Block Sparse Vector Recovery for Compressive Sensing via $\ell_1-\alpha\ell_q$-minimization Model

This paper solves the problem of block sparse vector recovery using the block $\ell_1-\alpha\ell_q$- minimization model. Based on the block restricted isometry property (B-RIP) condition, we obtain exact block sparse vector recovery result. We also obtain the theoretical bound for the block $\ell_1-\alpha\ell_q$- minimization model when measurements are depraved by the noises.