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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 2007-10-31T00:39:27Z
dc.date.available 2007-10-31T00:39:27Z
dc.date.issued 2006-03-01
dc.date.submitted 2006-03-22
dc.identifier.citation V. Chandrasekaran, M. Wakin, D. Baron and R. G. Baraniuk, "Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets," None, 2006.
dc.identifier.urihttps://hdl.handle.net/1911/19785
dc.description Journal Paper
dc.description.abstract We 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.
dc.language.iso eng
dc.subjectsource coding
image compression
video compression
wavelets
wedgelets
geometry
dc.subject.otherMultiscale geometry processing
dc.title Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets
dc.type Journal article
dc.citation.bibtexName article
dc.citation.journalTitle None
dc.date.modified 2006-07-19
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)
dc.subject.keywordsource coding
image compression
video compression
wavelets
wedgelets
geometry
dc.type.dcmi Text
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1109/TIT.2008.2008153


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  • DSP Publications [508]
    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1294]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students

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