+fnmvvvui8+/8FHdX/7yl+bQoUOmoKCg2Y+ep6SkmLVr15pDhw6ZFStW8NFzB8559erVJjU11fz1r39N+LdbW1vb7vvrLJw456/j01hNETvdwH/+8x8zbdo08+1vf9t4PB4zc+bMJv+xkWT++Mc/xn9ubGw0jz/+uPH5fMbtdpvbbrvNHDlypMXH6e6x48Q5v/baa0ZSs7fKysp22lnHe/rpp82AAQNMamqqGTNmjHn77bfjv3vggQfMLbfckjD/tddeM9nZ2SY1NdUMGjQo4cwv2Lp1q/nOd75jUlNTzXXXXWeKi4sd3kXn19bn/H//93/N/ttdsWKF85vpxJz49/xVxE5TLmOMae+XzgAAANoLn8YCAABWI3YAAIDViB0AAGA1YgcAAFiN2AEAAFYjdgAAgNWIHQAAYDViBwAAWI3YAQAAViN2AACA1YgdAABgtf8HyT6sQPPu5OoAAAAASUVORK5CYII=", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{Any,1}:\n", " PyObject " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(log10((En_array[1 : 180] - En_array[end])./(En_array[1] - En_array[end])))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Over-relaxed Forward-Backward\n", "-----------------------------\n", "It is possible to introduce a relaxation parameter $\\rho$ with $0 < \\rho < 1$. The over-relaxed foward-backward algorithm initializes $x^{(0)} \\in \\RR^N$,\n", "and then iterates, for $k=1,2,\\ldots$\n", "$$ z^{(k)} = \\text{prox}_{\\ga g}\\pa{\n", " x^{(k-1)} - \\ga \\nabla f( x^{(k-1)} ) }.\n", "$$\n", "$$ x^{(k)} = z^{(k)} +\n", " \\rho \\pa{ z^{(k)} - x^{(k-1)} } $$\n", "\n", "\n", "Let us assume $\\gamma=1/\\beta$. Convergence of the iterates $x^{(k)}$ and $z^{(k)}$ to a solution is guaranteed\n", "for $ 0 < \\rho < 1/2 $. The weaker property of convergence of $ E(x^{(k)}) $\n", "to $E^\\star$ is proved, when $ 1/2\\leq \\rho <1 $." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

\n", " \n", "__Exercise: write the code of the over-relaxed forward-backward iteration.__

" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "gamma = 1/beta\n", "nbiter = 1700\n", "rho = 0.95\n", "x = y\n", "En_array_overrelaxed = zeros(nbiter + 1)\n", "En_array_overrelaxed[1] = vecnorm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1))\n", "for iter in 1 : nbiter\n", " # put your code here\n", " En_array_overrelaxed[iter + 1] = vecnorm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1)) \n", "end" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "ename": "LoadError", "evalue": "BoundsError: attempt to access 1701-element Array{Float64,1} at index [1:1800]", "output_type": "error", "traceback": [ "BoundsError: attempt to access 1701-element Array{Float64,1} at index [1:1800]", "", " in throw_boundserror(::Array{Float64,1}, ::Tuple{UnitRange{Int64}}) at ./abstractarray.jl:355", " in checkbounds at ./abstractarray.jl:284 [inlined]", " in getindex(::Array{Float64,1}, ::UnitRange{Int64}) at ./array.jl:392" ] } ], "source": [ "plot(log10((En_array[1 : 1800] - En_array[end])./(En_array[1] - En_array[end])))\n", "plot(log10((En_array_overrelaxed[1 : 1800] - En_array[end])./(En_array[1] - En_array[end])))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "As we see, in this example, over-relaxation does not bring any speedup, because $\\gamma$ is lower than without over-relaxation. There are other setting parameters or other problems, for which over-relaxation does bring a significant speedup. " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "FISTA-like Accelerated Forward-Backward Algorithm\n", "---------------------------\n", "We consider the FISTA algorithm introduced in:\n", "\n", "\n", "A. Beck and M. Teboulle,\n", "\"A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems\",\n", "_SIAM Journal on Imaging Sciences_, 2009.\n", "\n", "More precisely, we consider a slightly modified version of FISTA, whose convergence is proved, see\n", "A. Chambolle and C. Dossal, \"On the convergence of the iterates of \"FISTA\"\", preprint, 2015." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Given an initial estimate $x^{(0)}$ of the solution and a parameter $a>2$, the algorithm sets $\\gamma=1/\\beta$, sets $z^{(0)}=x^{(0)} \\in \\RR^N$,\n", "and iterates, for $k=1,2,\\ldots$\n", "$$ x^{(k)} = \\text{prox}_{\\ga g}\\pa{\n", " z^{(k-1)} - \\ga \\nabla f( z^{(k-1)} ) }.\n", "$$\n", "$$ \\alpha_k=(k-1)/(k+a) $$\n", "$$ z^{(k)} = x^{(k)} +\n", " \\alpha_k\n", " \\pa{ x^{(k)} - x^{(k-1)} } $$\n", "\n", "\n", "It is proved that the iterates $x^{(k)}$ converge to a solution $x^\\star$ of the problem. Moreover, \n", "the optimal convergence rate for this class of problems is reached,\n", "namely\n", "$$ E_k - E^\\star = O(1/k^2), $$\n", "whereas the convergence rate for the normal forward-backward is only\n", "$O(1/k)$.\n", "\n", "Note the difference between the over-relaxed forward-backward and the accelerated forward-backward: the later is based on an inertia mechanism, of different nature than over-relaxation." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

\n", " \n", "__Exercise: write the code of the accelerated forward-backward iteration.__

" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "gamma = 1/beta\n", "nbiter = 1700\n", "a = 10\n", "x = y\n", "En_array_fista = zeros(nbiter + 1)\n", "En_array_fista[1] = vecnorm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1))\n", "for iter in 1 : nbiter\n", " # put your code here\n", " En_array_fista[iter + 1] = norm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1))\n", "end" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "ename": "LoadError", "evalue": "BoundsError: attempt to access 1701-element Array{Float64,1} at index [1:1800]", "output_type": "error", "traceback": [ "BoundsError: attempt to access 1701-element Array{Float64,1} at index [1:1800]", "", " in throw_boundserror(::Array{Float64,1}, ::Tuple{UnitRange{Int64}}) at ./abstractarray.jl:355", " in checkbounds at ./abstractarray.jl:284 [inlined]", " in getindex(::Array{Float64,1}, ::UnitRange{Int64}) at ./array.jl:392" ] } ], "source": [ "plot(log10((En_array[1 : 1800] - En_array[end])./(En_array[1] - En_array[end])))\n", "plot(log10((En_array_overrelaxed[1 : 1800] - En_array[end])./(En_array[1] - En_array[end])))\n", "plot(log10((En_array_fista[1 : 1800] - En_array[end])./(En_array[1] - En_array[end])))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

\n", " \n", "__Exercise: try different values of a. You can try a=3,10,30,50,100.__

" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We can note that the accelerated forward-backward is not monotonic: the cost function E is not decreasing along with the iterations and some oscillations are present." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Julia 0.5.0", "language": "julia", "name": "julia-0.5" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.5.0" } }, "nbformat": 4, "nbformat_minor": 0 }