Light-Weight Sequential SBL Algorithm: An Alternative to OMP

We present a Light-Weight Sequential Sparse Bayesian Learning (LWS-SBL) algorithm as an alternative to the orthogonal matching pursuit (OMP) algorithm for the general sparse signal recovery problem. The proposed approach formulates the recovery problem under the Type-II estimation framework and the stochastic maximum likelihood objective. We compare the computational complexity for the proposed algorithm with OMP and highlight the main differences. For the case of parametric dictionaries, a gridless version is developed by extending the proposed sequential SBL algorithm to locally optimize grid points near potential source locations and it is empirically shown that the performance approaches Cramer-Rao bound.´ Numerical results using the proposed approach demonstrate the support recovery performance improvements in different scenarios at a small computational price when compared to the OMP algorithm.