Analysis of Wavelet–domain Wiener Filters

We investigate Wiener filtering of wavelet coefficients for signal denoising. Empirically designed wavelet-domain Wiener filters have superior performance over other denoising algorithms using wavelet thresholding. However, it is not clear how we should choose the signal model that is used to design the filter, because the effect of model selection on the filter performance was hard to understand. We analyze the error involved in the Wiener filters designed with an empirically obtained signal model showing that we can almost always obtain better performance than hard thresholding algorithm by using Wiener filters in another wavelet domain with the signal model obtained by hard thresholding. Our analysis furthermore provides a method to choose various parameters in wavelet domain Wiener filtering scheme.