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||
²
2
+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.