Journal article
Recovery of Low Rank and Jointly Sparse Matrices with Two Sampling Matrices
IEEE signal processing letters, Vol.22(11), pp.1945-1949
11/2015
DOI: 10.1109/LSP.2015.2447455
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.
Details
- Title: Subtitle
- Recovery of Low Rank and Jointly Sparse Matrices with Two Sampling Matrices
- Creators
- Sampurna Biswas - Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USAHema K Achanta - Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USAMathews Jacob - Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USASoura Dasgupta - Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USARaghuraman Mudumbai - Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USA
- Resource Type
- Journal article
- Publication Details
- IEEE signal processing letters, Vol.22(11), pp.1945-1949
- Publisher
- IEEE
- DOI
- 10.1109/LSP.2015.2447455
- ISSN
- 1070-9908
- eISSN
- 1558-2361
- Grant note
- 1R21HL109710-01A1 / National Institutes of Health (10.13039/100000002) 1329657 / Division of Computer and Network Systems (10.13039/100000144) 1116067; 1302456 / Division of Computing and Communication Foundations (10.13039/100000143) N00014-13-1-0202 / Office of Naval Research (10.13039/100000006)
- Language
- English
- Date published
- 11/2015
- Academic Unit
- Electrical and Computer Engineering; Roy J. Carver Department of Biomedical Engineering; Radiology; Radiation Oncology; Iowa Neuroscience Institute
- Record Identifier
- 9984070208802771
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