CaltechAUTHORS
  A Caltech Library Service

Recovery of short, complex linear combinations via ℓ1 minimization

Tropp, Joel A. (2005) Recovery of short, complex linear combinations via ℓ1 minimization. IEEE Transactions on Information Theory, 2005 (4). pp. 1568-1570. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:TROieeetit05b

[img]
Preview
PDF
See Usage Policy.

117Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:TROieeetit05b

Abstract

This note provides a condition under which ℓ1 minimization (also known as basis pursuit) can recover short linear combinations of complex vectors chosen from fixed, overcomplete collection. This condition has already been established in the real setting by Fuchs, who used convex analysis. The proof given here is more direct.


Item Type:Article
Additional Information:© Copyright 2005 IEEE. Reprinted with permission. Manuscript received June 9, 2004; revised January 12, 2005. [Posted online: 2005-04-04] This work was supported by a National Science Foundation Graduate Fellowship. Communicated by V. A. Vaishampayan, Associate Editor At Large. The author wishes to thank both anonymous referees for their insightful remarks
Subject Keywords:Algorithms, approximation, basis pursuit, linear program, redundant dictionaries, sparse representations
Record Number:CaltechAUTHORS:TROieeetit05b
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:TROieeetit05b
Alternative URL:http://dx.doi.org/10.1109/TIT.2005.844057
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9039
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:22 Oct 2007
Last Modified:26 Dec 2012 09:44

Repository Staff Only: item control page