{
"metadata": {
"name": "compressed_sensing"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Compressed Sensing Example\n",
"\n",
"This workbook follows Cleve Moler's write-up\n",
"of compressed sensing from\n",
"http://www.mathworks.com/company/newsletters/articles/clevescorner-compressed-sensing.html\n",
"\n",
"### Background\n",
"\n",
"To apply CS, we need to know that our signal can be represented\n",
"with few non-zero coefficients in some base:\n",
"\n",
"
\n",
"$$ \\mathbf{f} = \\psi \\mathbf{x} $$\n",
"\n",
"
\n",
"where $\\mathbf{f}$ is the signal, $\\psi$ the matrix of basis functions,\n",
"and $\\mathbf{c}$ the coefficients (most of them zero). We start with\n",
"only a few samples, randomly taken from our signal, i.e.\n",
"\n",
"
\n",
"$$\\mathbf{b} = \\phi \\mathbf{f}$$\n",
"\n",
"
\n",
"where $\\phi$ is a decimation matrix (selected rows from the identity\n",
"matrix). From this, we can write\n",
"\n",
"
\n",
"$$\\mathbf{b} = \\phi \\psi \\mathbf{x}.$$\n",
"\n",
"
\n",
"To find $\\mathbf{c}$ then requires solving a highly under-determined\n",
"linear system, $A\\mathbf{x}=\\mathbf{b}$ with $A=\\phi \\psi$;\n",
"but (and this is the secret to CS) we know that\n",
"most of the saught coefficients should be zero. It therefore seems\n",
"natural to penalise the solution by the number of non-zeros,\n",
"but this problem is hard to solve. Instead, Donoho, Cand\u00e9s & Tao\n",
"showed that penalising with the $\\ell_1$-norm is very likely\n",
"to yield the same result.\n",
"\n",
"
\n",
"We therefore proceed to solve\n",
"\n",
"
\n",
"$$ \\| A \\mathbf{x} - \\mathbf{b} \\|_2^2 + \\lambda \\| \\mathbf{x} \\|_1. $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import scipy.fftpack as fft\n",
"import matplotlib.pyplot as plt\n",
"from sklearn import linear_model"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we generate a test signal by sampling a sum of two sine\n",
"waves (the \"A\" sounds from a touch tone phone):"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"F = 40000 # Sampling frequency\n",
"d = 1./8 # Total sampling duration\n",
"\n",
"T = 1./F # Sampling interval\n",
"t = np.linspace(0, d, d / T)\n",
"\n",
"f = np.sin(1394 * np.pi * t) + np.sin(3266 * np.pi * t)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now set up our sampling and decimation matrices:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Discrete cosine transform matrix\n",
"N = len(f)\n",
"C = fft.idct(np.eye(N, N), norm='ortho')\n",
"\n",
"# Decimation operator; randomly choose 500 points\n",
"r = np.random.permutation(np.arange(len(f)))\n",
"D = np.eye(N, N)[r[:500]]\n",
"\n",
"print \"Using %2.1f%% of points.\" % (len(D) / float(len(f)) * 100)\n",
"print \"Nyquist rate: %d Hz\" % (3266*2)\n",
"print \"Effective sampling rate: %d Hz\" % (len(D) / float(len(f)) * F)\n",
"\n",
"# Form the combined operator\n",
"A = D.dot(C)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Using 10.0% of points.\n",
"Nyquist rate: 6532 Hz\n",
"Effective sampling rate: 4000 Hz"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And visualise the effect of those matrices on the signal:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.subplot(211)\n",
"plt.plot(t, f)\n",
"plt.plot(D.dot(t), D.dot(f), '.')\n",
"plt.xlim(0, 0.02)\n",
"plt.title('Signal and sampled points')\n",
"\n",
"plt.subplot(212)\n",
"plt.plot(fft.dct(f)[:600])\n",
"plt.title('Discrete Cosine Transform')\n",
"\n",
"plt.subplots_adjust(hspace=0.5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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6lYXngGR8841158R8+HInvlhWDLexUE67jhBHXR2D8J70GNMXl5hQWWlffmpr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\nf4jCw8qLo3FoAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's use ``scikits.learn`` to find the $\\ell_1$ penalised solution:"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"L = linear_model.Lasso(alpha=0.001)\n",
"b = D.dot(f)\n",
"x = L.fit(A, b).coef_"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"#x, _, _, _ = np.linalg.lstsq(A, b) # minimise BIC criterium to find T\n",
"#T = 0.001\n",
"#y = (np.abs(x) - T)\n",
"#y[y < 0] = 0\n",
"#\n",
"#x = np.sign(x) * y\n",
"\n",
"# Above would only work for orthogonal A"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 177
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f_ = C.dot(x)\n",
"plt.plot(t, f_, label='reconstructed')\n",
"plt.xlim(0.1, 0.12)\n",
"\n",
"plt.plot(t, f, label='original')\n",
"plt.title('Original vs. reconstructed signal')\n",
"plt.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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9/fbby253QMl99+7djBgxAofDwdtvv40Qok9i7w9JLUl9sJ6syA4quee8frvI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XOhFFKxIJu0lnviR1BXJMR0SQevUObupw62B5ern4Wr27ZeRFMGypxEVZYJQ+rQeJG29BLcyxhN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\nPRy8h84zHYwP4s1bb2JX9y6S6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}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Notes to self\n",
"\n",
"- Change to LassoLars\n",
"- Can determine alpha with cross validation\n",
"- file bug report: fit doc should have return params: self\n",
"\n",
"
\n", "L = linear_model.Lasso() \n", "linear_model.LassoCV # not good for very few non-zeros\n", "\n", "-> use this one L = linear_model.LassoLarsCV()\n", "\n", "L = linear_model.OMP + nr of nonzeros (not convex, greedy)\n" ] }, { "cell_type": "code", "collapsed": true, "input": [ "b = D.dot(f)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "from scikits.learn import svm\n", "svm.l1_min_c(A, b, loss='l2')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 10, "text": [ "0.001004016064257028" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": true, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 151 } ], "metadata": {} } ] }