基于相邻尺度积系数的半软阈值小波滤波

针对相邻尺度积系数硬阈值滤波后的MSE函数不连续，最优阈值选取困难，该文构造了一种基于相邻尺度积系数的半软阈值函数。其为收缩因子函数与小波系数的乘积，对小波系数无穷可导、可在阈值邻域内对小波系数自适应收缩。进而通过极小化SURE(Stein Unbiased Risk Estimate)估计得到MSE意义下自适应于信号和噪声的最优阈值。大量仿真实验表明:采用本文构造的半软阈值函数，可改善基于相邻尺度积系数的滤波算法性能。

Denoising by Multiscale Product Coefficient Semi-soft Thresholding

In multiscale product coefficient hard thresholding, how to determine the optimal threshold is the main problem due to the discontinuity of MSE. Here a semi-soft thresholding function is constructed in the product form of shrinkage coefficient function and wavelet coefficients. This function is infinite-order differentiable with respect to wavelet coefficient, and can adaptively shrink wavelet coefficient in the neighborhood of the threshold. Through minimizing the Stein Unbiased Risk Estimate (SURE) based on the function, the optimal threshold, varying with the signal and noise, is obtained in the Mean Square Error (MSE) sense. In simulations to denoise multiple classic noisy signals, the multiscale product coefficient thresholding is improved through our semi-soft thresholding function.