Rank Awareness in Joint Sparse Recovery
Top Cited Papers
- 6 February 2012
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 58 (2), 1135-1146
- https://doi.org/10.1109/tit.2011.2173722
Abstract
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.Keywords
This publication has 38 references indexed in Scilit:
- Rank Awareness in Joint Sparse RecoveryIEEE Transactions on Information Theory, 2012
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm MinimizationSiam Review, 2010
- Compressed sensingIEEE Transactions on Information Theory, 2006
- Algorithms for simultaneous sparse approximation. Part I: Greedy pursuitSignal Processing, 2006
- Stable signal recovery from incomplete and inaccurate measurementsCommunications on Pure and Applied Mathematics, 2006
- Vector greedy algorithmsJournal of Complexity, 2003
- Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 minimizationProceedings of the National Academy of Sciences, 2003
- Optimum Array ProcessingPublished by Wiley ,2002
- Multiple emitter location and signal parameter estimationIEEE Transactions on Antennas and Propagation, 1986
- Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue ProblemsSiam Review, 1973