A Wavelet-Denoising Approach Using Polynomial Threshold Operators

This letter presents a new class of polynomial threshold operators for denoising signals using wavelet transforms. The operators are parameterized to include classical soft-and hard-thresholding operators and have many degrees of freedom to optimally suppress undesired noise and preserve signal details. To avoid the complicated process of signal model identification for specific type of signals, a least squares optimization method is proposed for the polynomial coefficients. Our study shows that the proposed term-by-term, fixed-threshold operator can perform as well as adaptively applied, scale-dependent soft and hard thresholding approaches.