Decay Properties of Restricted Isometry Constants
- 14 April 2009
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Signal Processing Letters
- Vol. 16 (7) , 572-575
- https://doi.org/10.1109/lsp.2009.2020882
Abstract
Many sparse approximation algorithms accurately recover the sparsest solution to an underdetermined system of equations provided the matrix's restricted isometry constants (RICs) satisfy certain bounds. There are no known large deterministic matrices that satisfy the desired RIC bounds; however, members of many random matrix ensembles typically satisfy RIC bounds. This experience with random matrices has colored the view of the RICs' behavior. By modifying matrices assumed to have bounded RICs, we construct matrices whose RICs behave in a markedly different fashion than the classical random matrices; RICs can satisfy desirable bounds and also take on values in a narrow range.Keywords
This publication has 12 references indexed in Scilit:
- CoSaMP: Iterative signal recovery from incomplete and inaccurate samplesApplied and Computational Harmonic Analysis, 2009
- Sparsest solutions of underdetermined linear systems via -minimization forApplied and Computational Harmonic Analysis, 2009
- Restricted Isometry Constants Where $\ell ^{p}$ Sparse Recovery Can Fail for $0≪ p \leq 1$IEEE Transactions on Information Theory, 2009
- On the conditioning of random subdictionariesApplied and Computational Harmonic Analysis, 2008
- Counting faces of randomly projected polytopes when the projection radically lowers dimensionJournal of the American Mathematical Society, 2008
- The restricted isometry property and its implications for compressed sensingComptes Rendus Mathematique, 2008
- Compressive samplingPublished by European Mathematical Society - EMS - Publishing House GmbH ,2007
- Stable signal recovery from incomplete and inaccurate measurementsCommunications on Pure and Applied Mathematics, 2006
- Decoding by Linear ProgrammingIEEE Transactions on Information Theory, 2005
- Atomic Decomposition by Basis PursuitSIAM Review, 2001