Statistics Papers
Document Type
Journal Article
Date of this Version
7-2009
Publication Source
IEEE Transactions on Information Theory
Volume
55
Issue
7
Start Page
3388
Last Page
3397
DOI
10.1109/TIT.2009.2021377
Abstract
This paper considers constrained lscr1 minimization methods in a unified framework for the recovery of high-dimensional sparse signals in three settings: noiseless, bounded error, and Gaussian noise. Both lscr1 minimization with an lscrinfin constraint (Dantzig selector) and lscr1 minimization under an llscr2 constraint are considered. The results of this paper improve the existing results in the literature by weakening the conditions and tightening the error bounds. The improvement on the conditions shows that signals with larger support can be recovered accurately. In particular, our results illustrate the relationship between lscr1 minimization with an llscr2 constraint and lscr1 minimization with an lscrinfin constraint. This paper also establishes connections between restricted isometry property and the mutual incoherence property. Some results of Candes, Romberg, and Tao (2006), Candes and Tao (2007), and Donoho, Elad, and Temlyakov (2006) are extended.
Keywords
minimisation, processing, Dantzig selector, Gaussian noise, constrained minimization methods, error bounds, isometry property, mutual incoherence property, sparse signal recovery, compressed sensing, equations, Gaussian noise, helium, least squares method, linear regression, noise measuremnt
Recommended Citation
Cai, T., Xu, G., & Zhang, J. (2009). On Recovery of Sparse Signals Via \ell _{1} Minimization. IEEE Transactions on Information Theory, 55 (7), 3388-3397. http://dx.doi.org/10.1109/TIT.2009.2021377
Date Posted: 27 November 2017
This document has been peer reviewed.