Analysis of sparse representations using bi-orthogonal dictionaries
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(Published version)
Date
2012
Authors
Vehkapera, M.
Kabashima, Y.
Chatterjee, S.
Aurell, E.
Skoglund, M.
Rasmussen, L.
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Conference paper
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Information theory workshop, 2012, iss.6404757, pp.647-651
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2012 IEEE Information theory workshop (3 Sep 2012 - 7 Sep 2012 : Lausanne, Switzerland)
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, 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.
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Copyright 2012 IEEE
Access Condition Notes: Accepted manuscript is available