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Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries
- Publication Year :
- 2012
-
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.<br />QC 20130219
Details
- Database :
- OAIster
- Notes :
- Vehkaperä, Mikko, Kabashima, Yoshiyuki, Chatterjee, Saikat, Aurell, Erik, Skoglund, Mikael, Rasmussen, Lars
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1234493124
- Document Type :
- Electronic Resource
- Full Text :
- https://doi.org/10.1109.ITW.2012.6404757