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Surflets: a sparse representation for multidimensional functions containing smooth discontinuities

Chandrasekaran, Venkat and Wakin, Michael B. and Baron, Dror and Baraniuk, Richard G. (2004) Surflets: a sparse representation for multidimensional functions containing smooth discontinuities. In: 2004 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, p. 565. ISBN 0-7803-8280-3 http://resolver.caltech.edu/CaltechAUTHORS:20121011-131626671

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Abstract

Discontinuities in data often provide vital information, and representing these discontinuities sparsely is an important goal for approximation and compression algorithms. Little work has been done on efficient representations for higher dimensional functions containing arbitrarily smooth discontinuities. We consider the N-dimensional Horizon class-N-dimensional functions containing a C^K smooth (N-1)-dimensional singularity separating two constant regions. We derive the optimal rate-distortion function for this class and introduce the multiscale surflet representation for sparse piecewise approximation of these functions. We propose a compression algorithm using surflets that achieves the optimal asymptotic rate-distortion performance for Horizon functions. This algorithm can be implemented using knowledge of only the N-dimensional function, without explicitly estimating the (N-1)-dimensional discontinuity.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2004.1365602DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1365602PublisherUNSPECIFIED
Additional Information:© 2004 IEEE. Date of Current Version: 10 January 2005. This work was supported by NSF grant CCR-9973188, ONR grant N00014-02-1-0353, AFOSR grant F49620-01-1-0378, and the Texas Instruments Leadership University Program.
Funders:
Funding AgencyGrant Number
NSFCCR-9973188
Office of Naval Research (ONR)N00014-02-1-0353
Air Force Office of Scientific Research (AFOSR)F49620-01-1-0378
Texas Instruments Leadership University ProgramUNSPECIFIED
Record Number:CaltechAUTHORS:20121011-131626671
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20121011-131626671
Official Citation:Chandrasekaran, V.; Wakin, M.B.; Baron, D.; Baraniuk, R.G.; , "Surflets: a sparse representation for multidimensional functions containing smooth discontinuities," Information Theory, 2004. ISIT 2004. Proceedings. International Symposium on , vol., no., pp. 563, 27 June-2 July 2004 doi: 10.1109/ISIT.2004.1365602 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1365602&isnumber=29909
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34853
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Oct 2012 20:57
Last Modified:27 Dec 2012 02:51

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