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Orthogonal Matching Pursuit#
Using orthogonal matching pursuit for recovering a sparse signal from a noisy measurement encoded with a dictionary
# Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import matplotlib.pyplot as plt import numpy as np from sklearn.datasets import make_sparse_coded_signal from sklearn.linear_model import OrthogonalMatchingPursuit, OrthogonalMatchingPursuitCV n_components, n_features = 512, 100 n_nonzero_coefs = 17 # generate the data # y = Xw # |x|_0 = n_nonzero_coefs y, 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, ) X = X.T (idx,) = w.nonzero() # distort the clean signal y_noisy = y + 0.05 * np.random.randn(len(y)) # plot the sparse signal 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 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 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 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 0.228 seconds)
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