Surflets: A sparse representation for multidimensional functions containing smooth discontinuities

Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

26 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationIEEE International Symposium on Information Theory - Proceedings
Pages563
Number of pages1
StatePublished - 2004
EventProceedings - 2004 IEEE International Symposium on Information Theory - Chicago, IL, United States
Duration: Jun 27 2004Jul 2 2004

Other

OtherProceedings - 2004 IEEE International Symposium on Information Theory
CountryUnited States
CityChicago, IL
Period6/27/047/2/04

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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