Multiscale image denoising using goodness-of-fit test based on EDF statistics

Two novel image denoising algorithms are proposed which employ goodness of fit (GoF) test at multiple image scales. Proposed methods operate by employing the GoF tests locally on the wavelet coefficients of a noisy image obtained via discrete wavelet transform (DWT) and the dual tree complex wavelet transform (DT-CWT) respectively. We next formulate image denoising as a binary hypothesis testing problem with the null hypothesis indicating the presence of noise and the alternate hypothesis representing the presence of desired signal only. The decision that a given wavelet coefficient corresponds to the null hypothesis or the alternate hypothesis involves the GoF testing based on empirical distribution function (EDF), applied locally on the noisy wavelet coefficients. The performance of the proposed methods is validated by comparing them against the state of the art image denoising methods.