使用贝叶斯优化一维时序信号NLM去噪的Python代码

以下是使用贝叶斯优化一维时序信号NLM去噪的Python代码：

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


def nlm_filter(signal_in, h, sigma):
    """Non-local means filter for 1D signal"""
    L = len(signal_in)
    signal_out = np.zeros(L)
    for i in range(L):
        w = np.exp(-(np.arange(L) - i) ** 2 / (2 * h ** 2))
        w /= np.sum(w)
        for j in range(L):
            d = signal_in[j:j + L] - signal_in[i:i + L]
            d = np.sum(d ** 2 * w)
            signal_out[i] += np.exp(-d / (2 * sigma ** 2)) * signal_in[j]
        signal_out[i] /= np.sum(np.exp(-d / (2 * sigma ** 2)) * w)
    return signal_out


def nlm_filter_loss(x, signal_in, signal_true):
    h, sigma = x
    signal_out = nlm_filter(signal_in, h, sigma)
    return np.mean((signal_out - signal_true) ** 2)


def optimize_nlm_filter(signal_in, signal_true):
    """Optimize NLM filter using Bayesian optimization"""
    bounds = [(0.01, 2), (0.01, 2)]
    res = gp_minimize(nlm_filter_loss, bounds, args=(signal_in, signal_true), n_calls=50)
    h, sigma = res.x
    return nlm_filter(signal_in, h, sigma)

其中，`nlm_filter`函数实现了一维时序信号的NLM去噪算法，`nlm_filter_loss`函数用于计算NLM去噪算法的损失函数，`optimize_nlm_filter`函数使用贝叶斯优化算法来寻找最优的NLM去噪超参数，并返回去噪后的信号。

使用方法如下：

# Generate noisy signal
t = np.linspace(0, 10, 1000)
signal_true = np.sin(t)
signal_in = signal_true + np.random.normal(0, 0.1, len(t))

# Optimize NLM filter
signal_out = optimize_nlm_filter(signal_in, signal_true)

# Plot results
import matplotlib.pyplot as plt
plt.plot(t, signal_in, label='Noisy signal')
plt.plot(t, signal_true, label='True signal')
plt.plot(t, signal_out, label='NLM filtered signal')
plt.legend()
plt.show()