Analysis of sparse representations using bi-orthogonal dictionaries

Mikko Vehkaperä, Yoshiyuki Kabashima, Saikat Chatterjee, Erik Aurell, Mikael Skoglund, Lars Rasmussen

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication2012 IEEE Information Theory Workshop, ITW 2012
Pages647-651
ISBN (Electronic)978-1-4673-0223-4
DOIs
Publication statusPublished - 1 Dec 2012
MoE publication typeA4 Article in a conference publication
Event2012 IEEE Information Theory Workshop, ITW 2012 - Lausanne, Switzerland
Duration: 3 Sep 20127 Sep 2012

Conference

Conference2012 IEEE Information Theory Workshop, ITW 2012
CountrySwitzerland
CityLausanne
Period3/09/127/09/12

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Vehkaperä, M., Kabashima, Y., Chatterjee, S., Aurell, E., Skoglund, M., & Rasmussen, L. (2012). Analysis of sparse representations using bi-orthogonal dictionaries. In 2012 IEEE Information Theory Workshop, ITW 2012 (pp. 647-651). [6404757] https://doi.org/10.1109/ITW.2012.6404757