Analysis of convergence for the alternating direction method applied to joint sparse recovery
Analysis of convergence for the alternating direction method applied to joint sparse recovery
复制标题
交替方向法联合稀疏恢复的收敛性分析
DOI：
10.1016/j.amc.2015.07.104
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发表时间：
2015-10-15
影响因子：
4
通讯作者：
Lei, Yuan
中科院分区：
文献类型：
--
作者：
Liao, Anping;Yang, Xiaobo;Lei, Yuan
多测量向量（MMV）的稀疏表示是压缩感知理论中的一个重要问题，旧的交替方向方法（ADM）是一种优化算法，由于其能够解决大规模或分布式问题而最近变得非常流行。 H. Lu等人提出了利用ADM解决MMV问题的MMV-ADM算法。 (2011)]24]，但该算法生成的矩阵迭代序列收敛的理论结果留作未来的研究课题。本文基于向量二范数的次微分性质，建立了与矩阵相关的收缩算子。利用该算子证明了收敛定理，表明MMV-ADM算法能够恢复联合稀疏向量。 (C) 2015 Elsevier Inc. 保留所有权利。
The sparse representation of a multiple measurement vector (MMV) is an important problem in compressed sensing theory, the old alternating direction method (ADM) is an optimization algorithm that has recently become very popular due to its capabilities to solve large-scale or distributed problems. The MMV-ADM algorithm to solve the MMV problem by ADM has been proposed by H. Lu, et al. (2011)] 24], but the theoretical result about the convergence of matrix iteration sequence generated by the algorithm is left as a future research topic. In this paper, based on the subdifferential property of the two-norm for vector, a shrink operator associated with matrix is established. By using the operator, a convergence theorem is proved, which shows the MMV-ADM algorithm can recover the jointly sparse vectors. (C) 2015 Elsevier Inc. All rights reserved.