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正交匹配追踪#

使用正交匹配追踪从带噪测量中恢复稀疏信号，该测量使用字典进行编码

Sparse signal recovery with Orthogonal Matching Pursuit, Sparse signal, Recovered signal from noise-free measurements, Recovered signal from noisy measurements, Recovered signal from noisy measurements with CV

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

# 生成数据

#```
# 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()

# 扭曲干净的信号
y_noisy = y + 0.05 * np.random.randn(len(y))

# 绘制稀疏信号
plt.figure(figsize=(7, 7))
plt.subplot(4, 1, 1)
plt.xlim(0, 512)
plt.title("Sparse signal")
plt.stem(idx, w[idx])

# 绘制无噪声重建图
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])

# 绘制有噪声的重建图
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])

# 绘制由交叉验证设定非零数目的噪声重建图
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()