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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. doi:10.1109/TIT.2005.844057.

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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.

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Tropp, Joel A.0000-0003-1024-1791
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
Issue or Number:4
Record Number:CaltechAUTHORS:TROieeetit05b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9039
Deposited By: Archive Administrator
Deposited On:22 Oct 2007
Last Modified:08 Nov 2021 20:55

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