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

This paper focuses on the sufficient condition of block sparse recovery with the [Formula: see text]-minimization. We show that if the measurement matrix satisfies the block restricted isometry property with [Formula: see text], then every block s-sparse signal can be exactly recovered via the [Formula: see text]-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 [Formula: see text] of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401-1412, 2013).