Variational Image Denoising Based on Autocorrelation Whiteness

Variational and PDE-based methods have been widely used over the past two decades for edge-preserving denoising of images. However, in general, these methods fail to preserve textural and other fine scale features but typically remove them in a similar manner as noise. We propose a strategy which fully exploits the prior information available when the noise is known to be white in order to better preserve fine scale features during the denoising process. In particular, based on the assumption that noise is additive and white, we propose a novel fidelity functional to be used in a variational framework in order to enforce whiteness of the residue image. Unlike the classical total variation $L_2$ functional, whose variational analysis yields local differential terms in the resulting Euler--Lagrange equation, our whiteness term exhibits a global first variation, thus transforming the classical Euler--Lagrange PDE into an integro-differential equation which is most conveniently solved using gradient descent techniques. Numerical results show the effectiveness of the proposed strategy.