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Proceedings Paper

Sparse dual frames in compressed sensing
Author(s): Shidong Li; Tiebin Mi; Yulong Liu
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Paper Abstract

A notion of sparse dual frames for a given non-exact frame is introduced. The sparse dual frame is motivated in a study of compressed sensing problems where signal are sparse with respect to a redundant and coherent dictionary (frames). A sparse-dual-based ℓ1-analysis is thereby proposed. We show that sparse dual frames are locally stable. An error bound ensuring the correct signal recovery is obtained. More importantly, solutions to very hard problems in compressed sensing with redundant dictionaries that are otherwise completely unsuccessful by known algorithms of ℓ1-synthesis and the 1-analysis are seen as satisfactory, by the new sparse-dual-based approach and an alternating iterative algorithm that we propose. Examples are provided.

Paper Details

Date Published: 27 September 2011
PDF: 12 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380S (27 September 2011); doi: 10.1117/12.895950
Show Author Affiliations
Shidong Li, San Francisco State Univ. (United States)
Tiebin Mi, Renmin Univ. of China (China)
Yulong Liu, Renmin Univ. of China (China)

Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)

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