Nonlinear adaptive filters and wavelets. A statistical analysis

The aim of this paper is to analyze some very fast nonlinear adaptive filters, proposed by Donoho, which can be used in the Discrete Wavelet Transform domain for compression or denoising. Being nonlinear, these filters can be not robust. This is the reason why we will present here a study of their robustness. We prove that these filters don´t polarize the signals processed and that these systems are robust. The processing systems that use these filters in conjunction with the direct and inverse wavelet transforms are presented. Two examples of application, proving the good qualities of these filters, the first for data compression and the second for denoising are presented. These examples underline the advantages of the use of wavelets in applications like compression or denoising