Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries
2012 (English)In: Information Theory Workshop (ITW), 2012 IEEE, IEEE , 2012, 647-651 p.Conference paper (Refereed)
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.
Signal Processing Other Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-107338DOI: 10.1109/ITW.2012.6404757ISI: 000313526400132ScopusID: 2-s2.0-84873181807ISBN: 978-146730223-4OAI: oai:DiVA.org:kth-107338DiVA: diva2:575618
IEEE Information Theory Workshop, ITW 2012; Lausanne;3 September 2012 through 7 September 2012
FunderSwedish Research Council, 621-2011-1024ICT - The Next Generation
QC 201302192012-12-102012-12-102013-04-11Bibliographically approved