贝叶斯优化一维时序信号非局部均值去噪Python代码

以下是使用贝叶斯优化进行一维时序信号非局部均值去噪的Python代码示例：

import numpy as np
from scipy.signal import savgol_filter
from bayes_opt import BayesianOptimization

# Generate noisy signal
t = np.linspace(0, 10, 1000)
signal = np.sin(t) + 0.1*np.random.randn(1000)

# Define non-local mean function
def non_local_mean(signal, window_size, filter_size):
    filtered_signal = np.zeros_like(signal)
    for i in range(len(signal)):
        weights = np.exp(-np.square(signal - signal[i]) / filter_size**2)
        weights = weights / np.sum(weights)
        filtered_signal[i] = np.sum(signal[i-window_size:i+window_size+1] * weights[i-window_size:i+window_size+1])
    return filtered_signal

# Define objective function to minimize using Bayesian optimization
def objective(window_size, filter_size):
    filtered_signal = non_local_mean(signal, int(window_size), filter_size)
    smoothed_signal = savgol_filter(filtered_signal, 31, 3)
    mse = np.mean(np.square(smoothed_signal - np.sin(t)))
    return -mse  # maximize negative mean squared error

# Specify parameter bounds for Bayesian optimization
pbounds = {'window_size': (5, 50),
           'filter_size': (0.01, 1)}

# Initialize Bayesian optimization
optimizer = BayesianOptimization(f=objective, pbounds=pbounds)

# Perform Bayesian optimization
optimizer.maximize(init_points=10, n_iter=30)

# Get optimized window size and filter size
window_size_opt = int(optimizer.max['params']['window_size'])
filter_size_opt = optimizer.max['params']['filter_size']

# Apply non-local mean filter and Savitzky-Golay smoothing to signal
filtered_signal_opt = non_local_mean(signal, window_size_opt, filter_size_opt)
smoothed_signal_opt = savgol_filter(filtered_signal_opt, 31, 3)

# Plot original signal, noisy signal, and optimized denoised signal
import matplotlib.pyplot as plt
plt.plot(t, np.sin(t), 'k', label='Original signal')
plt.plot(t, signal, 'r', alpha=0.5, label='Noisy signal')
plt.plot(t, smoothed_signal_opt, 'b', label='Optimized denoised signal')
plt.legend()
plt.show()

在此示例中，我们首先生成了一个包含噪声的正弦信号，然后定义了一个非局部均值滤波器函数。我们使用贝叶斯优化库（`bayes_opt`）来最小化平均平方误差（MSE）作为目标函数，以便找到最佳的滤波器窗口大小和滤波器大小。我们指定了窗口大小和滤波器大小的参数范围，并使用 `BayesianOptimization` 类来初始化并执行优化。我们使用找到的最佳窗口大小和滤波器大小来应用非局部均值滤波器和Savitzky-Golay平滑，以获得去噪信号，并将其与原始信号和噪声信号一起绘制。