Translation invariant DWT based denoising using goodness of fit test

A novel signal denoising method based on discrete wavelet transform (DWT) and goodness of fit (GOF) statistical tests employing empirical distribution function (EDF) statistics is proposed. We formulate the denoising problem into a hypothesis testing problem with a null hypothesis H
0
corresponding to the presence of noise, and alternate hypothesis H representing the presence of only desired signal in the samples being tested. The decision process involves GOF tests being applied directly on multiple scales obtained from DWT. Cycle spinning approach is next employed on the de-noised data to render translation invariance property to the proposed method. We evaluate the performance of the resulting method against standard and modern wavelet shrinkage denoising methods through extensive repeated simulations performed on standard test signals.