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Restricted isometry property of random subdictionaries
- Publication Year :
- 2015
-
Abstract
- We study statistical restricted isometry, a property closely related to sparse signal recovery, of deterministic sensing matrices of size $m \times N$. A matrix is said to have a statistical restricted isometry property (StRIP) of order $k$ if most submatrices with $k$ columns define a near-isometric map of ${\mathbb R}^k$ into ${\mathbb R}^m$. As our main result, we establish sufficient conditions for the StRIP property of a matrix in terms of the mutual coherence and mean square coherence. We show that for many existing deterministic families of sampling matrices, $m=O(k)$ rows suffice for $k$-StRIP, which is an improvement over the known estimates of either $m = \Theta(k \log N)$ or $m = \Theta(k\log k)$. We also give examples of matrix families that are shown to have the StRIP property using our sufficient conditions.<br />Comment: To appear in the IEEE Transactions on Information Theory, 2015. A detailed draft which is a predecessor of this paper appears as arXiv:1303.1847
- Subjects :
- Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1506.06345
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1109/TIT.2015.2448658