78 lines
1.9 KiB
Python
78 lines
1.9 KiB
Python
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"""
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===========================
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Orthogonal Matching Pursuit
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===========================
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Using orthogonal matching pursuit for recovering a sparse signal from a noisy
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measurement encoded with a dictionary
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.datasets import make_sparse_coded_signal
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from sklearn.linear_model import OrthogonalMatchingPursuit, OrthogonalMatchingPursuitCV
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n_components, n_features = 512, 100
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n_nonzero_coefs = 17
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# generate the data
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# y = Xw
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# |x|_0 = n_nonzero_coefs
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y, X, w = make_sparse_coded_signal(
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n_samples=1,
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n_components=n_components,
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n_features=n_features,
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n_nonzero_coefs=n_nonzero_coefs,
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random_state=0,
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)
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X = X.T
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(idx,) = w.nonzero()
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# distort the clean signal
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y_noisy = y + 0.05 * np.random.randn(len(y))
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# plot the sparse signal
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plt.figure(figsize=(7, 7))
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plt.subplot(4, 1, 1)
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plt.xlim(0, 512)
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plt.title("Sparse signal")
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plt.stem(idx, w[idx])
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# plot the noise-free reconstruction
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omp = OrthogonalMatchingPursuit(n_nonzero_coefs=n_nonzero_coefs)
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omp.fit(X, y)
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coef = omp.coef_
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(idx_r,) = coef.nonzero()
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plt.subplot(4, 1, 2)
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plt.xlim(0, 512)
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plt.title("Recovered signal from noise-free measurements")
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plt.stem(idx_r, coef[idx_r])
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# plot the noisy reconstruction
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omp.fit(X, y_noisy)
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coef = omp.coef_
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(idx_r,) = coef.nonzero()
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plt.subplot(4, 1, 3)
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plt.xlim(0, 512)
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plt.title("Recovered signal from noisy measurements")
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plt.stem(idx_r, coef[idx_r])
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# plot the noisy reconstruction with number of non-zeros set by CV
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omp_cv = OrthogonalMatchingPursuitCV()
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omp_cv.fit(X, y_noisy)
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coef = omp_cv.coef_
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(idx_r,) = coef.nonzero()
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plt.subplot(4, 1, 4)
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plt.xlim(0, 512)
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plt.title("Recovered signal from noisy measurements with CV")
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plt.stem(idx_r, coef[idx_r])
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plt.subplots_adjust(0.06, 0.04, 0.94, 0.90, 0.20, 0.38)
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plt.suptitle("Sparse signal recovery with Orthogonal Matching Pursuit", fontsize=16)
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plt.show()
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