DocumentCode :
106394
Title :
Recovery of Low Rank and Jointly Sparse Matrices with Two Sampling Matrices
Author :
Biswas, Sampurna ; Achanta, Hema K. ; Jacob, Mathews ; Dasgupta, Soura ; Mudumbai, Raghuraman
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USA
Volume :
22
Issue :
11
fYear :
2015
fDate :
Nov. 2015
Firstpage :
1945
Lastpage :
1949
Abstract :
We provide a two-step approach to recover a jointly k-sparse matrix X, (at most k rows of X are nonzero), with rank r <; <; k from its under sampled measurements. Unlike the classical recovery algorithms that use the same measurement matrix for every column of X, the proposed algorithm comprises two stages, in each of which the measurement is taken by a different measurement matrix. The first stage uses a standard algorithm, [4] to recover any r columns (e.g. the first r) of X. The second uses a new set of measurements and the subspace estimate provided by these columns to recover the rest. We derive conditions on the second measurement matrix to guarantee perfect subspace aware recovery for two cases: First a worst-case setting that applies to all matrices. The second a generic case that works for almost all matrices. We demonstrate both theoretically and through simulations that when r <; <; k our approach needs far fewer measurements. It compares favorably with recent results using dense linear combinations, that do not use column-wise measurements.
Keywords :
compressed sensing; sparse matrices; column-wise measurements; compressed sensing; dense linear combinations; low rank sparse matrices recovery; measurement matrix; sampling matrices; subspace estimation; Algorithm design and analysis; Current measurement; Government; Imaging; Jacobian matrices; Signal processing algorithms; Sparse matrices; Dynamic imaging; joint sparsity; low rank; rank aware ORMP;
fLanguage :
English
Journal_Title :
Signal Processing Letters, IEEE
Publisher :
ieee
ISSN :
1070-9908
Type :
jour
DOI :
10.1109/LSP.2015.2447455
Filename :
7128706
Link To Document :
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