Rank Awareness in Joint Sparse Recovery
Rank Awareness in Joint Sparse Recovery
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DOI：
10.1109/tit.2011.2173722
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发表时间：
2012-02-01
影响因子：
2.5
通讯作者：
Eldar, Yonina C.
中科院分区：
文献类型：
--
作者：
Davies, Mike E.;Eldar, Yonina C.
本文重新审视稀疏多重测量向量（MMV）问题，其目的是从不完整的测量中恢复一组联合稀疏多通道向量。这个问题是单通道稀疏恢复的延伸，是压缩感知的核心。受阵列信号处理链接的启发，人们考虑了一系列新的 MMV 算法，强调了等级在确定 MMV 恢复问题的难度方面的作用。最简单的此类方法是 MUSIC 的离散版本，它保证在温和条件下恢复满秩 MMV 设置中的稀疏向量。这个想法被扩展到排序感知追踪算法，该算法自然地在单一测量情况下简化为阶次递归匹配追踪（ORMP），同时还在全排序设置中提供有保证的恢复。相比之下，流行的 MMV 方法（例如同时正交匹配追踪 (SOMP) 和混合范数最小化技术）在最坏情况分析方面被证明是排名盲的。数值模拟表明，排名感知技术在处理多个测量方面明显优于现有方法。
This paper revisits the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem is an extension of single channel sparse recovery, which lies at the heart of compressed sensing. Inspired by the links to array signal processing, a new family of MMV algorithms is considered that highlight the role of rank in determining the difficulty of the MMV recovery problem. The simplest such method is a discrete version of MUSIC which is guaranteed to recover the sparse vectors in the full rank MMV setting, under mild conditions. This idea is extended to a rank aware pursuit algorithm that naturally reduces to Order Recursive Matching Pursuit (ORMP) in the single measurement case while also providing guaranteed recovery in the full rank setting. In contrast, popular MMV methods such as Simultaneous Orthogonal Matching Pursuit (SOMP) and mixed norm minimization techniques are shown to be rank blind in terms of worst case analysis. Numerical simulations demonstrate that the rank aware techniques are significantly better than existing methods in dealing with multiple measurements.