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dc.contributor.authorChandrasekaran, Venkat
Wakin, Michael
Baron, Dror
Baraniuk, Richard G.
dc.creatorChandrasekaran, Venkat
Wakin, Michael
Baron, Dror
Baraniuk, Richard G.
dc.date.accessioned 2007-10-31T00:38:58Z
dc.date.available 2007-10-31T00:38:58Z
dc.date.issued 2004-03-01
dc.date.submitted 2004-03-16
dc.identifier.urihttp://hdl.handle.net/1911/19773
dc.description Tech Report
dc.description.abstract Discontinuities in data often represent the key information of interest. Efficient representations for such discontinuities are important for many signal processing applications, including compression, but standard Fourier and wavelet representations fail to efficiently capture the structure of the discontinuities. These issues have been most notable in image processing, where progress has been made on modeling and representing one-dimensional edge discontinuities along C&sup2; curves. Little work, however, has been done on efficient representations for higher dimensional functions or on handling higher orders of smoothness in discontinuities. In this paper, we consider the class of N-dimensional Horizon functions containing a C<sup>K</sup> smooth singularity in N-1 dimensions, which serves as a manifold boundary between two constant regions; we first derive the optimal rate-distortion function for this class. We then introduce the surflet representation for approximation and compression of Horizon-class functions. Surflets enable a multiscale, piecewise polynomial approximation of the discontinuity. We propose a compression algorithm using surflets that achieves the optimal asymptotic rate-distortion performance for this function class. Equally important, the algorithm can be implemented using knowledge of only the N-dimensional function, without explicitly estimating the (N-1)-dimensional discontinuity. This technical report is a supplement to a CISS 2004 paper "Compression of Higher Dimensional Functions Containing Smooth Discontinuities". The body of the paper is the same, while the appendices contain additional details and proofs for all theorems.
dc.language.iso eng
dc.subjectwedgelets
surflets
wavelets
rate-distortion
approximation
edges
geometry
dc.subject.otherMultiscale geometry processing
dc.title Compressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysis
dc.type Report
dc.citation.bibtexName techreport
dc.citation.journalTitle Rice University ECE Technical Report
dc.date.modified 2006-07-19
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)
dc.subject.keywordwedgelets
surflets
wavelets
rate-distortion
approximation
edges
geometry
dc.citation.location Houston, TX
dc.type.dcmi Text
dc.type.dcmi Text
dc.identifier.citation V. Chandrasekaran, M. Wakin, D. Baron and R. G. Baraniuk, "Compressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysis," Rice University ECE Technical Report, 2004.


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  • DSP Publications [508]
    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1268]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students

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