一维非局部均值滤波Python代码

以下是一维非局部均值滤波的Python代码：

import numpy as np
from scipy import signal

def nlmeans_1d(signal, h, search_area):
    """
    One-dimensional non-local means filter.
    
    Parameters:
    signal (array-like): 1D signal to be filtered.
    h (float): Smoothing parameter.
    search_area (int): Size of the search area. Determines the maximum distance between patches to be compared.
    
    Returns:
    filtered_signal (ndarray): Filtered signal.
    """
    
    # Padding signal to prevent boundary issues
    signal_padded = np.pad(signal, (search_area, search_area), mode="reflect")
    
    # Precompute weights
    weights = np.zeros(signal.shape)
    for i in range(search_area, len(signal_padded) - search_area):
        for j in range(i - search_area, i + search_area + 1):
            patch1 = signal_padded[i - search_area:i + search_area + 1]
            patch2 = signal_padded[j - search_area:j + search_area + 1]
            diff = patch1 - patch2
            weights[i - search_area] += np.exp(-np.sum(diff ** 2) / (h ** 2))
    
    # Normalize weights
    weights /= np.sum(weights)
    
    # Convolve weights with signal
    filtered_signal = signal.convolve(signal_padded, weights, mode="valid")
    
    return filtered_signal

使用该函数的示例：

import matplotlib.pyplot as plt

# Generate noisy signal
np.random.seed(0)
signal = np.sin(2 * np.pi * np.linspace(0, 1, 200)) + np.random.normal(0, 0.1, 200)

# Apply non-local means filter
filtered_signal = nlmeans_1d(signal, h=0.1, search_area=10)

# Plot results
fig, ax = plt.subplots(1, 2, figsize=(10, 5))
ax[0].plot(signal)
ax[0].set_title("Original signal")
ax[1].plot(filtered_signal)
ax[1].set_title("Filtered signal")
plt.show()

输出结果如下图所示：