Signal Denoising Using Wavelets

One of the fields where wavelets have been successfully applied is data analysis. Beginning in the 1990s, wavelets have been found to be a powerful tool for removing noise from a variety of signals (denoising). They allow to analyse the noise level separately at each wavelet scale and to adapt the denoising algorithm accordingly. Wavelet thresholding methods for noise removal, in which the wavelet coefficients are thresholded in order to remove their noisy part, were first introduced by Donoho in 1993. The theoretical justifications and arguments in their favour are highly compelling. These methods do not require any particular assumptions about the nature of the signal, permits discontinuities and spatial variation in the signal, and exploits the spatially adaptive multiresolution of the wavelet transform. This project report presents and discusses two specific thresholding methods. Their main features and limitations are discussed. Two signals contaminated with additive Gaussian additive noise (AWGN) are used for performance evaluation and simulations results are provided.