Subspace Methods for Joint Sparse Recovery
Subspace Methods for Joint Sparse Recovery
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DOI：
10.1109/tit.2012.2189196
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发表时间：
2012-06-01
影响因子：
2.5
通讯作者：
Junge, Marius
中科院分区：
文献类型：
--
作者：
Lee, Kiryung;Bresler, Yoram;Junge, Marius
针对压缩感知中的联合稀疏恢复问题，提出了一种鲁棒高效的联合稀疏恢复算法，该算法能够同时从多个测量向量中恢复联合稀疏信号的支持度，这些测量向量是通过一个共同的感知矩阵获得的。在一个有利的情况下，未知矩阵，其中包括联合稀疏信号，具有线性无关的非零行。在这种情况下，多重信号分类（MUSIC）算法，最初由施密特提出的传感器阵列处理中的到达方向估计问题，后来提出和分析联合稀疏恢复冯和Bresler，提供了一个保证与最小数量的测量。相反，我们专注于不利的，但实际上重要的情况下，秩缺陷或病态。这种情况在测量向量的数量有限或高度相关的信号分量的情况下出现。在这种情况下，MUSIC失败，并且在实践中，现有方法中没有一种可以始终接近基本极限。我们提出了子空间增强的MUSIC（SA-MUSIC），它改进了MUSIC，使支持在这种不利的条件下可靠地恢复。结合一个基于子空间的贪婪算法，称为正交子空间匹配追踪，这也是本文提出和分析，SA-MUSIC提供了一个计算效率与性能保证的算法。性能保证是在一个版本的限制等距属性。特别是，我们还提出了一个非渐近扰动分析的信号子空间估计的步骤，这在以前的研究中失踪的MUSIC。
We propose robust and efficient algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common sensing matrix. In a favorable situation, the unknown matrix, which consists of the jointly sparse signals, has linearly independent nonzero rows. In this case, the MUltiple SIgnal Classification (MUSIC) algorithm, originally proposed by Schmidt for the direction of arrival estimation problem in sensor array processing and later proposed and analyzed for joint sparse recovery by Feng and Bresler, provides a guarantee with the minimum number of measurements. We focus instead on the unfavorable but practically significant case of rank defect or ill-conditioning. This situation arises with a limited number of measurement vectors, or with highly correlated signal components. In this case, MUSIC fails and, in practice, none of the existing methods can consistently approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC), which improves on MUSIC such that the support is reliably recovered under such unfavorable conditions. Combined with a subspace-based greedy algorithm, known as Orthogonal Subspace Matching Pursuit, which is also proposed and analyzed in this paper, SA-MUSIC provides a computationally efficient algorithm with a performance guarantee. The performance guarantees are given in terms of a version of the restricted isometry property. In particular, we also present a non-asymptotic perturbation analysis of the signal subspace estimation step, which has been missing in the previous studies of MUSIC.