Denoising of image patches via sparse representations with learned statistical dependencies

We address the problem of denoising for image patches. The approach taken is based on Bayesian modeling of sparse representations, which takes into account dependencies between the dictionary atoms. Following recent work, we use a Boltzman machine to model the sparsity pattern. In this work we focus on the special case of a unitary dictionary and obtain the exact MAP estimate for the sparse representation using an efficient message passing algorithm. We present an adaptive model-based scheme for sparse signal recovery, which is based on sparse coding via message passing and on learning the model parameters from the data. This adaptive approach is applied on noisy image patches in order to recover their sparse representations over a fixed unitary dictionary. We compare the denoising performance to that of previous sparse recovery methods, which do not exploit the statistical dependencies, and show the effectiveness of our approach.