压缩感知中块限制等距常数的一个新界限。
A new bound on the block restricted isometry constant in compressed sensing.
作者信息
Gao Yi, Ma Mingde
机构信息
School of Mathematics and Information Science, Beifang University of Nationalities, Wenchang Road, Yinchuan, 750021 China.
Editorial Department of University Journal, Beifang University of Nationalities, Wenchang Road, Yinchuan, 750021 China.
出版信息
J Inequal Appl. 2017;2017(1):174. doi: 10.1186/s13660-017-1448-2. Epub 2017 Aug 1.
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 -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).
本文聚焦于通过[公式：见正文]最小化实现块稀疏恢复的充分条件。我们证明，如果测量矩阵满足[公式：见正文]的块限制等距性质，那么在无噪声情况下，每个块稀疏信号都可以通过[公式：见正文]最小化方法精确恢复，并且在有噪声测量情况下能够稳定恢复。该结果改进了Lin和Li（《数学学报（英文版）》29(7):1401 - 1412, 2013）给出的块限制等距常数[公式：见正文]的界。
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