Compressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysis

Simple item page
dc.citation.bibtexNametechreporten_US
dc.citation.journalTitleRice University ECE Technical Reporten_US
dc.citation.locationHouston, TXen_US
dc.contributor.authorChandrasekaran, Venkaten_US
dc.contributor.authorWakin, Michaelen_US
dc.contributor.authorBaron, Droren_US
dc.contributor.authorBaraniuk, Richard G.en_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T00:38:58Zen_US
dc.date.available2007-10-31T00:38:58Zen_US
dc.date.issued2004-03-01en_US
dc.date.modified2006-07-19en_US
dc.date.submitted2004-03-16en_US
dc.descriptionTech Reporten_US
dc.description.abstractDiscontinuities 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 <i>C&sup2;</i> 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 <i>N</i>-dimensional Horizon functions containing a <i>C<sup>K</sup></i> 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 <i>surflet</i> 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 <i>N</i>-dimensional function, without explicitly estimating the (<i>N</i>-1)-dimensional discontinuity. <b><i>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.</i></b>en_US
dc.identifier.citationV. Chandrasekaran, M. Wakin, D. Baron and R. G. Baraniuk, "Compressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysis," <i>Rice University ECE Technical Report,</i> 2004.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19773en_US
dc.language.isoengen_US
dc.subjectwedgeletsen_US
dc.subjectsurfletsen_US
dc.subjectwaveletsen_US
dc.subjectrate-distortionen_US
dc.subjectapproximationen_US
dc.subjectedgesen_US
dc.subjectgeometryen_US
dc.subject.keywordwedgeletsen_US
dc.subject.keywordsurfletsen_US
dc.subject.keywordwaveletsen_US
dc.subject.keywordrate-distortionen_US
dc.subject.keywordapproximationen_US
dc.subject.keywordedgesen_US
dc.subject.keywordgeometryen_US
dc.subject.otherMultiscale geometry processingen_US
dc.titleCompressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysisen_US
dc.typeReporten_US
dc.type.dcmiTexten_US
Files
Original bundle
Now showing 1 - 2 of 2
Thumbnail Image
Name:
Cha2004Mar9Compressin.PDF
Size:
176.12 KB
Format:
Adobe Portable Document Format
Download
No Thumbnail Available
Name:
Cha2004Mar9Compressin.PS
Size:
388.08 KB
Format:
Postscript Files
Download
Collections
ECE Publications
DSP Publications