{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Sparse Representation in a Gabor Dictionary\n", "===========================================\n", "\n*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) 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"], "metadata": {}, "cell_type": "markdown"}, {"source": ["This numerical tour explores the use of L1 optimization to find sparse representation in a redundant Gabor dictionary.\n", "It shows application to denoising and stereo separation."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 2, "cell_type": "code", "language": "python", "metadata": {}, "input": ["addpath('toolbox_signal')\n", "addpath('toolbox_general')\n", "addpath('solutions/audio_3_gabor')"]}, {"source": ["Gabor Tight Frame Transform\n", "---------------------------\n", "The Gabor transform is a collection of short time Fourier transforms\n", "(STFT) computed with several windows. The redundancy |K*L| of the transform\n", "depends on the number |L| of windows used and of the overlapping factor |K|\n", "of each STFT.\n", "\n", "\n", "We decide to use a collection of windows with dyadic sizes.\n", "\n", "\n", "Sizes of the windows."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["wlist = 32*[4 8 16 32]; \n", "L = length(wlist);"]}, {"source": ["Overlap of the window, so that |K=2|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["K = 2;\n", "qlist = wlist/K;"]}, {"source": ["Overall redundancy."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "text": ["Approximate redundancy of the dictionary=8.\n"], "output_type": "display_data"}], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["disp( strcat(['Approximate redundancy of the dictionary=' num2str(K*L) '.']) );"]}, {"source": ["We load a sound."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 1024*32;\n", "options.n = n;\n", "[x0,fs] = load_sound('glockenspiel', n);"]}, {"source": ["Compute its short time Fourier transform with a collection of windows."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.multichannel = 0;\n", "S = perform_stft(x0,wlist,qlist, options);"]}, {"source": ["__Exercise 1__\n", "\n", "Compute the true redundancy of the transform. Check that the transform\n", "is a tight frame (energy conservation)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "text": ["True redundancy of the dictionary=8.0586.\n"], "output_type": "display_data"}], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display the coefficients."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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vIv2HIANob6QdakVLuyJlxrR1/Kb1raUj+LaeCn0t/gMdQXRCJxP6NtAOMWt9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cbiB/A1QAV6nb78PHB9wNmsBTYNNNHdfwiBn8um+9ugjFRV+vxXGvTqA0HsknLyR2oAny2EgQ+H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\nAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["plot_spectrogram(S, x0);"]}, {"source": ["Reconstructs the signal using the inverse Gabor transform."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["x1 = perform_stft(S,wlist,qlist, options);"]}, {"source": ["Check for reconstruction error."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "text": ["Reconstruction error (should be 0) = 1.58e-16\n"], "output_type": "display_data"}], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["e = norm(x0-x1)/norm(x0);\n", "disp(strcat(['Reconstruction error (should be 0) = ' num2str(e, 3)]));"]}, {"source": ["Gabor Tight Frame Denoising\n", "---------------------------\n", "We can perform denoising by thresholding the Gabor representation.\n", "\n", "\n", "We add noise to the signal."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["sigma = .05;\n", "x = x0 + sigma*randn(size(x0));"]}, {"source": ["Denoising with soft thresholding.\n", "Setting correctly the threshold is quite difficult because of the\n", "redundancy of the representation.\n", "\n", "transform"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["S = perform_stft(x,wlist,qlist, options);"]}, {"source": ["threshold"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["T = sigma;\n", "ST = perform_thresholding(S, T, 'soft');"]}, {"source": ["reconstruct"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["xT = perform_stft(ST,wlist,qlist, options);"]}, {"source": ["Display the result."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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7yCbkPeQ4cgk5jBxDDiIHkfeQi8gR5BiyBXkb+Qj5ADkE8LJskQ+Qc8gRZD9ymgsyRzZx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hH5MzWRvDAP7+t5akZPqJaB6/M1za9PJklCD7wYhEB9SZD6vgoQWBRetGggeNZPYkuwUP5OfTjn\nUh8O2VFXU/U5FeyoORBguXHi8C2zqkZQPHwntmd+lwmS6FP/inXBwh7pd0goUPV5hFJnVY3gZJme\nKRMrqMowkfqMiS82No/kQCzNkoQlap8g1g0k8hA1Sp4IjGiE1wJeGyP0oSNoChbSk6p/qPd1BtHm\nQRM1gK+EX3/QC+KCDwjCHHiNJNxhvhglFn84M10fCCgwf4r/282xz9xLFabp+TVGblZgCrO6SrIC\n85GHCf7pgfybGiLPrNoLWhwoIabkpy2vyYFg4WYs85VkrzQroVRINXG8n5KIr2Y/jscUqAm4jai5\nXE+pEC/O5MMp+iRrXzrkZgVWNr/Lc4oL1gNo3vUHcWrMxiBtyWQhMcOjvbbo5X88vpebg4UtlDs5\nOQUmDWPPCcLxPGjmBfAQZQN7PnBN0qWbMjlhq+wPFt4piJ9fLhcGC78VO4iLUiaZmOLqNhl0F8N7\ngnRWqwBB7wPS9WAeNUB/mGqAbqB6aiXEVZD4suo62R0sJCpJyqoKNFp8WXWW9H8jfwnqe3iPqg8Z\nQJKO36Wy83mj5bmCGiRrjNNgBdZDPWAhbjedIv3z9B8Ez9OzQX5PrcAuiSvLadHiEJN3PN1HXcCv\nTJso/aE5KOXEQUEaWk62UCqyk3G7X/AZadlZAS87cmJ0iViW5pq1TwmJSMYKxFXGZo48Tn0456Vb\ngfUEulAhB9IhB1W0OV29EMOgtfaCVH7HJe7ENh2fS8IIdq0IhhqNK5Q9ZmMDEZO7cu1LxM/JmBty\nQUisPKkIJNK4STgwYlfjvGAh6V/a0E9FcJNL2eCNqKjYY41TgoVkkC/pSrodxCykmQqn6kM3cXd0\n+EoOrLiWqCUplcjmJc8kCymly+hjRNjW0UAgWNcw5ZRLhvZQBuUT3ZOChS1HieD60U6iPlT4Sg6c\nOHImwJKSSIClnIDngHupefrrebXoTpaEp8BvlBt9dSAzO9wqSN/E8qHXeYJwOk1J9hbK+N0vIvYu\nMaQ9j0xf8o4gZxw1xstU+zyQ+YfMAiw7ggusNCsw0kEraKAGcLEIjJIXUL3nlyqJAWJY6aPOIzMq\nESYwHFx4VbDwakGYl+Jbp4IE468BrMXaYGH8wKDx5DWqD9yXfR9YIP3N+4Eg3sKDkrDBpvQIl59S\nAuwG/9f0kSQ0aTcLMhUHE0Z24dtZwQIsO3zWr/g2sHslkSKMDuW7hhqVvog3KqUzCL8lCcPG3YKw\n8WQOGeoY1G+gWgb8WiMoQlBCiqQR8Cjhehd0xvnfECUbzs9edh6ShCfFlYIyMcYjfkueFpwVGDH+\nGk9dSHAceF3cV/vSITcCzJBUgAUuUFIHkjJuJgdkHg4F4Cbqmh/HuuY8SWSj+1AQyWFzAe2lKcjM\nqSmgplk9B4hCOjVa7PdViVVdXknphR/0j0ACP7IgT0nC/vYfkYlLec7c6HMmwMrwQryNSkdfPTfo\ncYLOS0RF9Y8jdJql1VSegP9Ww1JCQq4bRinb+seCzFabV+ppwRQ/oVcC89Ia6synq7GKqsTMj/J3\nvb32pUNuBFjkMqvUnz6SNwWvVh0dfTBrBhKlDKZiGOm4kCBp1KHVIhgKg1LRMFWBDizbQekAbyVa\nkrTzjWOq5WmS8Ocko7s6KF9J0uvvVUEaV7NmEtV7Y8ceBCkrj2Lt8jyVIZrMaRLfRTloy7xZfFz7\n0iFPAsznnRFTgN0kPwpejZ4s/0p9NhWwLtQ+CbSpO6lGuyXQaIeo066M3bY/Ej+/qp14iamyHqTj\nGUnsnvPkNiIfGO7MulPdRTXv2+PWdcc3+js4MVpHpf97aD0Rg4/HiUarmufnOHKT9LvLfixurn3p\nkA8B5jNlkW6HJb0QyQcU4/Ztkx9DI7XlIjl5D2ZNJFMmVoQ6E/APBx7nhZTPQpi7JlK63MxjM+6Q\n/sgnjKtHeI7VjxupTv5Quo6R4prxF1tpkYFKihxIhxxUUZGtG33N8RbVxYO5+kCnNM2cOnOvqA4p\no7/vku3BwrfFQNn1qQhBE1H88KPPqU5+bR4mQJWQallTgbBIdqPPjrLd6GkBFjvdNcPERM6jtjDu\npk4lg5upgJ+RrrN8JaT/yBiVx3M/tS/y7YLah/gz4nO4ZiZhIkqZ4YXgcupL/DbjL1H2UK+GhEyS\nQuhH6DNHW2Il3QC1kd7/Roj31dMU2780Pt9TbX5JLrdTyY0AMyQWYBupB6zK7CmtE8c4coTq4pel\naLTJ1AV/q68ZwxvUM96Th2esQFrbuFRlr+T42xXFJ91ekbVHcJX5UA6kQw6qaLCVhGXHgU2Q/6Ca\ndqM01JhlfjzJg/apIpkUgik/KpDvo9ZYKomUgm+KwerXpIIsCLzZD6g3+yDV81/Kvg8oGf+vOMMu\nrH3pkCcBpshGhUhSHb1i7B7JhiiGIGsXcwDYQ13zxmpIStp1U1BJz2qN8YsDqxasQswIn0yqlADL\nKXkI+WKi+Zt6jym3/WWY8mEBlh3ZeiGeI4ntMP4QVFxIcFkWf00WM0aqBOMYfZm9R9NxqinO49GZ\nIaiEyaruIRU2DohPLPaORSzAxpvTYgV2GhCMskReUjelm8SkoRLauSPSn43sMkHtRXY68A31Zkkf\njqooYysAC7CsyWxDy2AQKwBi1QFcUZXOF397jmACwKyz/yH1FPh+6Q+0JFMQVW+JeRXVvF/ldFjJ\nnlxYW1Mm+x9HEuh7agsWYJli27rYBsakJJi6MGXewimSiDz/QWwLFiYYiwP5MCdvJyb5VdvGM7iq\nq4TDRZVUiLGdthLEwwTzWQAgNsoFnqv9+RMLsOzw+W5UYjsVphyqkhKe8ZhGNfjXRIPXnN71I6rm\nN+e2q1TCHTQelQwz4O1UKkMKAZZXiUVmTewObMBc91vD5JqJkph+x8+FSG0zWEehskiSUoBKF4Lr\n4/2cyj0xu4PIKnICRJrBr8WuWHepN3gFlhHBZL51JsASJD/9MvApXh13CKjaFoXjmXH4tKQiWSFI\nbViaLNhxMxglgdqmABenuOb4Od3UHizAsqacFdhd1AOmyWeRYg9i5rQja/8R2uHiAOUYTWYqyUNO\nExLeIdqQcllPE8z783YOpEMOqmiTmRdijRG1Aivk4iniUeFnSbnxWGKye5z3qZoHds58VBK+A8+R\nfgLlrJYSP84aavwYQHuwcDwy6+f+wzGeQT+IS6bI7/Ux4RlUAXgFlh22FjHZfmCxe3DQ+RvptqBN\nsL/GbGrw+sSogM4HftXHsfzNxtlz95nA4zxpBtPcjykAsFU/4J0CW3V/y3ybynFQxtbw2yknU0no\n41Qtgdbv1I3OTXqjzF5NbCdPFmDZUfaOzLX7QSbA6rtBpX8ajf84UOEh8mdqsLgwDyuwmiCbx3lC\nEtu7/FeMpb9yQurp7VT/WXIgwIh+VrP4BFXt87AkQmReEER+BBKzze47wj7Ol7iqOjvGuwLlQ+3U\nhRTRxOMXvh1fVl0uFwYLvxXj9hZJrckIiA85e9fEoN4CtuqCIciTAAu6b8TDt5dd6lkM6Z01QJS9\nEF/YUOoRW1Z528MHVxgVXF4UE1+HE/Q3S+lsFp/YbtlvyGO+kns2bCbOe6QCNa/KJli5SDUyjrKK\nJP4O2tmTUlYF/ZNRwkV5CnXmD+rM2Dt/1ga5USEakmejZxiGYRJT+9IhHyuw5Ksul9p/AQzDMEx5\n5GYFVt52KgzDMEy9khsBxjAMwzA2/zfeFWAYhmGYcsiHDey0xU6dpUryuGKOVP/mizp7HEV99DQE\nMh7k+nHqsqdlCwuwGsX+Dn1+lXnsu3YIBD9OrWE6Wx08C0o7JOfrcYLbH+b6cSoEqxBrFCll3XTQ\nunkQRZ09Tv0NhUKIuomfUc9SZy8oQ3gFxlSJevoO62Z8rEt8utD8wuutSFiAMRUndznAIqmbIVI9\ngv3fvFNP3YyJhFWITDWom2GlPkZ5g9SgLt5Rnb0dJhJemdY0deAbFtxNG3l+HNSpb1gd9DRFPeU3\nqMueli0swBiGYZhcwipEhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFy\nCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMY\nhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpew\nAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEY\nJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQsw\nhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFy\nCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyCQswhmEYJpewAGMYhmFyyf8DqAJxazJysykA\nAAAASUVORK5CYII=\n", "output_type": "display_data"}], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["err = snr(x0,xT);\n", "clf\n", "plot_spectrogram(ST, xT);\n", "subplot(length(ST)+1,1,1);\n", "title(strcat(['Denoised, SNR=' num2str(err,3), 'dB']));"]}, {"source": ["__Exercise 2__\n", "\n", "Find the best threshold, that gives the smallest error."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Basis Pursuit in the Gabor Frame\n", "--------------------------------\n", "Since the representation is highly redundant, it is possible to improve\n", "the quality of the representation using a basis pursuit denoising that\n", "optimize the L1 norm of the coefficients.\n", "\n", "\n", "The basis pursuit finds a set of coefficients |S1| by minimizing\n", "\n", "\n", "|min_{S1} 1/2*norm(x-x1)^2 + lambda*norm(S1,1) (*)|\n", "\n", "\n", "Where |x1| is the signal reconstructed from the Gabor coefficients |S1|.\n", "\n", "\n", "\n", "The parameter |lambda| should be optimized to match the noise level.\n", "Increasing |lambda| increases the sparsity of the solution, but then the\n", "approximation |x1| deviates from the noisy observations |x1|.\n", "\n", "\n", "Basis pursuit denoising |(*)| is solved by iterative thresholding, which\n", "iterates between a step of gradient descent, and a step of thresholding.\n", "\n", "\n", "Initialization of |x1| and |S1|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lambda = .1;\n", "x1 = x;\n", "S1 = perform_stft(x1,wlist,qlist, options);"]}, {"source": ["Step 1: gradient descent of |norm(x-x1)^2|.\n", "\n", "residual"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["r = x - x1;\n", "Sr = perform_stft(r, wlist, qlist, options);\n", "S1 = cell_add(S1, Sr);"]}, {"source": ["Step 2: thresholding and update of |x1|.\n", "\n", "\n", "threshold"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["S1 = perform_thresholding(S1, lambda, 'soft');"]}, {"source": ["update the denoised signal"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 23, "cell_type": "code", "language": "python", "metadata": {}, "input": ["x1 = perform_stft(S1,wlist,qlist, options);"]}, {"source": ["The difficulty is to set the value of |lambda|.\n", "If the basis were orthogonal, it should be set to\n", "approximately 3/2*sigma (soft thresholding). Because of the redundancy of\n", "the representation in Gabor frame, it should be set to a slightly larger\n", "value."], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 3__\n", "\n", "Perform the iterative thresholding by progressively decaying the value\n", "of |lambda| during the iterations, starting from |lambda=1.5*sigma| until\n", "|lambda=.5*sigma|. Retain the solution |xbp| together with the coefficients |Sbp|\n", "that provides the smallest\n", "error."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "prompt_number": 25, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display the solution computed by basis pursuit."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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ABCzgMTAddyxEOzb1ApBl7THUyyiIi62LP1nMkp7ui+qKfolwqw3OHl1v7ppQ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\nx63xvaD6S7sekJTgStnD3Pmc+rL5lJDSrJNnzJ3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"output_type": "display_data"}], "prompt_number": 26, "cell_type": "code", "language": "python", "metadata": {}, "input": ["e = snr(x0,xbp);\n", "clf\n", "plot_spectrogram(Sbp, xbp);\n", "subplot(length(Sbp)+1,1,1);\n", "title(strcat(['Denoised, SNR=' num2str(e,3), 'dB']));"]}, {"source": ["Sparsity to Improve Audio Separation\n", "------------------------------------\n", "The increase of sparsity produced by L1 minimization is helpful to\n", "improve audio stereo separation.\n", "\n", "\n", "Load 3 sounds."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 27, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 1024*32;\n", "options.n = n;\n", "s = 3; % number of sound\n", "p = 2; % number of micros\n", "options.subsampling = 1;\n", "x = zeros(n,3);\n", "[x(:,1),fs] = load_sound('bird', n, options);\n", "[x(:,2),fs] = load_sound('male', n, options);\n", "[x(:,3),fs] = load_sound('glockenspiel', n, options);"]}, {"source": ["normalize the energy of the signals"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 28, "cell_type": "code", "language": "python", "metadata": {}, "input": ["x = x./repmat(std(x,1), [n 1]);"]}, {"source": ["We mix the sound using a |2x3| transformation matrix.\n", "Here the direction are well-spaced, but you can try with more complicated\n", "mixing matrices.\n", "\n", "compute the mixing matrix"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 29, "cell_type": "code", "language": "python", "metadata": {}, "input": ["theta = linspace(0,pi(),s+1); theta(s+1) = [];\n", "theta(1) = .2;\n", "M = [cos(theta); sin(theta)];"]}, {"source": ["compute the mixed sources"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 30, "cell_type": "code", "language": "python", "metadata": {}, "input": ["y = x*M';"]}, {"source": ["We transform the stero pair using the multi-channel STFT (each channel is transformed independantly."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 31, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.multichannel = 1;\n", "S = perform_stft(y, wlist, qlist, options);"]}, {"source": ["check for reconstruction"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "text": ["Reconstruction error (should be 0)=1.5966e-16.\n"], "output_type": "display_data"}], "prompt_number": 32, "cell_type": "code", "language": "python", "metadata": {}, "input": ["y1 = perform_stft(S, wlist, qlist, options);\n", "disp(strcat(['Reconstruction error (should be 0)=' num2str(norm(y-y1,'fro')/norm(y, 'fro')) '.' ]));"]}, {"source": ["Now we perform a multi-channel basis pursuit to find a sparse approximation of the\n", "coefficients.\n", "\n", "regularization parameter"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 40, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lambdaV = .2;"]}, {"source": ["initialization"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 41, "cell_type": "code", "language": "python", "metadata": {}, "input": ["y1 = y;\n", "S1 = S;\n", "niter = 100;\n", "err = [];"]}, {"source": ["iterations"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 49, "cell_type": "code", "language": "python", "metadata": {}, "input": ["for i=1:niter\n", " % gradient\n", " r = y - y1;\n", " Sr = perform_stft(r, wlist, qlist, options);\n", " S1 = cell_add(S1, Sr);\n", " % multi-channel thresholding\n", " %%% BUG HERE %%%%\n", " % S1 = perform_thresholding(S1, lambdaV, 'soft-multichannel');\n", " % update the value of lambdaV to match noise\n", " y1 = perform_stft(S1,wlist,qlist, options);\n", "end"]}, {"source": ["Create the point cloud of both the tight frame and the sparse BP coefficients."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 50, "cell_type": "code", "language": "python", "metadata": {}, "input": ["P1 = []; P = [];\n", "for i=1:length(S)\n", " Si = reshape( S1{i}, [size(S1{i},1)*size(S1{i},2) 2] );\n", " P1 = cat(1, P1, Si);\n", " Si = reshape( S{i}, [size(S{i},1)*size(S{i},2) 2] );\n", " P = cat(1, P, Si);\n", "end\n", "P = [real(P);imag(P)];\n", "P1 = [real(P1);imag(P1)];"]}, {"source": ["Display the two point clouds."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 51, "cell_type": "code", "language": "python", "metadata": {}, "input": ["p = size(P,1);\n", "m = 10000;\n", "sel = randperm(p); sel = sel(1:m);\n", "clf;\n", "subplot(1,2,1);\n", "plot( P(sel,1),P(sel,2), '.' );\n", "title('Tight frame coefficients');\n", "axis([-10 10 -10 10]);\n", "subplot(1,2,2);\n", "plot( P1(sel,1),P1(sel,2), '.' );\n", "title('Basis Pursuit coefficients');\n", "axis([-10 10 -10 10]);"]}, {"source": ["Compute the angles of the points with largest energy."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 52, "cell_type": "code", "language": "python", "metadata": {}, "input": ["d = sqrt(sum(P.^2,2));\n", "d1 = sqrt(sum(P1.^2,2));\n", "I = find( d>.2 );\n", "I1 = find( d1>.2 );"]}, {"source": ["compute angles"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 53, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Theta = mod(atan2(P(I,2),P(I,1)), pi());\n", "Theta1 = mod(atan2(P1(I1,2),P1(I1,1)), pi());"]}, {"source": ["Compute and display the histogram of angles.\n", "We reaint only a small sub-set of most active coefficients.\n", "\n", "compute histograms"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 54, "cell_type": "code", "language": "python", "metadata": {}, "input": ["nbins = 150;\n", "[h,t] = hist(Theta, nbins);\n", "h = h/sum(h);\n", "[h1,t1] = hist(Theta1, nbins);\n", "h1 = h1/sum(h1);"]}, {"source": ["display histograms"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 55, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(2,1,1);\n", "bar(t,h); axis('tight');\n", "set_graphic_sizes([], 20);\n", "title('Tight frame coefficients');\n", "subplot(2,1,2);\n", "bar(t1,h1); axis('tight');\n", "set_graphic_sizes([], 20);\n", "title('Sparse coefficients');"]}, {"source": ["__Exercise 4__\n", "\n", "Compare the source separation obtained by masking with a tight frame Gabor\n", "transform and with the coefficients computed by a basis pursuit\n", "sparsification process."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 56, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "prompt_number": 57, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": []}], "metadata": {}}], "nbformat": 3, "metadata": {"kernelspec": {"name": "matlab_kernel", "language": "matlab", "display_name": "Matlab"}, "language_info": {"mimetype": "text/x-matlab", "name": "matlab", "file_extension": ".m", "help_links": [{"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md", "text": "MetaKernel Magics"}]}}}