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

Abstract

Abstract This paper focuses on the sufficient condition of block sparse recovery with the l 2 / l 1 $l_{2}/l_{1}$ -minimization. We show that if the measurement matrix satisfies the block restricted isometry property with δ 2 s | I < 0.6246 $\delta_{2s|\mathcal{I}}< 0.6246$ , then every block s-sparse signal can be exactly recovered via the l 2 / l 1 $l_{2}/l_{1}$ -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 δ 2 s | I $\delta_{2s|\mathcal {I}}$ of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401-1412, 2013).

Keywords

• compressed sensing
• l 2 / l 1 $l_{2}/l_{1}$ -minimization
• block sparse recovery
• block restricted isometry property
• null space property