NDLI: Performance of Sparse Representation Algorithms Using Randomly Generated Frames

Content Provider	IEEE Xplore Digital Library
Author	Akcakaya, M. Tarokh, V.
Copyright Year	1994
Abstract	We consider sparse representations of signals with at most L nonzero coefficients using a frame F of size M in C^N. For any F, we establish a universal numerical lower bound on the average distortion of the representation as a function of the sparsity epsiv = L/N of the representation and redundancy (tau - 1) = M/N - 1 of F. In low dimensions (e.g., N = 6, 8.10), this bound is much stronger than the analytical and asymptotic bounds given in another of our papers. In contrast, it is much less straightforward to compute. We then compare the performance of randomly generated frames to this numerical lower bound and to the analytical and asymptotic bounds given in the aforementioned paper. In low dimensions, it is shown that randomly generated frames perform about 2 dB away from the theoretical lower bound, when the optimal sparse representation algorithm is used. In higher dimensions, we evaluate the performance of randomly generated frames using the greedy orthogonal matching pursuit (OMP) algorithm. The results indicate that for small values of epsiv, OMP performs close to the lower bound and suggest that the loss of the suboptimal search using orthogonal matching pursuit algorithm grows as a function of epsiv. In all cases, the performance of randomly generated frames hardens about their average as N grows, even when using the OMP algorithm.
Sponsorship	IEEE Signal Processing Society
Starting Page	777
Ending Page	780
Page Count	4
File Size	327150
File Format	PDF
ISSN	10709908
Volume Number	14
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Matching pursuit algorithms Pursuit algorithms Signal generators Performance analysis Vectors Redundancy Dictionaries Sparse matrices Signal processing algorithms Distortion measurement sparse representations Distortion orthogonal matching pursuit performance bounds random frames
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Signal Processing Electrical and Electronic Engineering

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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