Translation invariant multi-scale signal denoising based on goodness-of-fit tests

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 cast the denoising problem into a hypothesis testing problem with a null hypothesis H0 corresponding to the presence of noise, and an alternative hypothesis H1 representing the presence of only desired signal in the samples being tested. The decision process involves GOF tests, employing statistics based on EDF, which is applied directly on multiple scales obtained from DWT. The resulting coefficients found to be belonging to noise are discarded while the remaining coefficients - corresponding to the desired signal - are retained. The cycle spinning approach is next employed on the denoised data to introduce translation invariance into the proposed method. The performance of the resulting method is evaluated against standard and modern wavelet shrinkage denoising methods through extensive repeated simulations performed on standard test signals. Simulation results on real world noisy images are also presented to demonstrate the effectiveness of the proposed method.