Group adaptive matching pursuit with intra-group correlation learning for sparse signal recovery

Abstract

In this paper, a Bayesian model is adopted for sparse signal recovery where sparsity is enforced on the reconstructed coefficients via probabilistic priors. In particular, we focus on a group spike-and-slab prior and a kernel matrix which capture both the underlying group structure and the element correlation within groups. A novel greedy based group adaptive matching pursuit (GAMP) algorithm is introduced, which integrates both prior parameter learning and intra-group correlation parameter learning into one single problem. The proposed approach improves the reconstruction accuracy and offers strong robustness to signal-to-noise ratio. We consider a fast implementation method of GAMP which applies the preconditioned conjugate gradient method. Simulations, MNIST dataset based experiments and multi-static radar imaging application are used to verify the superior performance of the proposed method over existing techniques.