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Created February 26, 2014 04:03
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Blog post on compressed sensing. This is the IPython Notebook corresponding to the blogpost.
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This post is ased on the blogpost http://brocabrain.blogspot.com/2012/10/compressed-sensing-with-sklearn-dtmf.html\n",
"I tried to expand and explain where helpful."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Suppose we have a time signal. This signal is not known, but we do know something about it - namely that it's *sparse* in *some* domain. Maybe that means it's only made up of certain frequencies, so when you look at the signal in the frequency domain it's mostly zeros, with a few non-zero values intermixed. \n",
"\n",
"Let's call this **unknown** signal $X$. Now, even though we don't know the whole signal, we can still make observations of it, or samples. Sampling could be expensive, time consuming or not technilogically feasible, which is why we want to limit the number of observations or samples to as small a number as possible.\n",
"\n",
"Furthermore, when we make observations of the signal we aren't going to do it in a repeting pattern (*e.g.* every 10th sample). No, instead we're going to **randomly** sample the data.\n",
"\n",
"Let's try this in Python:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"from matplotlib.pyplot import plot, show, figure, title\n",
"import matplotlib as plt\n",
"import numpy as np\n",
"\n",
"from scipy.fftpack import dct, idct\n",
"from scipy.sparse import coo_matrix"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 124
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Fs = 40e3 #Sample rate\n",
"duration = 1./8\n",
"N_samps = np.floor(duration*Fs)\n",
"M = 250 # Number of compressed \"basis\" functions - we're going from N_samps to M samps.\n",
"f1 = 200\n",
"f2 = 3950\n",
"\n",
"print \"Compression ratio {0}\".format(M/N_samps)\n",
"t = np.linspace(0,duration,N_samps)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Compression ratio 0.05\n"
]
}
],
"prompt_number": 153
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X = np.sin(2*np.pi*f1*t) + np.sin(2*np.pi*f2*t)\n",
"\n",
"figure(figsize=[10,4])\n",
"plot(t,X)\n",
"title('Original signal')\n",
"plt.pyplot.xlabel('Time (s)')\n",
"plt.pyplot.ylabel('X(t)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 154,
"text": [
"<matplotlib.text.Text at 0x34842a58>"
]
},
{
"metadata": {},
"output_type": "display_data",
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BPPAAP8yQW/njD+CZZ/K+V6eOM3kxCrsvEN2U449ITEPZHSduxlVFL7OAO3PGE3GdRaAB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\nvfxkGFTYp8vZueaQue7l2mv1d7tGMnpt7dFHuddZtoxrjw2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ePTrPQnI1doiVX7SPHSJl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\nB87cc9dHrQEYAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x3471bf98>"
]
}
],
"prompt_number": 154
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we're going to chose random points in time from which to sample the data. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"yi = np.random.randint(0,N_samps,(M,))\n",
"yi = np.sort(yi)\n",
"Y = X[yi]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 155
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figure(figsize=[10,4])\n",
"plot(t,X,'b',t[yi],Y,'r.')\n",
"title('Original Signal with Random Sampling Points')\n",
"plt.pyplot.xlabel('Time (s)')\n",
"plt.pyplot.ylabel('X(t) and X(random sample)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 156,
"text": [
"<matplotlib.text.Text at 0x3485cf28>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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UqlQJoQIL2OLj4xEYGIiWLVuiZcuWmDp1qqAssyBZMHqUciM0slq2d0Y/pFxJ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\nEAgEAoFA4GX8f4kMrG9w67vrAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x3471df60>"
]
}
],
"prompt_number": 156
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we know two things, A) we know our samples, $X(t_{samps})$ and we know the sample times, $t_{samps}$. Using this we can transform our samples into the *sparse domain*. In this case, we've chosen the Discrete Cosine Domain. This could just as easily been the Discrete Fourier domain. In fact, you might want to try both just to see the differences.\n",
"\n",
"We're computing the DCT for each of the possible sample points (N_samps) and then only choosing the ones we actually sampled at. $A$ is now the DCT basis functions corresponding to our random sample times *in the time domain*. It is literally a matrix where each column corresponds a cosine function at a different frequency. The frequencies correspond to the sample times we chose randomly. In other words, $A$ now represents what those samples look like in another domain. "
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"D = dct(np.eye(N_samps)) # Construct the DCT basis functions for each of the frequencies\n",
"A = D[yi] # Downsample based on our random sampling"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 157
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.shape(A)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 158,
"text": [
"(250L, 5000L)"
]
}
],
"prompt_number": 158
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This means we now *know* $A$, based on the sample times, and $Y$, which is our sampled data. We also know that the original data, $X$ was sparse in the DCT domain. We'll call the sparse DCT version of $X$, $\\tilde X$. *We are now trying to solve for $\\tilde X$ based on this knowledge*. In other words we're trying to find the solution to $\\tilde X$ that makes the equation $A\\tilde X = Y$ true. $A$ is the translation from our random time samples into the DCT domain, $\\tilde X$ is in DCT domain and is presumed sparse, and $Y$ is a time domain signal. In other words, we're trying to solve, $\\min (Y - A\\tilde X)$ in some fashion.\n",
"\n",
"We can use the LASSO to find the sparse solution. It's solving:\n",
"\n",
"$$ c * ||Y - A\\tilde X||^2_2 + alpha * ||\\tilde X||_1 $$\n",
"\n",
"where $c$ is some constant based on the number of samples, and $||\\tilde X||_1 $ is the $\\ell_1$ norm, which assures that the solution to $\\tilde X$ is sparse."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sklearn.linear_model import Lasso # http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 159
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"lasso = Lasso(alpha=0.01)\n",
"lasso.fit(A,Y)\n",
"\n",
"plot(lasso.coef_)\n",
"\n",
"sparseness = np.sum(lasso.coef_ == 0)/N_samps\n",
"print \"Solution is %{0} sparse\".format(100.*sparseness)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Solution is %96.22 sparse\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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fBPqCqlb7QqfT4ec//zlycnKwdu1aAJHviwG/dBZp/HSRJNiX9m5kFy5cwKOP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\n",
"text": [
"<matplotlib.figure.Figure at 0x1fbe29e8>"
]
}
],
"prompt_number": 160
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plot above shows how many DCT coefficients in the final solution are non-zero. Remember, this solution is what we approximate $X$ to be in the DCT domain. You can see that there are very very few coefficients that are not zero. To find out what we estimate the true signal to be in the time domain, $\\hat X$, we take the Inverse Discrete Cosine Transform (IDCT) of the LASSO solution."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Xhat = idct(lasso.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 161
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figure()\n",
"plot(t,Xhat)\n",
"title('Reconstructed signal')\n",
"figure()\n",
"plot(t,Xhat-X)\n",
"title('Error delta')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 162,
"text": [
"<matplotlib.text.Text at 0x41a56e80>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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aAPztb/pssTqeG27B3Pw8oGRsufFGeVsA4IILyj7LdL/47cJSje7r6YXRo/3t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\nRUMtP25dNub7e8cdtPzd4ra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ZujTeFlQskoTw7ry0ePFiPPvss/jggw9Q1SbAclJSEqZP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\nJqSwwDMMw4QUFniGYZiQwgLPMAwTUv4f4NUcBCg746QAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x41a3e278>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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CZ58pp73jDun3ffcJMWuWEJMmSc+feMI93bXXuj//9lshqqud5+Wdd+r/O5Yt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\ngaiGjgSagaCgoADV1dVery9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"text": [
"<matplotlib.figure.Figure at 0x41a48048>"
]
}
],
"prompt_number": 162
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plots above show the reconstructed signal in the time domain and the reconstructed signal, $\\hat X$ versus the original signal, $X$. You can see how the error tends to go up at the beginning and end of the signal. I presume this is due to the fact that we don't have unlimited data and are taking a window of fixed length."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figure(figsize=[12,6])\n",
"plot(t,Xhat)\n",
"plot(t,X)\n",
"title(\"Original and reconstructed signal plotted together (green is orig)\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 165,
"text": [
"<matplotlib.text.Text at 0x66eea240>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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AOAkHI3NKcjBowSA0eq8RmXjt/W1v/HPOPzFq5SgS+wBgifmbzPYrv72Csb+N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\nGYZhGIZhGCbI/wfZ3Q+Dh2O1LQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x419350f0>"
]
}
],
"prompt_number": 165
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Don't forget that this reconstruction is achieved using only a small fraction of the total sample. The compression ratio is:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Signal is reconstructed using only %{0} of the data!\".format(100.*M/N_samps)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Signal is reconstructed using only %5.0 of the data!\n"
]
}
],
"prompt_number": 168
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's a little hard to tell what's going on in the figure above. A better way to look at things would be to look at the signal in the frequency domain where, since that's where it's sparse."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f = np.linspace(-Fs/2,Fs/2,N_samps)\n",
"figure(figsize=[20,10])\n",
"plot(f,np.log10(np.fft.fftshift(np.abs(fft(Xhat)))))\n",
"title(\"Frequency spectrum of original signal & reconstruction\")\n",
"plot(f,np.log10(np.fft.fftshift(np.abs(fft(X)))),'r')\n",
"plt.pyplot.xlabel('Frequency -Fs/2 to Fs/2')\n",
"plt.pyplot.ylabel('Power (dB)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 171,
"text": [
"<matplotlib.text.Text at 0x67251da0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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PRERE4e7oUZQmtMTJhs3QHCeQm+v5sMMBFBeHpmh2q60NdQmMcQVnnE40biwC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Qotkb+qJdCzhQx2yvBt2VIeTZrsuygnBoCnrgAOdJCA1S75+TI5uyk+qXvZuLEYCapqzscfy25M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\nzDM544wzkrQ9ZezDP2+99dZ57733kiRvvfVWm3X9+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"text": [
"<matplotlib.figure.Figure at 0x67224f60>"
]
}
],
"prompt_number": 171
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
@terminsen
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Very nice introduction to compressed sensing ! Thank you.

One little detail: In the present version of numpy (I use 1.14.3) you need to use np.fft.fft(Xhat) and np.fft.fft(X) in the very last section for the fast fourier transform and not only fft.

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