New Bounds for Restricted Isometry Constants
- 16 August 2010
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 56 (9), 4388-4394
- https://doi.org/10.1109/tit.2010.2054730
Abstract
This paper discusses new bounds for restricted isometry constants in compressed sensing. Let Φ be an n × p real matrix and A; be a positive integer with k ≤ n. One of the main results of this paper shows that if the restricted isometry constant δk of Φ satisfies δk <; 0.307 then k-sparse signals are guaranteed to be recovered exactly via ℓ1 minimization when no noise is present and k-sparse signals can be estimated stably in the noisy case. It is also shown that the bound cannot be substantially improved. An explicit example is constructed in which δk = k-1/2k-1 <; 0.5, but it is impossible to recover certain k-sparse signals.Keywords
This publication has 14 references indexed in Scilit:
- Shifting Inequality and Recovery of Sparse SignalsIEEE Transactions on Signal Processing, 2009
- On Recovery of Sparse Signals Via $\ell _{1}$ MinimizationIEEE Transactions on Information Theory, 2009
- Sparsest solutions of underdetermined linear systems via ℓq-minimization forApplied and Computational Harmonic Analysis, 2009
- The restricted isometry property and its implications for compressed sensingComptes Rendus Mathematique, 2008
- Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?IEEE Transactions on Information Theory, 2006
- Compressed sensingIEEE Transactions on Information Theory, 2006
- Sparse reconstruction by convex relaxation: Fourier and Gaussian measurementsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2006
- Stable signal recovery from incomplete and inaccurate measurementsCommunications on Pure and Applied Mathematics, 2006
- Stable recovery of sparse overcomplete representations in the presence of noiseIEEE Transactions on Information Theory, 2005
- Uncertainty principles and ideal atomic decompositionIEEE Transactions on Information Theory, 2001