Exploiting Statistical Dependencies in Sparse Representations for Signal Recovery

Signal modeling lies at the core of numerous signal and image processing applications. A recent approach that has drawn considerable attention is sparse representation modeling, in which the signal is assumed to be generated as a combination of a few atoms from a given dictionary. In this work we consider a Bayesian setting and go beyond the classic assumption of independence between the atoms. The main goal of this paper is to introduce a statistical model that takes such dependencies into account and show how this model can be used for sparse signal recovery. We follow the suggestion of two recent works and assume that the sparsity pattern is modeled by a Boltzmann machine, a commonly used graphical model. We show that for general dependency models, exact MAP estimation of the sparse representation becomes computationally complex. To simplify the computations, we propose a greedy approximation for the MAP estimator. We then consider a special case where exact MAP is feasible, by assu...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Tomer Faktor, Yonina C. Eldar, Michael Elad
• Keywords: CORR 2010, Education, Sparse Representation, Sparse Representation Modeling, Sparse Signal Recovery