High-order block RIP for nonconvex block-sparse compressed sensing

Abstract This paper concentrates on the recovery of block-sparse signals, which are not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP, which could ensure the exact recovery of every block s -sparse signal in the noiseless case via mixed l2/lp l₂/l₏ minimization method, and the stable and robust recovery in the case that signals are not accurately block-sparse in the presence of noise. Additionally, a lower bound on necessary number of random Gaussian measurements is gained for the condition to be true with overwhelming probability. Furthermore, a series of numerical experiments are conducted to demonstrate the performance of the mixed l2/lp l₂/l₏ minimization. To the best of the authors’ knowledge, the recovery guarantees established in this paper are superior to those currently available.