Journal of Inequalities and Applications (Aug 2017)
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).
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