A new bound on the block restricted isometry constant in compressed sensing

摘要

This paper focuses on the sufficient condition of block sparse recovery with the l2/l1-minimization. We show that if the measurement matrix satisfies the block restricted isometry property with δ2s|ℐ  0.6246, then every block s-sparse signal can be exactly recovered via the l2/l1-minimization approach in the noiseless case and is stably recovered in the noisy measurement case. The result improves the bound on the block restricted isometry constant δ2s|ℐ of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401-1412, ).