New bounds on the restricted isometry constant [delta]2k

• Published in: Applied and computational harmonic analysis Vol. 31; no. 3; pp. 460 - 468
• Main Authors: Mo, Qun, Li, Song
• Format: Journal Article
• Language: English
• Published: 01-11-2011
• Subjects: Compressed; Fourier analysis; Harmonic analysis; Mathematical models; Noise; Optimization; Recovering
• ISSN: 1063-5203
• DOI: 10.1016/j.acha.2011.04.005

Restricted isometry constants play an important role in compressed sensing. In the literature, E.J. Candes has proven that [inline image] is a sufficient condition for the l sub(1 minimization problem having a k-sparse solution. Later, S. Foucart and M. Lai have improved the condition to [delta]2k0.4531 and S. Foucart has improved the bound to [delta]2k0.4652. In 2010, T. Cai, L. Wang and G. Xu have improved the condition to [delta]2k0.4721 for the cases such that k is a multiple of 4 or k is very large and S. Foucart has improved the bound to [delta]2k0.4734 for large values of k. In this paper, we have improved the sufficient condition to [delta]2k0.4931 for general k. Also, in some special cases, the sufficient condition can be improved to [delta]2k0.6569. These new bounds have several benefits on recovering compressible signals with noise.)