Penalizing local correlations in the residual improves image denoising performance

In this work, we address the problem of denoising an image corrupted by an additive white Gaussian noise. This hypothesis on the noise, despite being very common and justified as the result of a variance normalization step, is hardly used by classical denoising methods. Indeed, very few methods directly constrain the whiteness of the residual (the removed noise). We propose a new variational approach defining generic fidelity terms to locally control the residual distribution using the statistical moments and the correlation on patches. Using different regularizations such as TV or a nonlocal regularization, our approach achieves better performances than the L2 fidelity, with better texture and contrast preservation.