Adaptive support-driven Bayesian reweighted algorithm for sparse signal recovery

Abstract

This paper presents an adaptive support-driven Bayesian reweighted algorithm based on shrinkage thresholding, for large-scale sparse signal recovery. The proposed algorithm is based on the widely used sparse Bayesian learning (SBL) methods, which relies on parameterized prior. SBL leads to a nonconvex optimization problem that encourages model with few nonzero coefficients. In SBL, sparse signal recovery problems can be solved by a reweighted $$\ell _1$$ -regularization algorithm. However, this algorithm is expensive in computation and memory, especially for large-scale problem. To alleviate this problem, we proposed a restart strategy leading to the adaptive support estimate, which reduces the computational burden and memory simultaneously. Numerical experiments demonstrate the effectiveness and computational advantages of the proposed algorithm.