Bayesian Pursuit Algorithms
Résumé
This paper addresses the sparse representation (SR) problem within a general Bayesian framework. We show that the Lagrangian formulation of the standard SR problem can be regarded as a limit case of a general maximum a posteriori (MAP) problem involving Bernoulli-Gaussian variables. We then propose different tractable implementations of this MAP problem and explain several well-known pursuit algorithms (e.g., MP, OMP, StOMP, CoSaMP, SP) as particular cases of the proposed Bayesian formulation.