Boltzmann machine and mean-field approximation for structured sparse decompositions

Accepté à IEEE Trans. On Signal ProcessingTaking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a marginalized maximum a posteriori problem. To solve this problem, we resort to a mean-field approximation and the variational Bayes Expectation-Maximization" algorithm. This approach results in a soft procedure making no hard decision in the support or the values of the sparse representation. We show that this characteristic leads to an improvement of the performance over state-of-the-art algorithms