78 lines
1.9 KiB
Python
78 lines
1.9 KiB
Python
"""
|
|
===========================
|
|
Orthogonal Matching Pursuit
|
|
===========================
|
|
|
|
Using orthogonal matching pursuit for recovering a sparse signal from a noisy
|
|
measurement encoded with a dictionary
|
|
|
|
"""
|
|
|
|
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()
|