Chaotic signal denoising using an improved wavelet thresholding algorithm

In wavelet thresholding denoising algorithms, traditional hard thresholding function is prone to Gibbs phenomenon due to its' discontinuity, while soft thresholding function is inherently biased. Therefore, they are not effective when dealing with chaotic signals. Though some improved thresholding functions are currently available, they are generally asymptotically unbiased and can not completely eliminate the estimation bias. To address this problem, a new thresholding function is designed by introducing transition regions in the hard thresholding function. Polynomial interpolation is used in the transition region to achieve continuity and smoothness. The proposed thresholding function is unbiased outside the transition region. Furthermore, the width of the transition region can be adaptively adjusted according to the noise level. Simulation results show that the wavelet thresholding algorithm based on the proposed thresholding function is more effective than the existing algorithms.