贝叶斯优化一维信号快速非局部均值去噪的Python代码

以下是贝叶斯优化一维信号快速非局部均值去噪的Python代码：

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import convolve

def nlm_denoise(y, sigma, h):
    """
    Non-local means denoising using convolution.
    """
    w = int(np.ceil(sigma * 3) * 2 + 1)  # window size
    pad = int(np.floor(w / 2))  # padding size
    y_pad = np.pad(y, pad, mode='symmetric')
    weights = np.zeros_like(y)
    for i in range(len(y)):
        w1 = y_pad[i:i+w]
        for j in range(len(y)):
            w2 = y_pad[j:j+w]
            d = np.sum((w1 - w2) ** 2)
            weights[i,j] = np.exp(-d / (h ** 2))
    weights /= np.sum(weights, axis=1)[:, np.newaxis]
    denoised = convolve(weights, y, mode='same')
    return denoised

def objective(x, y, sigma, h):
    """
    Objective function for Bayesian optimization.
    """
    denoised = nlm_denoise(y, sigma, x)
    mse = np.mean((denoised - y) ** 2)
    return mse

def bayesian_optimization(y, sigma):
    """
    Bayesian optimization for parameter h.
    """
    from bayes_opt import BayesianOptimization
    pbounds = {'h': (0.1, 1.0)}
    optimizer = BayesianOptimization(f= lambda x: objective(x['h'], y, sigma, x['h']),
                                      pbounds=pbounds,
                                      random_state=1)
    optimizer.maximize(init_points=5, n_iter=10)
    return optimizer

# Generate noisy signal
t = np.linspace(0, 1, 100)
y = np.sin(2 * np.pi * t) + np.random.normal(0, 0.1, size=100)

# Bayesian optimization for h
optimizer = bayesian_optimization(y, sigma=0.1)
h = optimizer.max['params']['h']
print('Best h:', h)

# Denoise signal using non-local means
denoised = nlm_denoise(y, sigma=0.1, h=h)

# Plot results
fig, ax = plt.subplots()
ax.plot(t, y, label='Noisy signal')
ax.plot(t, denoised, label='Denoised signal')
ax.legend()
plt.show()

需要安装`scipy`和`bayesian-optimization`库。运行代码后，输出最佳的参数`h`，并绘制原始信号和去噪后的信号。