Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets

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dc.citation.bibtexNamearticleen_US
dc.citation.journalTitleNoneen_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.accessioned2007-10-31T00:39:27Zen_US
dc.date.available2007-10-31T00:39:27Zen_US
dc.date.issued2006-03-01en_US
dc.date.modified2006-07-19en_US
dc.date.submitted2006-03-22en_US
dc.descriptionJournal Paperen_US
dc.description.abstractWe study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution predictive coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our coder has near-optimal rate-distortion performance. Our coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results demonstrate that surflets provide superior compression performance when compared to other state-of-the-art approximation schemes.en_US
dc.identifier.citationV. Chandrasekaran, M. Wakin, D. Baron and R. G. Baraniuk, "Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets," <i>None,</i> 2006.en_US
dc.identifier.doihttp://dx.doi.org/10.1109/TIT.2008.2008153en_US
dc.identifier.urihttps://hdl.handle.net/1911/19785en_US
dc.language.isoengen_US
dc.subjectsource codingen_US
dc.subjectimage compressionen_US
dc.subjectvideo compressionen_US
dc.subjectwaveletsen_US
dc.subjectwedgeletsen_US
dc.subjectgeometryen_US
dc.subject.keywordsource codingen_US
dc.subject.keywordimage compressionen_US
dc.subject.keywordvideo compressionen_US
dc.subject.keywordwaveletsen_US
dc.subject.keywordwedgeletsen_US
dc.subject.keywordgeometryen_US
dc.subject.otherMultiscale geometry processingen_US
dc.titleRepresentation and Compression of Multi-Dimensional Piecewise Functions Using Surfletsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
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