贝叶斯优化一维时序信号NLM去噪的Python代码实现

以下是使用贝叶斯优化对一维时序信号进行NLM去噪的Python代码实现：

import numpy as np
from scipy import signal
from skopt import gp_minimize
from skopt.space import Real, Integer
from skopt.utils import use_named_args

def nlm_denoise(y, sigma, h, p, q):
    """
    Applies non-local means (NLM) denoising to a 1D signal y.
    :param y: 1D array, the signal to denoise
    :param sigma: float, the standard deviation of the noise
    :param h: float, the smoothing parameter
    :param p: int, the window size for similarity search
    :param q: int, the window size for patch search
    :return: 1D array, the denoised signal
    """
    n = len(y)
    y_denoised = np.zeros(n)
    for i in range(n):
        num = 0
        den = 0
        for j in range(n):
            if i != j:
                w1 = y[j-q:j+q+1]
                w2 = y[i-q:i+q+1]
                d = np.sum((w1-w2)**2)
                s1 = signal.windows.hann(2*p+1)
                s2 = signal.windows.hann(2*q+1)
                s = np.outer(s1, s2)
                w = np.exp(-d/(h**2*sigma**2)) * s
                num += w*y[j]
                den += w
        y_denoised[i] = num/den
    return y_denoised

@use_named_args([
    Real(0.01, 0.5, name='sigma'),
    Real(0.1, 1.0, name='h'),
    Integer(3, 11, name='p'),
    Integer(3, 11, name='q')
])
def objective(sigma, h, p, q):
    """
    Objective function to minimize using Bayesian optimization.
    :param sigma: float, the standard deviation of the noise
    :param h: float, the smoothing parameter
    :param p: int, the window size for similarity search
    :param q: int, the window size for patch search
    :return: float, the mean squared error between the denoised and original signals
    """
    y_denoised = nlm_denoise(y, sigma, h, p, q)
    mse = np.mean((y - y_denoised)**2)
    return mse

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

# optimize parameters using Bayesian optimization
bounds = [(0.01, 0.5), (0.1, 1.0), (3, 11), (3, 11)]
res = gp_minimize(objective, bounds, n_calls=50)

# denoise signal using optimized parameters
sigma_opt, h_opt, p_opt, q_opt = res.x
y_denoised = nlm_denoise(y, sigma_opt, h_opt, p_opt, q_opt)