DocumentCode :
3120562
Title :
Sparse signal separation in redundant dictionaries
Author :
Aubel, Celine ; Studer, Christoph ; Pope, G. ; Bolcskei, Helmut
Author_Institution :
Dept. of IT &EE, ETH Zurich, Zurich, Switzerland
fYear :
2012
fDate :
1-6 July 2012
Firstpage :
2047
Lastpage :
2051
Abstract :
We formulate a unified framework for the separation of signals that are sparse in “morphologically” different redundant dictionaries. This formulation incorporates the so-called “analysis” and “synthesis” approaches as special cases and contains novel hybrid setups. We find corresponding coherence-based recovery guarantees for an ℓ1-norm based separation algorithm. Our results recover those reported in Studer and Baraniuk, ACHA, submitted, for the synthesis setting, provide new recovery guarantees for the analysis setting, and form a basis for comparing performance in the analysis and synthesis settings. As an aside our findings complement the D-RIP recovery results reported in Candès et al., ACHA, 2011, for the “analysis” signal recovery problem minimize x ||Ψx̃||1 subject to ||y - Ax̃||2 ≤ ϵ by delivering corresponding coherence-based recovery results.
Keywords :
coherence; redundancy; source separation; sparse matrices; ACHA; Baraniuk; D-RIP recovery; Studer; coherence-based recovery; hybrid setups; redundant dictionaries; signal recovery problem; sparse signal separation; unified framework; Coherence; Dictionaries; Educational institutions; Image restoration; Sparse matrices; USA Councils; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
ISSN :
2157-8095
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
Type :
conf
DOI :
10.1109/ISIT.2012.6283720
Filename :
6283720
Link To Document :
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