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Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-2638-6047
KTH, School of Computer Science and Communication (CSC), Computational Biology, CB. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
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2012 (English)In: Information Theory Workshop (ITW), 2012 IEEE, IEEE , 2012, 647-651 p.Conference paper, Published paper (Refereed)
Abstract [en]

The sparse representation problem of recovering an N dimensional sparse vector x from M < N linear observations y = Dx given dictionary D is considered. The standard approach is to let the elements of the dictionary be independent and identically distributed (IID) zero-mean Gaussian and minimize the l1-norm of x under the constraint y = Dx. In this paper, the performance of l1-reconstruction is analyzed, when the dictionary is bi-orthogonal D = [O1 O2], where O1, O 2 are independent and drawn uniformly according to the Haar measure on the group of orthogonal M × M matrices. By an application of the replica method, we obtain the critical conditions under which perfect l 1-recovery is possible with bi-orthogonal dictionaries.

Place, publisher, year, edition, pages
IEEE , 2012. 647-651 p.
National Category
Signal Processing Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-107338DOI: 10.1109/ITW.2012.6404757ISI: 000313526400132Scopus ID: 2-s2.0-84873181807ISBN: 978-146730223-4 (print)OAI: oai:DiVA.org:kth-107338DiVA: diva2:575618
Conference
IEEE Information Theory Workshop, ITW 2012; Lausanne;3 September 2012 through 7 September 2012
Funder
Swedish Research Council, 621-2011-1024ICT - The Next Generation
Note

QC 20130219

Available from: 2012-12-10 Created: 2012-12-10 Last updated: 2013-04-11Bibliographically approved

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Chatterjee, SaikatSkoglund, MikaelRasmussen, Lars

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Vehkaperä, MikkoChatterjee, SaikatAurell, ErikSkoglund, MikaelRasmussen, Lars
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Communication TheoryACCESS Linnaeus CentreComputational Biology, CB
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