{"metadata": {"signature": "sha256:eb4906828415a441e62cc9285fbfd8364f7968b79c11dc22bd74c62ecfc92c21", "name": ""}, "worksheets": [{"metadata": {}, "cells": [{"level": 1, "metadata": {}, "cell_type": "heading", "source": ["Image Deconvolution using Variational Method"]}, {"metadata": {}, "cell_type": "markdown", "source": ["This numerical tour explores the use of\n", "Sobolev and TV regularization to perform image deconvolution."]}, {"metadata": {}, "cell_type": "markdown", "source": ["*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", "$\\newcommand{\\Om}{\\Omega}$\n"]}, {"prompt_number": 1, "metadata": {}, "cell_type": "code", "outputs": [{"output_type": "stream", "stream": "stdout", "text": ["Populating the interactive namespace from numpy and matplotlib\n"]}, {"output_type": "stream", "stream": "stderr", "text": ["WARNING: pylab import has clobbered these variables: ['pylab']\n", "`%matplotlib` prevents importing * from pylab and numpy\n"]}], "input": ["from __future__ import division\n", "from nt_toolbox.general import *\n", "from nt_toolbox.signal import *\n", "%pylab inline\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["This tour is concerned with the deconvolution problem. The measurement\n", "are assumed to be blurry and noisy:\n", " $$y=\\Phi f_0 + w = h \\star f_0 + w$$\n", "\n", "\n", "\n", "Where here |h| is the filter (low pass) and |w| some noise (here assumed\n", "to be white Gaussian).\n", "\n", "\n", "We consider variational deconvolution methods, that finds a regularizer\n", "through a convex optimization:\n", " $$f^\\star \\in \\text{argmin}_f \\frac{1}{2}\\|y-\\Phi f\\|^2 + \\lambda J(f)$$\n", "\n", "\n", "\n", "Where $J(f)$ is a prior energy. In this tour we consider a simple L2\n", "prior (the image is assumed to have a bounded energy), a Sobolev prior\n", "(the image is uniformly smooth) and an approximate total variation (the\n", "image has edges of bounded perimeter).\n", "\n", "\n", "Note that the parameter $\\lambda$ should be carefully chosen to fit the\n", "noise level."]}, {"level": 2, "metadata": {}, "cell_type": "heading", "source": ["Image Blurring"]}, {"metadata": {}, "cell_type": "markdown", "source": ["Deconvolution corresponds to removing a blur from an image.\n", "We use here a Gaussian blur.\n", "\n", "\n", "First we load the image to be inpainted."]}, {"prompt_number": 2, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["n = 256\n", "name = 'nt_toolbox/data/hibiscus.bmp'\n", "f0 = load_image(name, n);"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Initial image $f_0$."]}, {"prompt_number": 3, "metadata": {}, "cell_type": "code", "outputs": 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D/bskwwc7Jmi320omkyZYPoDCuvoEiU/eSDJL5rlr/mVRQ6GQjo6O1G63FQ6H9dGPflTJ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"text": [""]}], "input": ["imageplot(f0, 'Image f0', [1, 2, 1])"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["We build a convolution kernel.\n", "Since we are going to use Fourier to compute the convolution,\n", "we set the center of the kernel in the (1,1) pixel location."]}, {"metadata": {}, "cell_type": "markdown", "source": ["Width $s$ of the kernel, in pixel."]}, {"prompt_number": 4, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["s = 3"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Define the convolution kernel $h$."]}, {"prompt_number": 5, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["x = concatenate( (arange(0,n/2), arange(-n/2,0)) );\n", "[Y, X] = meshgrid(x, x)\n", "h = exp((-X**2-Y**2)/ (2*s**2))\n", "h = h/sum(h.flatten())"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Useful for later : the Fourier transform (should be real because of symmetry)."]}, {"prompt_number": 6, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["hF = real(fft2(h))"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the kernel and its transform.\n", "We use |fftshift| to center the filter for display."]}, {"prompt_number": 7, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["imageplot(fftshift(h), 'Filter', [1, 2, 1])\n", "imageplot(fftshift(hF), 'Fourier transform', [1, 2, 2])"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["We use this short hand for the filtering.\n", "Note that this is a symmetric operator."]}, {"prompt_number": 8, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Phi = lambda x,h: real(ifft2(fft2(x) * fft2(h)))"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["*Important* Scilab user should define a function |Phi| in a separate file |Phi.sci|\n", "to perform this.\n", "\n", "\n", "Apply the filter."]}, {"prompt_number": 9, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["y0 = Phi(f0, h)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the filtered observation."]}, {"prompt_number": 10, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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gedfb6empptOpBoNBm2mVnsbtKQhVm82AXZNJchmZ9Emmq+5PjU5GYFY28zCE\nVQlfqP25+Z3z02VJqmt9fc8y+deXS2A/rMxexFLq1ELJRFyjzgHgnlmHPv12GvsSo9GoXZZhJ/rx\n8VFXV1c6Pz/XfD5vBcf30Wn0oOfeBEak+sy/qcvBXGey05Ik9k8iDKsYksztBXOGjP49rUcyYeL0\nhIFdsMXPrBsr9pXfN3nGdRBdvIgQKTWMtBo/Hg6H7TF/hEF7e8tzMP1CDu8rdoTn4eFBBwcHurq6\nahNE5+fnrZM7GAw0nU4lqY0a3dzc6OzsrBUoQyK3g4IgrS6B6LIGFcNSa/uZipkMv0iEjZmb4Kf0\n9KWCFCJG19zP6nWzVSSnWjTHurvgUhcj9ymDdX4DBc+C7cV0Vm7Poa0JgbRqHi3J3CLJNSH839p/\nOByunCjhWP/JyclK1GA2m+nh4UHT6bR1jO/u7nR0dKSrqyu9fv26hUbexZQnUtCxTGbv09L8bsYz\npcbqYpx0cvl8amxCG8IihlgT2vF5hpD7rEK2mT5bXx4grei6vERFrNPkrbr28Z5DW9tZZvJAO1Tn\nd5BZM/tVQ4ZAtggZrXA51uYnJyc6OTnRxcWFJGk2m0lqGGo2m2k6nbZp9uFw+dpTh0q9AI2x9r7J\nzf51RYd4TwWZuhzrivkYFSKTrYNcVWRNWg04dAlAtqMKZVbYvWtM1vVz0/vY7hcDh6TVAXR48s2b\nN3r33Xfbd5E5ps9N85JaiMMjOGxJnPV1BOHy8lLn5+etBpzNZprPm7VCPu/y4OCgXX7tOvw8d6xV\n2jphSt8kZ3KLVG3iSc2Zyw6YQ/E9VfTH1zOcSNiTeYDKx6Bj3CccpD4BqIS7C3JV90tP94q8CCHI\ngXbCyi/hfu+991qL4D0BNHNeFuG1Pnl893A41Hg81ps3b3R/f6/JZNKuJ2JYLRemWRiSeVK7JiSq\nwpNJ1fUuK5FxcNdJS2EsnAwgrVoJ/s59xmlFKwtg6tpG2SWw65KLFIZ1mr8Km2adlUV9Dm1VCBi6\nM+Y3BOJ7ttJJqzSQNT+1o49eeXx8bJdCcJGctBp/t1UhljYRc3fROh+h67d8jkkwalBbOzJqlTzL\nECvrST8gQ6Hpp7m8nLMuAdg0YdWH9/1bBbFSOVXfN4VUpq0JAU8iPjo6ajfBnJ2daTKZtBEiafUI\nckkrWtxkIXD5knRwcKDT09P2RX2DwaDdacV7zUi2KPmdDJKm2XVVa4v6qCvJZUtVxfMHg0GrGKp3\nDVgQujLHsJTgAAAgAElEQVTXhHQUgK6QtPvGXV+pZdnfrj3ZnLt1isS0SaSJZeVYPYe25hPYCd7f\n39fJyYlevXrVOrOeaGppaTVU2CcIjJvb0T07O5Okdr+B9w0w5On/K+IhXtkeWiN+5veso2J84nZm\nqV23oRsxPceIbUmGo6Vg6JkMngkyan9TFV3axOlNhVGNTyqZbH9af5bjuXwRcEhaCgJPjiMEkvRE\nCNLJy8QVtUFiX9dDvEyGk7qXQNsypEPPNqXG6mN+1uXJs7PK1Z8Zw6eQkXkrh52Oc5IZnN/N7NV3\nQsF1vo3LrPIi/N3j0ecfrBOsHMNNLHBFWxUCY//T01Odnp62J0lLaqMyuS4kJ6RySqtJMSRyXsG5\nA68Renx8XDmlLdcK0dfgZu/Ex5VQVhbLjO9PrpzNl4u7fp61anI7c8NQQriEP3mWj3/jizloec1k\n1W5A10sN3IXRybhVSLgSmiwzmZ++XoUQ1tHW8gS0AMfHx60lcLgvX/eZQkCTSC2Q2oADwokntBgO\nl+/HSkFgHalB/UkGSEtUOb1mJh4cZcbPw7J8LLn9AQqMmZ8RrYQ2bq8Fh1rez+aLMlxGhfVpYTIy\nVUEm9j3nyHNKvuBnPp/W0ArEqwMcMXwRcMgTUa3iTIzMI1D8bKWl/L1L87JuanOuo+k7jsTX7HDy\nu8tlVINlpElnH8nsnlALhD+lZXyewkrYwQVu9Bnc3xyDFBT+VfOV41dd45xwnPo0c+Xs8pOCQsFk\nEMAWwErlRQiBQ5de4+8lENKSEfMvoQknIgUhP9NCEAensLkNkp4IpbTqnHmfNAc9ozXWotlWM7xX\nu/q7N8QnHHJZklYWB9K3snLhUhPp6UsOaQ0cnk4hcDsrpvRnQi8T8zDcKps+AMthHRVRsRg2uh4f\nLeMxJFzchLYmBHyxHjWamSvhREZKiB27fIHK/JJokag9nW8gZufOpTTJ1nzVZFoj+hq1l7U+J5C4\nlmeHssy9veblJnzlKpen+zrHjiFTMnD6CVX0Jf0e/pZQJR1iChLHmHNQfXZ9TwvqcaQVsF+5KW39\nVGqaTVJfxECq4Upf5KJLUKQlo1JjZv3Zxgp6bWKG+ZwZ3hNJq1MJL3faJWP52uHhYWsh/EkYkYyd\nwpsOtr+n09vni1X1mPrgzzpoxPo5J4yiZcJvE9qaJeC7A2zaq1AcBaYSgC7mrga1iiSxDlsFay/X\n6bbZMqTj7d+oYSsHmZEgn4bh77n0gw4oHVRbHTv1DjJY+3uzkIXDkI9RII4P4RTXZ5GZ0jp4HCzE\nvpb+G/vRRfSjKjhU+QOS2mCCLaj7+mI21XADhLSa7U14k0LQxVzJ2F1RG3/ve85tzOeGw+HKa6Xy\ns8uZNoPc39+3mH86nerq6qrFtO67J7Iqm467tTwFZTBYvvikek1V+kRWRIwOcS8HmZJjln2iYOSY\n9eF83pOWJ3/jGFhxOOnJZTBdzn0fbX1nWTJpZVYTmlS4tYJUGRXpoi5/Ieszg1aburv+z3yAGSej\nQrRG7Ctj6VU7paUP47Z5FW2fL0Tlkt+7mN9WMYMWOQ9JOVd94+V+VhAofSmG0CsnflP6pvAJpKcJ\nEF9L7cIJrAQkn+1a8FVFkxLqZHv5XMWUVaiWDq61193dXavF+N617Mv+/n6bJ6ggkSnhRmpiClhC\nn8w8k5lYZ+Y32JbKJ6ja06fcGHUjGuA4e6fgdDrVhx9+qMvLy1aReByeawWkLR+5knhP6oYqlTZj\nORXc8fc07+u0+Lp2V89mu6k5jVt9MjTPCM1oiomTSRiTiStbp2TyZHbuy+YbPjPEm8fLVHg/+1iN\nRTVGvD8VXs6P66PFmU6nevv2rW5ubvT27VtdXV217WF/nzOf0jfBSzr8Pyk1al+n1kUQMi2fv1tI\nnjtwWVZlwTiBCYH40gxqO08orQEZhSHXtKhV8ssh1Nw1ln5ZwpBURPnXlwDLMa6+ZxkZ7MiQ8cPD\ng66vr3V9fd2eIkIlYsqc0ia0tZd0+C+dItI6IfBvlfnk71L/AVfUtFlf1S7mNVLLmfm5JMLOMCeP\n66JYDy0Al3lUgQM6tH5xOb9b6zMhxrd6UjBMlQKqrDCXTlR4Pj8r4jhyLmazmS4vL3V7e9u+fchw\n8urqql0iQSHw2jD6KZvSVoSAx4Z7AB3WWgd/TOusQ58AdTF5mnc6pZx4+iRdUM6TQQeOr1O1NUif\nws6t6zBkcb3+3fcmBDLjWzh8LdcGdcHDSoFwnLpgaFq0LkXUB1utOG5ubnR5edl+0ipYIHKhXFre\n59DWLYHNdRdskTYPs1FjJnEiklKzVwJIrdZnebIMhhT7IAbzDRYCMv7j42N7erbzAVxzldGdhDyM\nArnsLkXRBWPWzUVXnN91ZLQuFYCvOZRspWGNn3maypJwZcGmtBUh8Ko/b3gnLn1Otq+KJuRv0lMB\nIIySlmuF0unrqiuXBGRIMb9XkSgyPx1B4n4rh3RwnWVmaNREzJ9LItICUDjdR1KXVagox6RL4+eY\n+ndr9tvbW11dXeny8rI9FYTzYmIoOYWJL1rZhLYiBHyR3GAwWHHcGIKstKxpndmWVjG+8SvLz7LM\nFEmV852QKH8nmUH4SSxOweNLQiS1MGYwGLQHCnvxHdfLVIvkXIcFgCfpVZuVsn9d4119sq9p1bMs\nWiy3xT6TX8Xrs2Qzk+7yqjbTB3sObc0nYNJlnZZJ6oIflRnMwapMKMtaR5Xz3FUG62Ymmho/nyOD\ncpzsM+XSB0Ip9pHhU372jRfL9Wcqi4R6XWPUBTsJyQz/pOWLx40QGEHbBA5nUOI5tFVL4PcPpDMq\nrYca1J4065wk4nhOTE4Smcf1dE1wV2w8idEe1284k5NfmXS328fASFqJ7/v1RHQEXQedZG9ZtVNM\nCFgxGMciLRjbVimCTCjyWvoq7rOZ/fLyUm/fvtXl5aUuLi7a4zJdhseM0JFzwDpfhCWws5OLzohV\nu6hyKCunU6ohT1JGfHwvtWzXs4n1XScn3FpY0kqkxvfahFdC7N+McX0cjf0Dn5rH2PjBwUF7jOVk\nMlk50tIC2BXFyXFJzU2lk4zH+/iso1gcG9d3d3enq6srXV9f68MPP9SHH36o6+vrdk2VtHwbkZ+h\nIFR8wbVYm9JWhIDrP7h3QHrqnFZaty+qUTFml4PKa9Iqzu9ifsKhxL8ZNSJDSMswMIXOzm0uRWB5\nXsV6c3PTHhbAgwPo6FsIfCarDx7LQ8Wq8SZjpRBwfJnoczm8n1EprmZ1GV7vc3V1pY8++khXV1f6\n2te+po8++qjNAbj/Ob99Ppv78yLgkImxXTJwJQRdTnIffs0sZNfzm1iMpGT8SiAoCPP5fEUICHkY\nneJnFwNm1pibYaj1vWmJO8849smc/LR1Yb/oxFaRpSob7T4zPGoIRCfYSTDnAWh9WDcFPp3vLqu2\njrb6Cle/btXwiFseycTZYV6zuaWDSAFKDFtBrVy56TZ2wTJOTjI725POKe8xs9gnMCSi+U9o8fDw\nsHKOauL/vb3lqd6Hh4ftAQbVtkla4NwC2ackGJ61X0fKsKyTd+6Hk2G3t7d6+/atvv71r7drgnxI\ncvIKYRjnhD7Onwpt9e2VhkWz2ax1+rhTKqnS2pm293XXwQRLlyWgRqycu3XOb0Zm5vP5ivPn69aM\nVgKEQdJy1WhCqtyA5EiKy7Lm90nehkA+1tKC4n657sTaVSQoLR6FyMsaHJFhMMBzyZPFB4PBylKI\nt2/f6u3bty0EYnIw36/M8fZ4sm3MlTxXMLa2lJrhLDOqtWiX1q8SaV0mMDV/nxOY7VpXfj6fWj6F\nIi0EfQJrTgsALUHG+Tk21IxWBr43M8W+zv6Z8bk/IgXDn12+DuGRnVH6AWyLrV+eEUSnnuFc7g5j\nOzkGOR6pyDalrVkCa8NcQ8OMaZdZToauYI9/k56eAdTVHteT1/hZOdJk6sSp9/f3Tza55IT5mh1l\njgW1ovF9CoTv4c4wt9ftMlyyMLou35cBgT5FweScn2Gkz30xhGM9HGcfCpBQMuEbT65gOzgGdoZd\n93Noa0JgDeIN4R4cDgDxaWokYv50rCuqnGl+ryIRKWhdMCqTXhkSpHbNSJjUwCBqY5bLdf9c/2/8\nz/e2mdGpob3TjFidjGNr4nYSd+euMffJWtpwK3M79FG4GoC+kZnf858ngrNMHq9i4j0WFH8+l7Ym\nBMwYZxSIklxpdjJlF86n5ehyrKvvSV1WoCqXTE8HOMvydTKGzT2TS6nh+foqC4GxPzfJVz6RVC/b\nqP78LMvKflugnMiz8LhteaiaLQOjRdxrQYuaQtAVcMg2EVY/h7YWHfIaj8Fg0B6fl5u83TFGjDJS\nkNnDdJ4qZqy0fn5Pf4KUGNl1JWXYVFoNj3IphLQ8VMvlmtH9LrXj4+OVMbLDe3Jy0mpkWwGXYWvr\nT2J6RnGkJfZ22xNqeiz8nTkJvzOM457Wh3kHWjv7Cfm8qdqIRGLG/MUIAeHPw8ODJpOJbm9vV94j\nwMHK/EFlQSQ90Sa+ZmFaR9VE8zsdxxSk1Fx9cMm/cbIsAFQAg8GgfXfDaDTS2dnZk7VDhkx+LpNY\nDmH6nFeGXMmk8/n8CRStImSpcKjxK2XE/qQWT4vB8eJzXGFK/4AKkD7DixACrlsZDodtvLnvROHK\nESZxkP3p69JTTf2NRIGS0olORznb5naw724LNSeZ3CFG4v6MYlHIcvmFtbsjMnkmDxUOgxKbQEQ/\nn8oq21U9S4WQEJjWg2NqyohfhndfhBA4Oba/v6/ZbKbRaKSLiwsNh82b5BkXJ3U5qPxeCYe0mrGs\ntDyv89l0yDOPUDnWiatZPrWi/5wj4SFaro9wx3BI0oompNbusgQ3NzcthLJVoODaErjtjiRxC2w6\n9GmF1wlOjnVG1ThXhFC+3/DPm248DoRuDgg8h7YiBE6PS8tFZScnJ5Kkk5OTlUiIKTWW1J3VzclJ\nfF+FUytni+Xlb4z5JyWcY71kMpfpl5IfHh5qPB6vwKW9vb329VW5Vij7kQJB/2A2m7XQyXVyrNxm\nwyHmK0wJP/sohZ+fKURdgQzCIrfJPgTL4WpaCsimtDU4xFCWdxAdHh5qOp3q+Pj4CcPTLCbGlupc\nAKEHmSefrajLed4EJuSEUogycmRc7QOK/R5mM7SVBDfEVPUyZJyWzsLgrK7fc0DtXpVbMWYFT9ZR\nV5SpGp/qkz4WLXIKaiqBTWmrG+3J0H57jCd8PB4/cQSlVZyZmoVUTVgySd7r7yw/I0H+nVrWk1M5\ng1mWnXSGRv2iEq//J1SxVTQlBGKwIC0T4aEjMHa+KYRdY+JPtychlJ+rFEPXNdZfjbnHL/+vhJAJ\nOgr6i9ho78kydvPA3NzctLjv9PRUe3t77Qv3aBYJcXJgErOnE5WUpjh/8ycdtT4o5bbwfvbZGNZa\nfn9/+Q5nQkDXyRAmJz4FgQKZwud7eKI1nXHe91wL2WcZ2fe0jMTxm84J58G5Ewoz+/wc2uqyCWI6\nryG/uLhoneSzs7M2f1ARB4twg791UTrU0tMdVIRiKQRMDNF5TCxLRmC5xud2VJ1hrXDxJmPZ1Rcy\nfSWIXJjXFyToG8eue/sg0Loys5y0yAzvuq+bjFVFW1tAR6a1dru9vW0jGNPptIVCmZ5nGWmuqc0S\nH/NZUhXZYHQiY/F0WofD4UqkJn2ZdKCt1Q2D/K7lo6Ojtp005xkarLQkhSW/mwiZ/L/bTuvZp503\nFYyu59d977o/rb7H2XmGPGFvnZAlbfU9xtxN5USIhcDJMzOLE0YJEaTV3EG+5SYtQyVI/k5KAaje\nrXZ/f9++W8CbQUhVZMplct2/4/+SVtpvGMOJpaBlToF9Su2eQuD22bnk/fQ1UnlwzIjt0xlP6vId\nuiixfmWteSQNLS+XVW9CW31xH+EE/QT7Bt5xJKldF29nMR3krsFnnZUG6tJKZDKubLQwSFrB2JVj\n2hXJYnsSLvm3FB4KMCMkFixqSJbB+1Oj+j6WS0FIRVKNU7bZVPU3YU0fUSj57KZteQ5tRQiMg6Xl\nElivR/ex5Y+Pjy1Wns1mKyl9LiSTlomjdIKrSIipgkdmCFoNaiCv5XEY09EWf0+tSGKZXIZsK8jJ\nTo3s5zK+TitA60GqnPhqDLIct63KRbActqsS6HX0HD+kmpdUJM+1ONIWhYCQyJ2yNjW88DEcDw8P\n7dsuB4OBJpPJk6W0kp4so018nhrR3yt4QWhF8zocDtulC66DmjM1fKWRzWyGgD5XKPuUm10S4tD8\ns56KcSsGqaBOZVUzAZfPZj+7tHMXc6bF6RIGWq1KqRE+Poe25hNIy04xkcMQIN9Q6N1LDoslI/g7\nKQeeTMJ7LCiEFdbQ1MTGz8ahvo9tznqrvIa/J0Z3ueuYhfVQ8KoxqOp2nzLE3KdBq7Gr/q8sYRfk\n7NPaXYLA/IK0uuI0LdKmtNUX90laOT2B2/SkBubYP/ALLpxP8J5ahi75lybTROZjmNODaaHzSQiO\nnrx69Up3d3ftWT7z+XzlZRv0D9IacJdUJu7ohHLJgu/hp1SfnJ19rIjMSiXEcUmfIsePFi+pgpf5\nf+WXEesnM1d+XpZVQdBcJLiOtiIExvqGGnd3dy3ESGfI2WWf7T8cDtslFo+Pj0+ek5aOt7/7k0kl\nJtNsjeyP+E0ofh0Qtyz6DNXhcLhydlJqefokjBqRsWktMreQfeJn5ehWMCbrTK1NK2VI1ud8r4NE\npD6hzN8ISRP+9UEk+i70X15MdMgdrn7jpyfakIkQSaqPCGRZXRqNDGMm9lsl/XpVHgHCgbYloTOe\nVDFe1TZJK9Gnru2l+XxVDy0Nf8/+dvkKXX1JC9sncM+FIuueSciX8JIZc+ZqnkNbXTaRO4ZoAaSl\nc+pjWbz8ejqdtvkER45YbmZ7PWHW2j7ygwz9+Nich3NxcdHCobu7uyeOmNskLYWnYtTqGpmM+34J\n7egTUPCzTP7f1Q62tXJu7YN4nPqcymRAWtKqTdXzXdcrh5pJxoRQbqvhsxWXczYvwjHm8eNc8JTh\nLkeJ5vN5y7iOzhDPZ3Y3LYDL8iBdX1+vvPHEbbCgeWK9nuf169c6PT1tz/OxwGZiS9IT4ZPqpcPs\nb75Oic9yTVAfnKmsBiFCZbUIcdyeXAKSVrRKznXBtor6IkdUggmLfR+Vkbfo8l1mL0YIciOEmZdS\n7994SJXXEfGgJzI/mYjZWlsBM7lPQLMf4PXo3Ofqk5+9x3c8HrcrPMlYGeFxmzixVSydfaS5T8bz\n9wrqVXkRlp2ZZ/6eESI/Q2b0GFaOLnM0CaX6IFwfXNnEj+A93EOQf8+hrS2lpvb2bipDlWpDtd8B\nTKZPBvIOLU8QGZybuYnv+Tqg+/v7Nl4/Go306tUrTSYTvfvuuzo7O2t/s+VwsswT7T7RwXR91rKp\nvX2d6/urCff9qRWlbiGgBaiEVXr6wvPctN4lmHmd88U8BdvC39j+SnNXDnEKgK17bs/t8m26aKvv\nMTYMYOIo3zRCjWrHldDAjDUYDNqokyeQB7xmvN9xfsIamvr9/f32SMPj4+M2S2wz7EnwhHL9CmPX\nUncsnX2wQEla0bJmYIZTXUZlOclsfDaPXiG2rjQw25wQM60w58nktlBwU2m5bI99Xu8KBHgO7AdM\np9OVN9u/CCFwZ2kNqCESK/OMUiax+Ixj/dRMPONSWm7P41p0aZlpNvTKpRPMRZChUmv3wZk+U+++\nGObRivRBGhKZzv9Xz7oPHs8uRmObzaSpwbNfVTg1fTMqG1oaltU3Zh57B0x4AkX6ZZvSVleRGrpQ\nU3B/sffceqWlIxl+nQ8jQV6IR+jBvcx7e3ttBMabWAaD5syjvb291legj5J/aeKT6avlGbyeSRwy\nrt/fdnd39wRzU8vlOLKudIJ5shuZMsOcFU5P4WDwwtY3LV6OAxmeY0GlREu0iV/kiNDV1ZXOz891\ndXXVQmjzz4sQAjK6O+hkDc8eOj4+brdY8vSDm5ub0ik1w3iieIQLrYCdXfsRklZeozQcDts9v3wh\ntjUo4/iGNtLTUKiZhNCrCi1WK1BzCQe1c+Wo+hkziZVAHl2YmtztrrRu5dS6Prc3d9CxjelXVJq6\nL4qU5czn81ZZefOVoRCfeREZY3cstSgZdW9vb+WsHWdofW8O8qb1EoqZmS14Hry0Rt4GaW2ce3VN\n6yaUQsL/fS2FhBo1rUqlKekMMyjg/vZp/L6oTd7nz4zwsR3ZRn6uoxQAWi/7jfmmIxMXIW5KW4ND\n7pwZ0Zr45OSkZcjT09P2HKLsKKWd+065XMKWw//T9Bse+TBcD7I3wR8fH+v09LQNj9KHoJVJ5iCZ\nkfuiHxUD03pRg/L+dE5Zv51GL0l3X3luaF8Ys+96lx9B55ZERZHRrKrc7JefNwIwBLIVYF6HAvMc\n2mp0iJtWzOg+W8fYfTKZaDAYtOHLx8fHla2OTJgRXtFU01lkVEdannvkZ+bzeSsE9h0Ih9ISJAzo\nczSrMZC0Yu55P/cCmyoMTo0pLU/zsBC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"text": [""]}], "input": ["imageplot(y0, 'Observation without noise', [1, 2, 2])"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Variance $\\sigma^2$ of the noise $w$."]}, {"prompt_number": 11, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["sigma = .02"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Add some noise to obtain the measurements $y = \\Phi f_0 + w$."]}, {"prompt_number": 12, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["y = y0 + randn(n,n)*sigma"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display."]}, {"prompt_number": 13, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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GwCg9oyXJxv8wUEmGwfmaLIFTMpvwsDiG3gVekFGhT8MwtOk437X1zaR6vW4N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\nSyQYDoc/dAr58hWeVI1OlQBfXl7mS66h3lQJ3nCxWKRC0y2NvKUXVT0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"text": [""]}], "input": ["imageplot(clamp(y), 'Observation with noise', [1, 2, 2])"], "collapsed": false, "language": "python"}, {"prompt_number": 14, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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PuTPnAVBxcFKG3W6n8Xiser0e5Tp0GFI7b0lGc2F8FotFrK7kPzYqmUwmwQxJ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\nIQMrQTiZmhrMrqq5w13ZGdFN4bBKutPT0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"text": [""]}], "input": ["imageplot(y, 'Observation, SNR = ' + str(round(snr(f0, y),2)) + 'dB')"], "collapsed": false, "language": "python"}, {"level": 2, "metadata": {}, "cell_type": "heading", "source": ["Deconvolution with L2 Regularization"]}, {"metadata": {}, "cell_type": "markdown", "source": ["Deconvolution is obtained by dividing the Fourier transform of $y$\n", "by $\\hat h$.\n", " $$f^\\star(\\omega) = \\frac{\\hat y(\\omega)}{\\hat h(\\omega)} = \\hat f_0(\\omega) + \\hat w(\\omega)/{\\hat h(\\omega)}$$\n", "\n", "\n", "Unfortunately this creates an explosion of the Noise.\n", "\n", "\n", "To avoid this explosion, we consider a simple regularization.\n", " $$f^{\\star} = \\text{argmin}_f \\: \\|y-\\Phi f\\|^2 + \\lambda \\|f\\|^2$$\n", "\n", "\n", "\n", "Since the filtering is diagonalized over Fourier, the solution is simply\n", "computed over the Fourier domain as:\n", " $$\\hat f^\\star(\\omega) = \\frac{\\hat y(\\omega) \\hat h(\\omega)}{ \\|\\hat h(\\omega)\\|^2 + \\lambda }$$\n", "\n", "\n", "\n", "Useful for later: Fourier transform of the observations."]}, {"prompt_number": 15, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["yF = fft2(y)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Select a value for the regularization parameter."]}, {"prompt_number": 16, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Lambda = 0.02"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Perform the inversion."]}, {"prompt_number": 17, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["fL2 = real(ifft2(yF * hF / (abs(hF)**2 + Lambda)))"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display."]}, {"prompt_number": 18, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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sMe7lFm1GT3tt35+Cr2ZI3FYPmu+7i4FkTEpDZFjCezgfQuaRi3ByNR/lSiUl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\nB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"text": [""]}], "input": ["imageplot(clamp(fL2), 'L2 deconvolution, SNR = ' + str(round(snr(f0, fL2),2)) + 'dB')"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 1:** Find the optimal solution fL2 by testing several value of $\\lambda$."]}, {"prompt_number": 19, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["run -i nt_solutions/inverse_2_deconvolution_variational/exo1"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display optimal result."]}, {"prompt_number": 20, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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TsFNBFoeHh3V5eVmTyaT3FiuukfkBZGN9yjXN3A861gonMqxMRpZ6ksnPlPdj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"text": [""]}], "input": ["imageplot(clamp(fL2), 'L2 deconvolution, SNR = ' + str(round(snr(f0, fL2), 2)) + 'dB' )"], "collapsed": false, "language": "python"}, {"level": 2, "metadata": {}, "cell_type": "heading", "source": ["Deconvolution by Sobolev Regularization."]}, {"metadata": {}, "cell_type": "markdown", "source": ["L2 regularization did not perform any denoising. To remove some noise, we\n", "can penalize high frequencies using Sobolev regularization (quadratic\n", "grow).\n", "\n", "\n", "The Sobolev prior reads (note the conversion from spacial domain to\n", "Fourier domain)\n", " $$J(f) = \\sum_x \\|\\nabla f(x)\\|^2 = \\sum_{\\omega} S(\\omega) \\|\\hat f(\\omega)\\|^2 $$\n", "where $S(\\omega)=\\|\\omega\\|^2$.\n", "\n", "\n", "\n", "\n", "\n", "Since this prior can be written over the Fourier domain, one can compute\n", "the solution to the deblurring with Sobolev prior simply with the Fourier\n", "coefficients:\n", " $$\\hat f^\\star(\\omega) = \\frac{\\hat y(\\omega) \\hat h(\\omega)}{ \\|\\hat h(\\omega)\\|^2 + \\lambda S(\\omega) }$$\n", "\n", "\n", "\n", "\n", "Compute the Sobolev prior penalty |S|(rescale to [0,1])."]}, {"prompt_number": 21, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["S = (X**2 + Y**2) * (2/n)**2"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Regularization parameter:"]}, {"prompt_number": 22, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Lambda = 0.2"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Perform the inversion."]}, {"prompt_number": 23, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["fSob = real(ifft2(yF * hF / (abs(hF)**2 + Lambda*S)))"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the result."]}, {"prompt_number": 24, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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MYszLrTFQK4EPrfWycAbdxkLBINirkbtZaZtnKqjTlDATVOkFKQ4lzKgoPBuj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"text": [""]}], "input": ["imageplot(clamp(fSob), 'Sobolev deconvolution, SNR = ' + str( round(snr(f0, fSob), 2) ) + 'dB' )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 2:** Find the optimal solution fSob by testing several value of\n", "$\\lambda$."]}, {"prompt_number": 25, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["run -i nt_solutions/inverse_2_deconvolution_variational/exo2"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display optimal result."]}, {"prompt_number": 26, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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JOByDTMpNvcintd4DAwOM3TbunbNGydTyN+q1srs+6wG/ZX4kWUqGsLnIykZL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\nIyBBJ4hpTeWurq76R2I/+uijqhqCA9NvSWUxaAvHlJjzEaqpvethoDJ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"text": [""]}], "input": ["imageplot(clamp(fSob), 'Sobolev deconvolution, SNR = ' + str( round(snr(f0, fSob), 2) ) + 'dB' )"], "collapsed": false, "language": "python"}, {"level": 2, "metadata": {}, "cell_type": "heading", "source": ["Deconvolution by Total Variation Regularization"]}, {"metadata": {}, "cell_type": "markdown", "source": ["Sobolev regularization perform a denoising but also tends to blur the\n", "edges, thus producing a poor results on cartoon images.\n", "\n", "\n", "The TV prior is able to better reconstruct sharp edges. It reads:\n", " $$J(f) = \\sum_x \\| \\nabla f(x)\\|$$\n", "\n", "\n", "\n", "With respect to the Sobolev energy, it simply corresponding to measuring\n", "the L1 norm instead of the L2 norm, thus dropping the square in the\n", "functional.\n", "\n", "\n", "Unfortunately, the TV functional $J(f)$ is not a smooth function of the image\n", "$f$. It thus requires the use of advanced convex optimization method to\n", "be minimized for regularization.\n", "\n", "\n", "An alternative is to replace the absolute value by a smooth absolute value.\n", "The smoothed TV norm reads:\n", " $$J(f) = \\sum_x \\sqrt{\\|\\nabla f(x)\\|^2+\\varepsilon^2}$$\n", "\n", "\n", "\n", "Regularization parameter for the TV norm:"]}, {"prompt_number": 27, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["epsilon = 0.4*1e-2"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["When $\\epsilon$ gets close to zero, the smoothed energy becomes closer to\n", "the original total variation, but the optimization becomes more\n", "difficult. When |epsilon| becomes large, the smoothed energy becomes\n", "closer to the Sobolev energy, thus blurring the edges.\n", "\n", "\n", "Unfortunately, this prior is non-quadratic, and cannot be expressed over\n", "the Fourier domain. One thus need to use an iterative scheme such as a\n", "gradient descent to approximate the solution.\n", "\n", "\n", "An iteration of the gradient descent reads:\n", " $$f^{(k+1)} = f^{(k)} - \\tau \\left( h \\star (h \\star f^{(k)} - y) + \\lambda \\text{Grad} J(f^{(k)}) \\right)$$\n", "\n", "\n", "\n", "Regularization parameter."]}, {"prompt_number": 28, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Lambda = 0.06"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["The value of $\\tau$, the step size, should be smaller than twice the\n", "Lipschitz constant of the Gradient of the functional to be minimized,\n", "hence:\n", "$$ \\tau< \\frac{2}{1 + \\lambda 8/\\varepsilon }.$$"]}, {"prompt_number": 29, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["tau = 1.9 / (1 + Lambda * 8 / epsilon)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Initialization."]}, {"prompt_number": 30, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["fTV = y"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Number of iteration (quite a large number is required)."]}, {"prompt_number": 31, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["niter = 300"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["We first check that the discretized grad and -div are adjoint one of each other."]}, {"prompt_number": 32, "metadata": {}, "cell_type": "code", "outputs": [{"output_type": "stream", "stream": "stdout", "text": ["Should be 0: -1.08002495836e-12\n"]}], "input": ["a = randn(n,n)\n", "b = randn(n,n,2)\n", "dotp = lambda x,y: sum(x.flatten()*y.flatten())\n", "print(\"Should be 0: \" + str(dotp(grad(a),b) + dotp(a,div(b))) )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["The gradient of the smoothed TV energy is:\n", " $$\\text{Grad} J(f) = -\\text{div}\\left( \\frac{\\nabla f}{ \\sqrt{\\|\\nabla f\\|^2+\\varepsilon^2} } \\right)$$\n", "\n", "\n", "\n", "Compute the gradient of the smoothed TV functional."]}, {"prompt_number": 33, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["repeat3 = lambda x,k: resize( repeat( x, k, axis=1), [n, n, k])\n", "Gr = grad(fTV)\n", "d = sqrt(epsilon**2 + sum(Gr**2, axis=2))\n", "G = -div(Gr / repeat3(d,2) )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Compute the TV norm, usefull to keep track of its decay through\n", "iterations."]}, {"prompt_number": 34, "metadata": {}, "cell_type": "code", "outputs": [{"output_type": "stream", "stream": "stdout", "text": ["Smoothed TV norm of the image: 2479.77\n"]}], "input": ["tv = sum(d.flatten())\n", "print('Smoothed TV norm of the image: ' + str(round(tv,2)) )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Perform a step of gradient descent for the inversion."]}, {"prompt_number": 35, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["e = Phi(fTV, h)-y\n", "fTV = fTV - tau*(Phi(e, h) + Lambda*G)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 3:** Perform the deblurring by a gradient descent.\n", "Keep track of the function being minimized."]}, {"prompt_number": 36, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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LgbOBT0bv/xY4BXg/cBbwInAY8Hvg2LK/rfrqoKK5c+Hmm+Gkk+opsiSlV7NdHbSWcNIf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\nB/t/y6wYEGPf+YgAAAAASUVORK5CYII=\n", "text": [""]}], "input": ["run -i nt_solutions/inverse_2_deconvolution_variational/exo3"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the result."]}, {"prompt_number": 39, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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lxy6i8kVOvIjtePEabyvqf4p8OfV6vbCVHLsrMf4QMMeOXVY2CjTvPDhwI6Di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"text": [""]}], "input": ["imageplot(clamp(fTV))"], "collapsed": false, "language": "python"}, {"level": 3, "metadata": {}, "cell_type": "heading", "source": ["Exercise 4"]}, {"metadata": {}, "cell_type": "markdown", "source": ["Explore the different values of |lambda| to find the optimal solution.\n", "Display the SNR as a function of |lambda|."]}, {"prompt_number": 40, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["run -i nt_solutions/inverse_2_deconvolution_variational/exo4"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the result."]}, {"prompt_number": 41, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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8MXquro3HD7QddJfUkuQsk5KuNjwUjla5RU4aA9CJ78ht0/26dEmlEC3Vsjwd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\n3HZBdYXpUDfqlyaGUQlH8F2ViKOJ1WoVBmdz5an7orzMoZBtUIXyJ+L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AaYoxuqNbtVtl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"text": [""]}], "input": ["imageplot(clamp(fBest), 'TV deconvolution, SNR = ' + str( round(snr(f0, fBest), 2) ) + 'dB' )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "code", "outputs": [], "input": [], "collapsed": false, "language": "python"}]}], "nbformat_minor": 0, "nbformat": 3}