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- Title
Structured random measurements in signal processing.
- Authors
Krahmer, Felix; Rauhut, Holger
- Abstract
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples. While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices. Near optimal recovery guarantees for such structured measurements have been developed over the past years in a variety of contexts. This article surveys the theory in three scenarios: compressed sensing (sparse recovery), low rank matrix recovery, and phaseless estimation. The random measurement matrices to be considered include random partial Fourier matrices, partial random circulant matrices (subsampled convolutions), matrix completion, and phase estimation from magnitudes of Fourier type measurements. The article concludes with a brief discussion of the mathematical techniques for the analysis of such structured random measurements. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
- Subjects
COMPRESSED sensing; SIGNAL processing; IRREGULAR sampling (Signal processing); FOURIER analysis; CIRCULANT matrices
- Publication
GAMM Mitteilungen, 2014, Vol 37, Issue 2, p217
- ISSN
0936-7195
- Publication type
Article
- DOI
10.1002/gamm.201410010