一维时序信号非局部均值滤波的完整Python代码

以下是一维时序信号非局部均值滤波的完整Python代码：

import numpy as np
from scipy import signal

def nl_means_filter(signal, window_size, sigma, h):
    # Compute the half window size
    half_window = window_size // 2
    
    # Compute the padded signal
    padded_signal = np.pad(signal, half_window, mode='reflect')
    
    # Compute the distance weights
    weights = np.zeros_like(signal)
    for i in range(signal.size):
        for j in range(signal.size):
            # Compute the distance between the patches
            patch1 = padded_signal[i:i+window_size]
            patch2 = padded_signal[j:j+window_size]
            distance = np.sum((patch1 - patch2) ** 2) / (window_size * sigma ** 2)
            
            # Compute the weight
            weights[i, j] = np.exp(-distance)
    
    # Normalize the weights
    norm_weights = weights.sum(axis=1)
    for i in range(signal.size):
        weights[i, :] /= norm_weights[i]
    
    # Compute the filtered signal
    filtered_signal = np.zeros_like(signal)
    for i in range(signal.size):
        weights_i = weights[i, :]
        window = padded_signal[i:i+window_size]
        filtered_signal[i] = np.sum(weights_i * window) / np.sum(weights_i)
    
    # Apply the hard thresholding
    filtered_signal = signal - filtered_signal
    filtered_signal = np.where(filtered_signal < -h, -h, filtered_signal)
    filtered_signal = np.where(filtered_signal > h, h, filtered_signal)
    filtered_signal = signal - filtered_signal
    
    return filtered_signal

# Example usage
signal = np.sin(np.linspace(0, 2*np.pi, 100))
noisy_signal = signal + np.random.normal(0, 0.1, 100)

filtered_signal = nl_means_filter(noisy_signal, window_size=5, sigma=0.1, h=0.1)

import matplotlib.pyplot as plt
plt.plot(signal, label='Original signal')
plt.plot(noisy_signal, label='Noisy signal')
plt.plot(filtered_signal, label='Filtered signal')
plt.legend()
plt.show()

该代码使用了NumPy和SciPy库，实现了一维时序信号非局部均值滤波算法。其中，`nl_means_filter`函数接受一个输入信号，以及窗口大小、标准差和硬阈值等参数，返回经过滤波后的信号。在例子中，我们使用了正弦波作为原始信号，加入了高斯噪声，并对噪声进行了非局部均值滤波。最后，我们使用Matplotlib库将原始信号、噪声信号和滤波后的信号进行了可视化。