Using orthogonal matching pursuit for recovering a sparse signal from a noisy measurement encoded with a dictionary
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | print(__doc__)import matplotlib.pyplot as pltimport numpy as npfrom sklearn.linear_model import OrthogonalMatchingPursuitfrom sklearn.linear_model import OrthogonalMatchingPursuitCVfrom sklearn.datasets import make_sparse_coded_signaln_components, n_features = 512, 100n_nonzero_coefs = 17# generate the data#################### y = Xw# |x|_0 = n_nonzero_coefsy, X, w = make_sparse_coded_signal(n_samples=1, n_components=n_components, n_features=n_features, n_nonzero_coefs=n_nonzero_coefs, random_state=0)idx, = w.nonzero()# distort the clean signal |
1 2 3 | y_noisy = y + 0.05 * np.random.randn(len(y))# plot the sparse signal |
1 2 3 4 5 6 7 | plt.figure(figsize=(7, 7))plt.subplot(4, 1, 1)plt.xlim(0, 512)plt.title("Sparse signal")plt.stem(idx, w[idx])# plot the noise-free reconstruction |
1 2 3 4 5 6 7 8 9 10 | omp = OrthogonalMatchingPursuit(n_nonzero_coefs=n_nonzero_coefs)omp.fit(X, y)coef = omp.coef_idx_r, = coef.nonzero()plt.subplot(4, 1, 2)plt.xlim(0, 512)plt.title("Recovered signal from noise-free measurements")plt.stem(idx_r, coef[idx_r])# plot the noisy reconstruction |
1 2 3 4 5 6 7 8 9 | omp.fit(X, y_noisy)coef = omp.coef_idx_r, = coef.nonzero()plt.subplot(4, 1, 3)plt.xlim(0, 512)plt.title("Recovered signal from noisy measurements")plt.stem(idx_r, coef[idx_r])# plot the noisy reconstruction with number of non-zeros set by CV |
1 2 3 4 5 6 7 8 9 10 11 12 13 | omp_cv = OrthogonalMatchingPursuitCV()omp_cv.fit(X, y_noisy)coef = omp_cv.coef_idx_r, = coef.nonzero()plt.subplot(4, 1, 4)plt.xlim(0, 512)plt.title("Recovered signal from noisy measurements with CV")plt.stem(idx_r, coef[idx_r])plt.subplots_adjust(0.06, 0.04, 0.94, 0.90, 0.20, 0.38)plt.suptitle('Sparse signal recovery with Orthogonal Matching Pursuit', fontsize=16)plt.show() |
Total running time of the script: (0 minutes 0.526 seconds)
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plot_omp.py
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