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Analysis of sparse representations using bi-orthogonal dictionaries

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dc.contributor.authorVehkapera, M.
dc.contributor.authorKabashima, Y.
dc.contributor.authorChatterjee, S.
dc.contributor.authorAurell, E.
dc.contributor.authorSkoglund, M.
dc.contributor.authorRasmussen, L.
dc.contributor.conference2012 IEEE Information theory workshop (3 Sep 2012 - 7 Sep 2012 : Lausanne, Switzerland)
dc.date.issued2012
dc.description.abstractThe 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, O2 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 l1-recovery is possible with bi-orthogonal dictionaries.
dc.identifier.citationInformation theory workshop, 2012, iss.6404757, pp.647-651
dc.identifier.doi10.1109/ITW.2012.6404757
dc.identifier.isbn9781467302241
dc.identifier.urihttps://hdl.handle.net/1959.8/124268
dc.language.isoen
dc.publisherIEEE
dc.publisher.placeUS
dc.rightsCopyright 2012 IEEE Access Condition Notes: Accepted manuscript is available
dc.source.urihttps://doi.org/10.1109/ITW.2012.6404757
dc.titleAnalysis of sparse representations using bi-orthogonal dictionaries
dc.typeConference paper
pubs.publication-statusPublished
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ror.mmsid9915909772801831

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