Show simple item record

dc.contributor.authorChandrasekaran, Venkat
Wakin, Michael
Baron, Dror
Baraniuk, Richard G.
dc.creatorChandrasekaran, Venkat
Wakin, Michael
Baron, Dror
Baraniuk, Richard G.
dc.date.accessioned 2007-10-31T00:38:55Z
dc.date.available 2007-10-31T00:38:55Z
dc.date.issued 2004-03-01
dc.date.submitted 2004-03-01
dc.identifier.urihttps://hdl.handle.net/1911/19772
dc.description Conference paper
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.
dc.language.iso eng
dc.subjectwedgelets
surflets
wavelets
rate-distortion
approximation
edges
geometry
dc.subject.otherMultiscale geometry processing
dc.title Compression of Higher Dimensional Functions Containing Smooth Discontinuities
dc.type Conference paper
dc.date.note 2004-03-16
dc.citation.bibtexName inproceedings
dc.date.modified 2006-06-19
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)
dc.subject.keywordwedgelets
surflets
wavelets
rate-distortion
approximation
edges
geometry
dc.citation.location Princeton, NJ
dc.citation.conferenceName Conference on Information Sciences and Systems
dc.type.dcmi Text
dc.type.dcmi Text
dc.identifier.citation V. Chandrasekaran, M. Wakin, D. Baron and R. G. Baraniuk, "Compression of Higher Dimensional Functions Containing Smooth Discontinuities," 2004.


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

  • DSP Publications [508]
    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1321]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students

Show simple item record