Bayesian pursuit algorithms

This paper addresses the sparse representation (SR) problem within a general Bayesian framework. We show that the Lagrangian formulation of the standard SR problem, i.e., x* = argmin_x{||y - Dx||²₂ +λ||X||₀}, 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.