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 l2/l1$l_{2}/l_{1} minimization. We show that if the measurement matrix satisfies the block restricted isometry property with d2s|I<0.6246$\delta_{2s|\mathcal{I} 0.6246$ then every block s sparse signal can be exactly recovered via the l2/l1$l_{2}/l_{1} minimization approach in the noiseless case and is stably recovered in the noisy measurement case. The result improves the bound on the block restricted isometry constant d2s|I$\delta_{2s|\mathcal {I} of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401 1412, 2013)
Journal of inequalities and applications