贝叶斯优化时序信号快速非局部均值去噪Python代码

以下是使用贝叶斯优化的时序信号快速非局部均值去噪的Python代码：

import numpy as np
from scipy.signal import fftconvolve
from skopt import gp_minimize

def non_local_means_denoise(signal, kernel_size, h, sigma):
    """
    使用贝叶斯优化的时序信号快速非局部均值去噪

    参数：
    signal: ndarray，待去噪的信号
    kernel_size: int，滤波器的大小
    h: float，平滑参数
    sigma: float，噪声标准差

    返回值：
    ndarray，去噪后的信号
    """
    # 构造滑动窗口，用于计算局部均值
    window = np.ones(kernel_size) / kernel_size

    def objective(x):
        """
        目标函数，计算该参数下的误差

        参数：
        x: tuple，(h, sigma)

        返回值：
        float，误差
        """
        # 计算平滑参数和噪声标准差
        h, sigma = x

        # 计算非局部均值
        mean = fftconvolve(signal, window, mode='same')
        diff = signal - mean
        weights = np.exp(-diff ** 2 / (2 * sigma ** 2))
        weights /= np.sum(weights, axis=0)

        denoised_signal = np.sum(weights * signal, axis=0)

        # 计算误差
        mse = np.mean((denoised_signal - signal) ** 2)
        return mse

    # 使用贝叶斯优化寻找最优参数
    result = gp_minimize(
        objective,
        [(0.001, 0.1), (0.001, 0.1)],
        n_random_starts=5,
        n_calls=20,
        verbose=False
    )

    # 使用最优参数进行去噪
    h, sigma = result.x
    mean = fftconvolve(signal, window, mode='same')
    diff = signal - mean
    weights = np.exp(-diff ** 2 / (2 * sigma ** 2))
    weights /= np.sum(weights, axis=0)

    denoised_signal = np.sum(weights * signal, axis=0)

    return denoised_signal

使用示例：

import matplotlib.pyplot as plt

# 构造带噪声的信号
t = np.linspace(0, 1, 200)
signal = np.sin(2 * np.pi * t) + 0.1 * np.random.randn(200)

# 去噪
denoised_signal = non_local_means_denoise(signal, 10, 0.05, 0.1)

# 绘制原始信号和去噪后的信号
plt.plot(t, signal, label='原始信号')
plt.plot(t, denoised_signal, label='去噪后的信号')
plt.legend()
plt.show()