{ "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": [], "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": [], "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": 4, "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": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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bM2fOVFlZWeCYz+dTWVmZiouLQ15zwQUX6NChQzpx4kTg2Mcffyyn06kxY8ZY2VwANtDc7yEtcwNRhrQAnMryIa3Fixfrqaee0tNPP61t27bp1ltvVWNjY2DW1pIlSzR37tzA+ddee62GDx+u+fPn66OPPtJbb72lu+66S9/85jeVmppqdXMBxFnXwoMMaQGIHsunpc+ZM0eHDx/W0qVLVVVVpenTp2v9+vWBQubKykrt27cvcP6QIUO0YcMG3XbbbZo1a5aGDx+ua665Rj/60Y+sbioAG+jPwoPdzyfwAAjF8sAjSYsWLdKiRYtCPrd27dpTjk2ePFkbNmywuFUA7Kj/Cw8mdV7PkBaAU9lulhaA01vTABYe7H49AHRH4AFgKwMe0mol8AA4FYEHgK30Z7d0//mdQ1rtBB4ApyLwALCVrmnp/RvSYlo6gFAIPABspf97aXUuPMiQFoAQCDwAbKW5n7O0AgsPMqQFIAQCDwBbaernkFbXOjwMaQE4FYEHgG0YhtHvomVmaQHoDYEHgG20tPsCv2dIC0A0EXgA2Eb3sJKSHGHRcuf5HT5D7V5fH2cDON0QeADYhhl43ElOuZyOiK5NcXd9O6OXB8DJCDwAbMOcoZUaYe+OJLldTpkZqZntJQCchMADwDZa2vsfeBwOR1cdD4EHwEkIPABswxyKinSGlsms+2FIC8DJCDwAbMPsmYm0YNmU2lnHQ+ABcDICDwDbCPTwJPfvW5M5FNbCkBaAkxB4ANhGywCHtMzA00TgAXASAg8A2xjILC2pKygxpAXgZAQeALZh9vD0u4aHomUAPSDwALCN5s6tJQbaw9NC4AFwEgIPANuI2rR0angAnITAA8A2BrLwYPfrKFoGcDICDwDbGOg6PGkMaQHoAYEHgG0MdEiLomUAPSHwALCN5gEOaaW4qeEBEBqBB4BttAx0HR56eAD0gMADwDbMoJIy0CEtengAnITAA8A2BjqkxUrLAHpC4AFgG12ztAa2eSiBB8DJCDwAbGPA6/BQtAygBwQeALbRHKW9tFiHB8DJCDwAbCOwW/oAt5ZgpWUAJyPwALCNlgFuHppG0TKAHhB4ANhCh9enNi+7pQOwBoEHgC20dPgCvx/o1hLtXkPtXl8fZwM4ncQk8KxcuVIFBQVKSUlRUVGRNm3aFNZ177zzjpKSkjR9+nSLWwgg3rrPrPIk9e9bU/diZ3p5AHRneeB5/vnntXjxYi1btkybN2/WtGnTVFpaqpqaml6vq62t1dy5c3XppZda3UQANtB9SrrD4ejXa3iSnHJ2XsrUdADdWR54VqxYoQULFmj+/Pk6++yztWrVKqWlpWn16tW9XnfLLbfo2muvVXFxsdVNBGADA90pXZIcDgeLDwIIydLA09bWpoqKCpWUlHS9odOpkpISlZeX93jdmjVrtGvXLi1btqzP92htbVV9fX3QA8Dg0zzAjUNNbC8BIBRLA8+RI0fk9XqVl5cXdDwvL09VVVUhr/nkk090zz336He/+52SkpL6fI/ly5crMzMz8Bg7dmxU2g4gtroWHRzYt6UUNhAFEIKtZml5vV5de+21uu+++3TWWWeFdc2SJUtUV1cXeOzfv9/iVgKwQjSGtCT20wIQWt9dKAOQk5Mjl8ul6urqoOPV1dXKz88/5fyGhga9//772rJlixYtWiRJ8vl8MgxDSUlJ+stf/qLPf/7zQdd4PB55PB7rPgSAmGiJ0pBWGvtpAQjB0h4et9utmTNnqqysLHDM5/OprKwsZDFyRkaG/vnPf2rr1q2Bxy233KJJkyZp69atKioqsrK5AOJooPtomVLo4QEQgqU9PJK0ePFizZs3T7NmzdLs2bP12GOPqbGxUfPnz5fkH5I6ePCgfvvb38rpdOqcc84Jun7EiBFKSUk55TiAxNI8wJ3STeyYDiAUywPPnDlzdPjwYS1dulRVVVWaPn261q9fHyhkrqys1L59+6xuBgCbG+jGoSZ2TAcQiuWBR5IWLVoUqMk52dq1a3u99t5779W9994b/UYBsJWWaPXwMKQFIARbzdICcPqKVg2P2UPUxJAWgG4IPABsobmtc6d0pqUDsACBB4AtRLtouYUeHgDdEHgA2EK0aniYlg4gFAIPAFswZ2mlRGlIixoeAN0ReADYQrSGtMyVlpmWDqA7Ag8AW4j6woMEHgDdEHgA2EKghsfNbukAoo/AA8AWAjU8UVt40DfgNgFIHAQeALYQ/b20OgbcJgCJg8ADwBa6hrRYeBBA9BF4ANhCYPNQdksHYAECD4C4MwwjekNagd3SqeEB0IXAAyDu2rw++Qz/76O18GCb16cOL6EHgB+BB0DctbR1BZNoDWlJ1PEA6ELgARB3ZjBJcjqU7BrYtyVPklMOR/DrAgCBB0DcRat+R5IcDkdXHU8bQ1oA/Ag8AOIuWhuHmpiaDuBkBB4AcRfNHh6p2/YSBB4AnQg8AOKuJcqBxyxcbmK1ZQCdCDwA4i7aQ1ppbnMtHnp4APgReADEXdeQVnS+JXXtmE7RMgA/Ag+AuIt2DQ9FywBORuABEHfR2jjUROABcDICD4C4C9TwRLlouZmiZQCdCDwA4s7siYl+4KGGB4AfgQdA3JmBJ40aHgAWIfAAiDtzSCstyjU8TEsHYCLwAIi7qG8tERjSIvAA8CPwAIi7JoumpTfRwwOgE4EHQNy1RHtIix4eACch8ACIu6ZoT0unhgfASQg8AOIuMEvLnRSV12O3dAAnI/AAiDurdktnSAuAicADIO7MIa1obS1h1gLRwwPAROABEHeWbR5KDw+ATjEJPCtXrlRBQYFSUlJUVFSkTZs29Xju73//e33hC19Qbm6uMjIyVFxcrFdffTUWzQQQJ81R7uGhhgfAySwPPM8//7wWL16sZcuWafPmzZo2bZpKS0tVU1MT8vy33npLX/jCF/TnP/9ZFRUVuuSSS3T11Vdry5YtVjcVQBwYhtGtaDnKNTwEHgCdLA88K1as0IIFCzR//nydffbZWrVqldLS0rR69eqQ5z/22GP63ve+p89+9rOaOHGifvKTn2jixIn64x//aHVTAcRBm9cnr8+QFP1p6W0dXa8N4PRmaeBpa2tTRUWFSkpKut7Q6VRJSYnKy8vDeg2fz6eGhgZlZ2eHfL61tVX19fVBDwCDR0u3Hc2j1cPT/XXo5QEgWRx4jhw5Iq/Xq7y8vKDjeXl5qqqqCus1Hn74YZ04cULXXHNNyOeXL1+uzMzMwGPs2LEDbjeA2Glq75AkJTkdSnZF51uSJ6nrdShcBiDZfJbWM888o/vuu08vvPCCRowYEfKcJUuWqK6uLvDYv39/jFsJYCCiXbAsSQ6Hg9WWAQSJzrKmPcjJyZHL5VJ1dXXQ8erqauXn5/d67XPPPaebbrpJL774YtCQ2Mk8Ho88Hk9U2gsg9qI9Jd2U6napud3LkBYASRb38Ljdbs2cOVNlZWWBYz6fT2VlZSouLu7xumeffVbz58/Xs88+q6uuusrKJgKIMyt6eKRuO6YzpAVAFvfwSNLixYs1b948zZo1S7Nnz9Zjjz2mxsZGzZ8/X5J/SOrgwYP67W9/K8k/jDVv3jz97Gc/U1FRUaDWJzU1VZmZmVY3F0CMWdnDI1HDA8DP8sAzZ84cHT58WEuXLlVVVZWmT5+u9evXBwqZKysrtW/fvsD5Tz75pDo6OrRw4UItXLgwcHzevHlau3at1c0FEGPR3lbCRA0PgO4sDzyStGjRIi1atCjkcyeHmI0bN1rfIAC20RLlRQdNqay2DKAbW8/SApD4Aj08UR7SSmFIC0A3BB4AcdVVtBzdDufUZP+3tyZ6eACIwAMgzrqKlqP77SitM0C10MMDQAQeAHFm9vCkRbmHhx3TAXRH4AEQV2YgidbGoSaKlgF0R+ABEFdWFS2nuv3f3ihaBiAReADEmeXT0gk8AETgARBnTW3+3dJToh14OmuCGNICIBF4AMRZc7tPkpRGDQ8ACxF4AMRVi1VbS3TW8LC1BACJwAMgzpra/UNaVu2lRQ0PAInAAyDOmq3aWqLz9ZoIPABE4AEQZ1YFnsBKywxpARCBB0CcNbNbOoAYIPAAiCtzyCnqKy2bCw8SeACIwAMgjnw+Q60dndPSo9zDk0LRMoBuCDwA4qZ774tVs7RaO3zy+oyovjaAwYfAAyBuugeelCRripYlCpcBEHgAxFFzoH7HKafTEdXX9iR1fXujjgcAgQdA3JhBJNpT0iXJ6XQoJZkd0wH4EXgAxI0ZRLoPP0WTGaQY0gJA4AEQN03dhrSsYAYpVlsGQOABEDct7db28ASGtOjhAU57BB4AcdNk0bYSJnOqO4EHAIEHQNwEipajvAaPKVDDw5AWcNoj8ACIGytnaUndVlumhwc47RF4AMRNc1uHJOt6eMztKihaBkDgARA3zW3+fbQsH9Kihwc47RF4AMRNU3tnD4/VRcv08ACnPQIPgLhpCSw8SA0PAGsReADETdfCg9YOaVHDA4DAAyBumtut7eExX5caHgAEHgBx08K0dAAxQuABEDeBlZatmqVF0TKATgQeAHFj9cKDqfTwAOhE4AEQN81W9/Ak08MDwC8mgWflypUqKChQSkqKioqKtGnTpl7P37hxo2bMmCGPx6MzzzxTa9eujUUzAcSY1UXLbB4KwGR54Hn++ee1ePFiLVu2TJs3b9a0adNUWlqqmpqakOfv3r1bV111lS655BJt3bpVd9xxh2666Sa9+uqrVjcVQIzFalo6gQdAktVvsGLFCi1YsEDz58+XJK1atUqvvPKKVq9erXvuueeU81etWqXCwkI98sgjkqQpU6bo7bff1qOPPqrS0tJTzm9tbVVra2vgz/X19ZKkub95T8mp6RG31yFHxNd0uziWl/mv7fd79v9d+/2eA/rS9u/igbxnfzkG8Kb9vTLZ5VSa26U0t0upbpfS3UnKTndr9LBUjR+epokjhsrljMMXow9dCw9a863I7OGx627p7V6fPq5u0P5jTTpwvFnHm9rU1OZVc5tXjW1eNbd1qM1ryDAMSZJhSIYM/6/dfy9JnX8GBqv25kZLX9/SwNPW1qaKigotWbIkcMzpdKqkpETl5eUhrykvL1dJSUnQsdLSUt1xxx0hz1++fLnuu+++U45v3lcrp6dtAK0HEsdQT5JmjB+mL5ydp6/OGGNZzUwkDMNQk8VFy+ZQWaONAs+J1g69+P5+vb69RhV7j7MoItDJ19pk6etbGniOHDkir9ervLy8oON5eXnavn17yGuqqqpCnl9fX6/m5malpqYGPbdkyRItXrw48Of6+nqNHTtWj86ZpvQhQyNqrzGA/xz199KBvWf/Lo7P54z9/zwH3de2n9ca8vcUNLZ2qLnNq6Z2r5paO3T4RKsOHG/WrsONamjt0JsfH9abHx/Ww3/Zobn/Ml63XnxmXINPa4dPXp//Q6d7rAo8/m9xTZ27ssdTQ0u7fvHGTj3z3j41tHS1JyMlSYW5QzRmWKpyh3i69dQlKc3tUrLLKafD31vpkCPQa+lw+Ps9ux83/wwMRo0nGvQfj1n3+pYPaVnN4/HI4/GccvwLZ+crIyMjDi0C7MXrM7Stsl7v7Dyi3723V/uPNevnr+/Uhm01evL6mRqbnRaXdp1o7fqhn27RkFa6x/+67V5DrR1eeZLiE/B21pzQzf/3fe067O+yn5CTruv+ZbwuOHO4zhoxVE4bDjcCsVZfH3kZSiQsDTw5OTlyuVyqrq4OOl5dXa38/PyQ1+Tn54c8PyMj45TeHQB9czkdOmd0ps4ZnambLpqg//mgUsv++0Ntq6zX1b94W09cN0Pnn5ET83Y1dgaeNLfLsh/46d16sJpa4xN4yrZV69vPbdWJ1g7lZ6To/3z5HF06eQQhB4gxS2dpud1uzZw5U2VlZYFjPp9PZWVlKi4uDnlNcXFx0PmStGHDhh7PBxA+l9Ohf5s6Sn+87UJNHZOp2qZ2LXj6fe06fCLmbWlstbZgWZKSXE55kvzf5rr3KMXKh4fqdOu6zTrR2qHZBdn6420X6gtn5xF2gDiwfFo1metFAAAgAElEQVT64sWL9dRTT+npp5/Wtm3bdOutt6qxsTEwa2vJkiWaO3du4PxbbrlFu3bt0ve+9z1t375dTzzxhF544QV95zvfsbqpwGljVFaqXvjPYhUVZquxzauFz2yJ+QabjZ11NUMsqt8xDekc1mqMcR3PidYOLXpmi9o6fLpkUq7WLShS7tBTh98BxIblgWfOnDl6+OGHtXTpUk2fPl1bt27V+vXrA4XJlZWV2rdvX+D8wsJCvfLKK9qwYYOmTZumRx55RL/+9a9DTkkH0H8pyS79/BvnaXi6W9sq6/V//vRRTN/f7HEx62ysYr5+Ywx7eAzD0Pd//0/tPtKoUZkpWnHNdCW7WNgeiKeYFC0vWrRIixYtCvlcqFWUL774Ym3ZssXiVgHIy0jRijnTNW/1Jq17b59KP5Ovz52VG5P3buoc0rKqYNkUmJreGrserP/5oEov//2QXE6HHr/2PA1Ld8fsvQGExn85gNPcv56VqxvOL5Ak/eL1nTF738ZAD0+MhrRi1MNjGIYe7/w6fuviMzRzfHZM3hdA7wg8AHTrxWfI7XJq055jen/PsZi8Z6yHtGJVtLxxx2Ftq6xXutulmy6cEJP3BNA3Ag8A5WWk6CszRkuSfrnx05i8p9njMsTiwGO+fqxWNDa/ftcWjVNmWnJM3hNA3wg8ACRJ//mvZ8jpkMq212h7Vb3l79do8T5aJrOGJxY9PO/vOaZNe47J7XLqpovo3QHshMADQJJUmJOuK84dKUlaFYNenq4eHmtreGI5S2vVm/6v21dnjlZeRorl7wcgfAQeAAE3d/ZKrP+wSs0WDwE1xqiGJ1ZFy8cb2/TGjsOSRO8OYEMEHgABU8dkasywVLW0+/Tmx4ctfa+Yr8NjcYB7bVu1vD5DU0Zm6IzcIZa+F4DIEXgABDgcDpV+xr/P3V8+rLL0vcwiYqunpZuvb3UPz6sf+vcALP1MnqXvA6B/CDwAgpiB57Vt1Wr3+ix7n0APj8VFy+brW1m03NTWof/9xN8jZn79ANgLgQdAkJnjh2l4ulv1LR16b5d1a/LEalp6LIqW39xxWK0dPo3LTtPk/KGWvQ+A/iPwAAjicjr0hbP9wzKvWjisFeuiZSvX4TG/TqWfyZPDwU7ogB0ReACcIlDH81GVfD7DkvdojFENT5rH2nV42jp8KtteI4nhLMDOCDwATnH+mcM1xJOk6vpW/eNgXdRf3zCMhJmW/t7uo2po6VDOEI9mjBtmyXsAGDgCD4BTeJJcuuDM4ZKk93Ydjfrrt3b41NHZczTYp6WbdU7/elaunE6GswC7IvAACGlW5y7f7+89HvXX7t7bkpZs8bT0zq0l2jp8lsw6e3+vP/B8toDeHcDOCDwAQpox3v8DfPPe4zKM6NbxmAXEKclOJbms/TbUvQcp2sNa7V6f/r7fP+Q3czyBB7AzAg+AkM4ZnSG3y6mjjW3ae7Qpqq99IkZT0iUp2eWUO8kZ9L7Rsr2yQc3tXmWkJLG6MmBzBB4AIXmSXDp3TKYkqSLKw1qxKlg2WTU1vaJzOGvG+GHU7wA2R+AB0KNZncM00a7jMXta0ixeZdmU5rZmarr5dZnFcBZgewQeAD3qXscTTWZPyxCL1+AxWTU13fy6zCDwALZH4AHQI3NdmY9rGlTX3B61143VTummru0lojekdai2WYfqWuRyOjRtTFbUXheANQg8AHqUO9Sj8cPTZBjS1v21UXvdWNfwWLGf1uZ9/t6dKSOHxuxzAOg/Ag+AXs3s7OWp2BO9jUTNIS1zjRyrme/T2Ba9wPP+Hn/gmcnqysCgQOAB0KuZnQvqVeyLXh1PvIa0olm0vKXz6zGzIDtqrwnAOgQeAL2aOtpfn/LRofqoLUDYGMN1eLq/T1OUang6vD5tr2qQJE0dnRmV1wRgLQIPgF5NzBsip0M63tSuww2tUXnNwT4tfc/RJrV2+JSa7NK47LSovCYAaxF4APQqJdmlguHpkhTo1Rgos6clVtPSo120vKPz63BW3hAWHAQGCQIPgD5NHjlUUtcP+oEyi4cH60rLO6rqJUmT8zOi8noArEfgAdCnSXn+H+zR6uEZ7EXL5tdhUv7QqLweAOsReAD0yfzBvqO6PiqvF1iHJ0Y1PIFp6dEa0qr2B57JBB5g0CDwAOiT+YP94+oT6vD6Bvx65orH6TGu4YlGD09ja0dg93h6eIDBg8ADoE/jstOUmuxSW4dPezp/2A+EWcMTq2np6VGs4fm4s3cnZ4hHw4d4Bvx6AGKDwAOgT06nQ2flDZEUncLlWG8tEc3NQ83Pz3AWMLgQeACEJVDHUzWwOp7WDq/avf4FDGNVwxPNdXgoWAYGJwIPgLBMyo/OTK3uqx3HqobH7OFp7fANuAZpB4EHGJQsCzzHjh3Tddddp4yMDGVlZenGG2/UiRMnejy/vb1dd999t84991ylp6dr1KhRmjt3rg4dOmRVEwFEYEpgptbAAo/Zy+JJcirJFZv/c3UfOmscQB2PYRja3tnDNYU1eIBBxbLvNtddd50+/PBDbdiwQX/605/01ltv6eabb+7x/KamJm3evFk//OEPtXnzZv3+97/Xjh079MUvftGqJgKIgNmjsfdo04BqYWJdsCxJ7iSn3J3haiBtP9zQquNN7XI6/FtuABg8LPmOs23bNq1fv15/+9vfNGvWLEnS448/riuvvFIPP/ywRo0adco1mZmZ2rBhQ9CxX/ziF5o9e7b27duncePGWdFUAGEaPsSjnCEeHTnRqo+rG3TeuGH9eh0zcKTFaDjLlOZxqa3JN6DAY/ZuFQxPV0pybNsPYGAs6eEpLy9XVlZWIOxIUklJiZxOp957772wX6eurk4Oh0NZWVk9ntPa2qr6+vqgBwBrTBzh79XYdbix368RWIMnRgXLJvP9BjKk9WmNf1j+zBH07gCDjSWBp6qqSiNGjAg6lpSUpOzsbFVVVYX1Gi0tLbr77rv1jW98QxkZPY+VL1++XJmZmYHH2LFjB9R2AD0rzPVvIrr7yEACT+yHtLq/30B6eMzPbX4dAAweEQWee+65Rw6Ho9fH9u3bB9yo9vZ2XXPNNTIMQ7/85S97PXfJkiWqq6sLPPbv3z/g9wcQWmHnrum7j/Y/8JwIDGnFNvCYQ2gDmZq+u3PRRfPrAGDwiOg7zp133qkbbrih13MmTJig/Px81dTUBB3v6OjQsWPHlJ+f3+v1ZtjZu3evXn/99V57dyTJ4/HI42G1UyAWCnM6A8+AhrTMHp7Y1sBEp4fHP6Rlfh0ADB4RBZ7c3Fzl5ub2eV5xcbFqa2tVUVGhmTNnSpJef/11+Xw+FRUV9XidGXY++eQTvfHGGxo+fHgkzQNgsYLOH/R7jjbKMAw5HI6IX6OhJT5DWkNTkoLeP1KtHV4dPN4sicADDEaW1PBMmTJFl19+uRYsWKBNmzbpnXfe0aJFi/T1r389aIbW5MmT9dJLL0nyh53/+I//0Pvvv69169bJ6/WqqqpKVVVVamtrs6KZACI0LjtNTod/T6qahtZ+vUZtc7skaViaO5pN61Nmqv/9apva+3X9/mNN8hn+nddzh9KrDAw2lq3Ds27dOk2ePFmXXnqprrzySl144YV68skng87ZsWOH6urqJEkHDx7Uyy+/rAMHDmj69OkaOXJk4PHuu+9a1UwAEXAnOTVmWJqk/hcuH2/y/wcmK8aBZ1hactD7R2r3EX/9TkFOer96tgDEl2V9ytnZ2XrmmWd6PccwjMDvCwoKgv4MwJ4Kc9K171iTdh9p1L9MiHzY2exhMQNIrJg9SrX9DjzU7wCDGXtpAYiI+QN/Tz97eGoDPTyxDTyZne9nDqlFyuzhmUDgAQYlAg+AiJiBZ1e/A48/cMR+SMv/fsf7WcNj9vAUEHiAQYnAAyAiA+3hMWtoYl20bA6h9XdIa09nDw9DWsDgROABEBHzB/7eo03y+iKru/P5DNU1mz08sR3SygoEnsh7eBpbO1RV3yKJwAMMVgQeABEZlZUqt8upNq9Ph2qbI7q2oaVDZkaKfeDx9yjVt7RHHNT2dK4sPSwtOeZDcQCig8ADICIup0Pjhvdvaro5nJXmdsmTFNuVlrNS/QHLMBToZQrXnm5T0gEMTgQeABELbDERYeAxZ0iZ4SOWklxODe1c3TnSOh6mpAODH4EHQMT6G3jiteigKSvdXHwwsh4ec0o6m4YCgxeBB0DE+t3DY87QSo99D4/U/8UHAz08uQQeYLAi8ACIWMHwrk1EIxFYgyc1Pj08man9m6m152hnDQ89PMCgReABELEJnT0d+481qa3DF/Z1x5viMyXd1LX4YPg9PHVN7TrW6D+fGh5g8CLwAIjYiKEepbld8hnS/uNNYV9XG6dFB03D+rEWz+7OXqy8DI/SPZZtPwjAYgQeABFzOByB4Z3dh8Mf1qqNcw9PplnD0xx+D09gSwmGs4BBjcADoF/MAt5I6njiPUvL7OGJZJZWYNNQCpaBQY3AA6BfzCnakWwiavbwDItzDU8ks7TMmWj08ACDG4EHQL/0ZxNRcygpfkNakdfwmJ+PgmVgcCPwAOiXgn6sxVPbaNbwxGtIy+zhCS/wGIYR+HwEHmBwI/AA6JcJnQGgsq5FzW3ePs9v9/rU0NohKf6ztMKdln7kRJtOtHbI4VBg/zAAgxOBB0C/DEt3BxbyC6dwufuGnRkp8ZnebS542NTmVWtH3yHN7N0ZnZUa881OAUQXgQdAv0VSx2MWCmekJCnJFZ9vPUNTkuR0+H9fF8awFvU7QOIg8ADoNzMIhDNTy5wKPiw9PsNZkuR0OgL1Q+FMTd9F4AESBoEHQL9Fsolo1z5a8ZmhZcoK7KfVdx1PYNNQAg8w6BF4APRbJENa8V500JQVweKDezoXHSTwAIMfgQdAv0XWw2PuoxXfHp5wFx/0+YxAMTaBBxj8CDwA+s1ci+doY1vQLKxQuvbRim8PT2DxwT7aW1nfotYOn5JdDo3OSo1F0wBYiMADoN+GeJKUO9Qjqe9enuNx3jjUNCxQtNx7D4+5KerY7LS4zSoDED38KwYwIGd0bqr5ac2JXs/rGtKKbw+POaRmrvrck501DZKkM3KHWN4mANYj8AAYkLPyhkqSPukz8NijhyfTrOFp7r2Hx/w8Z+UReIBEQOABMCATR/gDwSfVDb2eZ5dZWsPCnKX1SbU/8EwcMdTyNgGwHoEHwICcOSKyHp7BMEvLMAx93DmkdeYIeniAREDgATAgEzuHfPYfb+pxE9EOr09HTrRKknKGeGLWtlDMIuuquhYZhhHynKONbaptapfDQQ0PkCgIPAAGJGeIR9npbhmG9Onh0L08B443q8NnyJPkVH5GSoxbGGxctn/X8/qWjh6HtczhrHHZaUp1s2kokAgIPAAGzBz2+aQmdB3P7s4F/AqGp8tp7t4ZJynJLo3K9IeunqbSm59jIsNZQMIg8AAYsK7C5dA9PObWEwU5aTFrU28K+tgSw/wcZ1KwDCQMAg+AAQsEnh4Kl7sCjz22aCjoY0sMeniAxEPgATBgEzvX4tnZQ+DZfbRzE87h9gg8ZjvMobaTmZ9jImvwAAnDssBz7NgxXXfddcrIyFBWVpZuvPFGnTjR+7TV7m655RY5HA499thjVjURQJSYwWDv0Ua1tJ86U8uuPTyhhrSONbbpyAn/lHWmpAOJw7LAc9111+nDDz/Uhg0b9Kc//UlvvfWWbr755rCufemll/TXv/5Vo0aNsqp5AKIod4hHmanJ8hnSrsPBIaKtw6cDxzt7eGwSeAo7a4n2HGk8ZWq6uYDimGGpSnMnxbxtAKxhSeDZtm2b1q9fr1//+tcqKirShRdeqMcff1zPPfecDh061Ou1Bw8e1G233aZ169YpObnvBcpaW1tVX18f9AAQWw6Ho1sdT/BMrX3HmuQzpDS3SyOGxncNHtPY7DQ5HVJjm1eHO9cHMpl1SNTvAInFksBTXl6urKwszZo1K3CspKRETqdT7733Xo/X+Xw+XX/99brrrrv0mc98Jqz3Wr58uTIzMwOPsWPHDrj9ACJnDmudXMcTGM4ani6HI75T0k2eJJdGD0uVJO050hT0XFf9DjO0gERiSeCpqqrSiBEjgo4lJSUpOztbVVVVPV7305/+VElJSbr99tvDfq8lS5aorq4u8Ni/f3+/2w2g/8w9p7ZVBvfw7OksDLbLcJapYHjoOp5tlf5eYup3gMQSUeC555575HA4en1s3769Xw2pqKjQz372M61duzai/wV6PB5lZGQEPQDE3ozxwyRJ7+06qnavL3B8t83W4DGZAWxXt8DT2NqhLftqJUkzOz8PgMQQUUXenXfeqRtuuKHXcyZMmKD8/HzV1NQEHe/o6NCxY8eUn58f8rr//d//VU1NjcaNGxc45vV6deedd+qxxx7Tnj17ImkqgBibOjpT2eluHWts0+a9x1U0Ybikrh6eAptMSTeF6uEp//So2rw+jc1O1QSb9UgBGJiIAk9ubq5yc3P7PK+4uFi1tbWqqKjQzJkzJUmvv/66fD6fioqKQl5z/fXXq6SkJOhYaWmprr/+es2fPz+SZgKIA6fToc9NzNEfth7Sxo8PdwWeI/aaoWUy27On21o8Gz/2/0ft4rNG2KbeCEB0WFLDM2XKFF1++eVasGCBNm3apHfeeUeLFi3S17/+9aCp5pMnT9ZLL70kSRo+fLjOOeecoEdycrLy8/M1adIkK5oJIMounuSv3du447AkqaXdq0N1zZLsswaPqaBb4PH5DBmGEWj3xZP6/o8dgMHFsnV41q1bp8mTJ+vSSy/VlVdeqQsvvFBPPvlk0Dk7duxQXV2dVU0AEGOfOytXDoe/8Le6vkX7jjXJMKShniQNT3fHu3lBxgxLlcvpUEu7T9UNLfr0cKMOHG+W2+VU8RnD4908AFFm2apa2dnZeuaZZ3o95+QFv05G3Q4wuGSnuzV1TJb+vr9Wb+44LE+y//9Uhbn2mZJuSnY5NS47TbuPNGpbZX1gwcSiCdksOAgkIP5VA4iqi8/K1d/312rNu3u0/5i/fmfamKw4tyq06WOztPtIoxa/8HflDvEvivivZzGcBSQiNg8FEFWXTPbX8WyrrNeJ1g79y4Rs3XW5PevwfvhvZ2v62CzVNrUHVlg22w8gsRB4AETV1NGZyunsLblq6kg9/c3Zykjpe5uYeMhOd+uZBUW6pLNIuWB4GtPRgQTFkBaAqHI6HXpy7kztrDmh/5gxRk6nvWp3TpbmTtJTc2fpxYoDOnd0pu1qjQBEh8Poq3J4kKmvr1dmZqbq6upYdRkAgEHC6p/fDGkBAICER+ABAAAJj8ADAAASHoEHAAAkPAIPAABIeAQeAACQ8Ag8AAAg4RF4AABAwiPwAACAhEfgAQAACY/AAwAAEh6BBwAAJDwCDwAASHhJ8W5AtJmbv9fX18e5JQAAIFzmz23z53i0JVzgOXr0qCRp7NixcW4JAACI1NGjR5WZmRn11024wJOdnS1J2rdvnyVfMLuqr6/X2LFjtX//fmVkZMS7OTHD5+Zznw743Hzu00FdXZ3GjRsX+DkebQkXeJxOf1lSZmbmafUXxZSRkcHnPo3wuU8vfO7Ty+n6uc2f41F/XUteFQAAwEYIPAAAIOG57r333nvj3Yhoc7lcuvjii5WUlHAjdr3ic/O5Twd8bj736YDPHf3P7TCsmv8FAABgEwxpAQCAhEfgAQAACY/AAwAAEh6BBwAAJDwCDwAASHiDOvD8+Mc/1vnnn6+0tDRlZWWFPGffvn266qqrlJaWphEjRuiuu+5SR0dH0Dn/+Mc/dNFFFyklJUVjx47Vgw8+GIvmR8XGjRvlcDhCPv72t78Fzgv1/HPPPRfHlg9cQUHBKZ/pgQceCDonnPs/mOzZs0c33nijCgsLlZqaqjPOOEPLli1TW1tb0HmJeL8laeXKlSooKFBKSoqKioq0adOmeDcpqpYvX67PfvazGjp0qEaMGKEvf/nL2rFjR9A5N9xwwyn39vLLL49Ti6Pj3nvvPeUzTZ48OfC8YRhaunSpRo4cqdTUVJWUlOiTTz6JY4ujI9T3MIfDoYULF0pKnHv91ltv6eqrr9aoUaPkcDj0hz/8Iej5cO5vS0uLFi5cqOHDh2vIkCH66le/qurq6ojaMagDT1tbm772ta/p1ltvDfm81+vVVVddpba2Nr377rt6+umntXbtWi1dujRwTn19vS677DKNHz9eFRUVeuihh3TvvffqySefjNXHGJDzzz9flZWVQY+bbrpJhYWFmjVrVtC5a9asCTrvy1/+cpxaHT33339/0Ge67bbbAs+Fc/8Hm+3bt8vn8+lXv/qVPvzwQz366KNatWqVvv/9759ybqLd7+eff16LFy/WsmXLtHnzZk2bNk2lpaWqqamJd9Oi5s0339TChQv117/+VRs2bFB7e7suu+wyNTY2Bp13+eWXB93bZ599Nk4tjp7PfOYzQZ/p7bffDjz34IMP6uc//7lWrVql9957T+np6SotLVVLS0scWzxwf/vb34I+84YNGyRJX/va1wLnJMK9bmxs1LRp07Ry5cqQz4dzf7/zne/oj3/8o1588UW9+eabOnTokL7yla9E1hAjAaxZs8bIzMw85fif//xnw+l0GlVVVYFjv/zlL42MjAyjtbXVMAzDeOKJJ4xhw4YF/mwYhnH33XcbkyZNsr7hFmhrazNyc3ON+++/P+i4JOOll16KU6usMX78eOPRRx/t8flw7n8iePDBB43CwsKgY4l4v2fPnm0sXLgw8Gev12uMGjXKWL58eRxbZa2amhpDkvHmm28Gjs2bN8/40pe+FMdWRd+yZcuMadOmhXzO5/MZ+fn5xkMPPRQ4Vltba3g8HuPZZ5+NVRNj4tvf/rZxxhlnGD6fzzCMxLzXJ39vCuf+1tbWGsnJycaLL74YOGfbtm2GJKO8vDzs9x7UPTx9KS8v17nnnqu8vLzAsdLSUtXX1+vDDz8MnPO5z31Obrc76JwdO3bo+PHjMW/zQL388ss6evSo5s+ff8pzCxcuVE5OjmbPnq3Vq1fLSIA1Jx944AENHz5c5513nh566KGg4apw7n8iqKurC7m7cCLd77a2NlVUVKikpCRwzOl0qqSkROXl5XFsmbXq6uok6ZT7u3HjRo0YMUKTJk3SrbfeqqNHj8ajeVH1ySefaNSoUZowYYKuu+467du3T5K0e/duVVVVBd37zMxMFRUVJdS9b2tr0+9+9zt985vflMPhCBxPxHvdXTj3t6KiQu3t7UHnTJ48WePGjYvo70BCr1ldVVUV9MNOUuDPVVVVgV8LCwt7PGfYsGExaGn0/OY3v1FpaanGjBkTdPz+++/X5z//eaWlpekvf/mLvvWtb+nEiRO6/fbb49TSgbv99ts1Y8YMZWdn691339WSJUtUWVmpFStWSArv/g92O3fu1OOPP66HH3446Hii3e8jR47I6/WGvJ/bt2+PU6us5fP5dMcdd+iCCy7QOeecEzh++eWX6ytf+YoKCwv16aef6vvf/76uuOIKlZeXy+VyxbHF/VdUVKS1a9dq0qRJqqys1H333aeLLrpIH3zwQeDfaqh7nyj/jiXpD3/4g2pra3XDDTcEjiXivT5ZOPe3qqpKbrf7lFrdSP8O2C7w3HPPPfrpT3/a6znbtm0LKmhLRP35Ohw4cECvvvqqXnjhhVPO/eEPfxj4/XnnnaempiY99NBDtvsBGMnnXrx4ceDY1KlT5fF4dPPNN2v58uXyeDxWNzWq+nO/Dx48qMsvv1xf+9rXtGDBgqBzB8v9Rs8WLlyoDz74IKiWRZK+/vWvB35/7rnnaurUqTrjjDO0ceNGXXrppbFuZlRcccUVgd9PnTpVRUVFGj9+vF544QVNmTIlji2Lnd/85je64oorNGrUqMCxRLzX8WS7wHPnnXcGJdxQJkyYENZr5efnnzKLw6zqzs/PD/x6cqX3yefEQ3++DmvWrNHw4cP1xS9+sc/Xnz17tu6//361trbaKhwM5P7Pnj1bHR0d2rNnjyZNmhTW/beLSD/3oUOHdMkll+j8888Pq8Dervc7XDk5OXK5XCH/rdrtXkbDokWL9Kc//UlvvfXWKb21J5swYYJycnK0c+fOhPkhmJWVpbPOOks7d+7UJZdcIsl/r0eOHBk4p7q6WtOnT49XE6Nq7969eu211/T73/++1/MS8V6b/357u7/5+flqa2tTbW1tUC9PpP/+bRd4cnNzlZubG5XXKi4u1o9//GPV1NRoxIgRkqQNGzYoIyNDZ599duCcH/zgB2pvb1dycnLgnEmTJsV1OCvSr4NhGFqzZo3mzp0b+By92bp1q4YNG2a7H34Duf9bt26V0+kM3Otw7r9dRPK5Dx48qEsuuUQzZ87UmjVr5HT2XYpn1/sdLrfbrZkzZ6qsrCww28zn86msrEyLFi2Kc+uixzAM3XbbbXrppZe0cePGU4bbQzlw4ICOHj0a9MNisDtx4oR27typ66+/XoWFhcrPz1dZWVngB2B9fb3ee++9HmfoDjZr1qzRiBEjdNVVV/V6XiLe63Du78yZM5WcnKyysjJ99atflSTt2LFD+/btU3FxcfhvNsCC67jau3evsWXLFuO+++4zhgwZYmzZssXYsmWL0dDQYBiGYXR0dBjnnHOOcdlllxlbt2411q9fb+Tm5hpLliwJvEZtba2Rl5dnXH/99cYHH3xgPPfcc0ZaWprxq1/9Kl4fq19ee+01Q5Kxbdu2U557+eWXjaeeesr45z//aXzyySfGE088YaSlpRlLly6NQ0uj49133zUeffRRY+vWrcann35q/O53vzNyc3ONuXPnBs4J5/4PNgcOHDDOPPNM49JLLzUOHDhgVFZWBh6mRLzfhmEYzz33nOHxeIy1a9caH330kXHzzTcbWVlZQbPwBrtbb73VyMzMNDZu3Bh0b5uamgzDMIyGhgbju9/9rlFeXm7s3r3beO2114wZM1c9WWIAAAIsSURBVGYYEydONFpaWuLc+v678847jY0bNxq7d+823nnnHaOkpMTIyckxampqDMMwjAceeMDIysoy/vu//9v4xz/+YXzpS18yCgsLjebm5ji3fOC8Xq8xbtw44+677w46nkj3uqGhIfDzWZKxYsUKY8uWLcbevXsNwwjv/t5yyy3GuHHjjNdff914//33jeLiYqO4uDiidgzqwDNv3jxD0imPN954I3DOnj17jCuuuMJITU01cnJyjDvvvNNob28Pep2///3vxoUXXmh4PB5j9OjRxgMPPBDjTzJw3/jGN4zzzz8/5HP/8z//Y0yfPt0YMmSIkZ6ebkybNs1YtWqV4fV6Y9zK6KmoqDCKioqMzMxMIyUlxZgyZYrxk5/85JRvBOHc/8FkzZo1If/Od/+/SyLeb9Pjjz9ujBs3znC73cbs2bONv/71r/FuUlT1dG/XrFljGIZhNDU1GZdddpmRm5trJCcnG+PHjzcWLFgw6EPfnDlzjJEjRxput9sYPXq0MWfOHGPnzp2B530+n/HDH/7QyMvLMzwej3HppZcaO3bsiGOLo+fVV181JJ3yeRLpXr/xxhsh/17PmzfPMIzw7m9zc7PxrW99yxg2bJiRlpZm/Pu//3vQf/TC4TCMQTxXFQAAIAwJvQ4PAACAROABAACnAQIPAABIeAQeAACQ8Ag8AAAg4RF4AABAwiPwAACAhEfgAQAACY/AAwAAEh6BBwAAJDwCDwAASHj/H490sx9yoTktAAAAAElFTkSuQmCC", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(-100,100)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(t, h)\n", "xlim(-100, 100)" ] }, { "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": [ "1-element Array{Any,1}:\n", " PyObject " ] }, "execution_count": 7, "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": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "srand(80);" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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));" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "y = opA(xsharp) + noiselevel * randn(N);" ] }, { "cell_type": "code", "execution_count": 12, "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": 12, "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": 13, "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": 13, "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": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": [], "source": [ "grad_f = x -> opA(opA(x)-y);" ] }, { "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": [], "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": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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", " x = prox_gamma_g(x - gamma.*grad_f(x), gamma, Lambda)\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": 23, "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": 23, "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": 24, "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": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(log10((En_array[1 : 1800] - 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": 25, "metadata": { "collapsed": false, "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", " xprevious = x\n", " x = prox_gamma_g(x - gamma.*grad_f(x), gamma, Lambda)\n", " x += rho .* (x - xprevious)\n", " En_array_overrelaxed[iter + 1] = vecnorm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1)) \n", "end\n", "x_restored = x;" ] }, { "cell_type": "code", "execution_count": 26, "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": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(log10((En_array[1 : 1700] - En_array[end])./(En_array[1] - En_array[end])))\n", "plot(log10((En_array_overrelaxed[1 : 1700] - En_array[end])./(En_array[1] - En_array[end])))\n", "# I changed 1800 to 1700 because En_array_overrelaxed is of length 1701" ] }, { "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": 28, "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", "z = x\n", "for iter in 1 : nbiter\n", " xprevious = x\n", " x = prox_gamma_g(z - gamma.*grad_f(z), gamma, Lambda)\n", " alpha = iter/(iter + 1 + a)\n", " z = x + alpha .* (x - xprevious)\n", " En_array_fista[iter + 1] = norm(opA(x) - y)^2/2 + Lambda*maximum(sum(abs(x), 1))\n", "end\n", "x_restored = x;" ] }, { "cell_type": "code", "execution_count": 29, "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": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(log10((En_array[1 : 1700] - En_array[end])./(En_array[1] - En_array[end])))\n", "plot(log10((En_array_overrelaxed[1 : 1700] - En_array[end])./(En_array[1] - En_array[end])))\n", "plot(log10((abs(En_array_fista[1 : 1700] - En_array[end]))./(En_array[1] - En_array[end])))\n" ] }, { "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." ] }, { "cell_type": "raw", "metadata": {}, "source": [ "" ] } ], "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 }