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On rank awareness,thresholding, and MUSIC for joint sparse recovery |
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| Institution: | 1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China;2. Department of Mathematics, Beijing Institute of Petrochemical Technology, Beijing 102617, China;3. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Canada;1. Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, WI 53706, USA;2. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand;1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States of America;2. School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, United States of America;1. School of Electrical and Electronic Engineering, Block S1, 50 Nanyang Avenue, 639798, Singapore;2. School of Marine Science and Technology, Northwestern Polytechnical University, China;3. Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China;4. School of Electronic Information, Wuhan University, China |
| Abstract: | This letter establishes sufficient conditions for the sparse multiple measurement vector (MMV) or row-sparse matrix approximation problem for the Rank Aware Row Thresholding (RART) algorithm. Using the rank aware selection operator to define RART results in discrete MUltiple SIgnal Classification (MUSIC) from array signal processing. When the sensing matrix is drawn from the random Gaussian matrix ensemble, we establish that the rank of the row-sparse measurement matrix in the noiseless row-sparse recovery problem allows RART (MUSIC) to reduce the effect of the penalty term that is present in traditional compressed sensing results and simultaneously provides a row-rank deficient recovery result for MUSIC. Empirical evidence shows that Thresholding closely matches RART in successful row-sparse approximation. The theoretical and empirical evidence provides further support for the conjecture that the thresholding operator in more sophisticated greedy algorithms is the source of their observed rank awareness. |
| Keywords: | Compressed sensing Multiple measurement vectors Row-sparse approximation Rank aware Thresholding MUSIC Joint sparsity |
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