Group Adaptive Matching Pursuit with Intra-group Correlation Learning for Sparse Signal Recovery

•A novel generative model in sparse signal recovery is provided, which takes into consideration the group structure and correlation learning within groups. A group spike-and-slab prior is applied to capture the group structure of the signals, whereas a kernel matrix is used to learn the correlations within groups.•A greedy based group adaptive matching pursuit (GAMP) algorithm is proposed to deal with the non-convex optimization problem resulting from the employed prior. This algorithm integrates the prior parameter learning and correlation parameter estimation into one single problem.•A fast implementation method of the GAMP is proposed which exploits the preconditioned conjugate gradient method.