Wavelet-based denoising by customized thresholding

The problem of estimating a signal that is corrupted by additive noise has been of interest to many researchers for practical, as well as theoretical, reasons. Many of the traditional denoising methods use linear methods such as Wiener filtering. Recently, nonlinear methods, especially those based on wavelets, have become increasingly popular, due to a number of advantages over the linear methods. It has been shown that wavelet-thresholding has near-optimal properties in the minimax sense, and guarantees a better rate of convergence, despite its simplicity. Even though much work has been done in the field of wavelet-thresholding, most of it was focused on statistical modeling of the wavelet coefficients and the optimal choice of the thresholds. We propose a custom thresholding function which can improve the denoised results significantly. Simulation results are given to demonstrate the advantage of the new thresholding function.