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Surflets: A Sparse Representation for Multidimensional Functions Containing Smooth Discontinuities

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Title: Surflets: A Sparse Representation for Multidimensional Functions Containing Smooth Discontinuities
Author: Chandrasekaran, Venkat; Wakin, Michael; Baron, Dror; Baraniuk, Richard G.
Type: Conference Paper
Keywords: data compression; image compression; wedgelets; wavelets; surflets; geometry; edges
Citation: V. Chandrasekaran, M. Wakin, D. Baron and R. G. Baraniuk,"Surflets: A Sparse Representation for Multidimensional Functions Containing Smooth Discontinuities," in IEEE Symposium on Information Theory,
Abstract: Discontinuities in data often provide vital information, and representing these discontinuities sparsely is an important goal for approximation and compression algorithms. Little work has been done on efficient representations for higher dimensional functions containing arbitrarily smooth discontinuities. We consider the N-dimensional Horizon class -- N-dimensional functions containing a C^K smooth (N-1)-dimensional singularity separating two constant regions. We derive the optimal rate-distortion function for this class and introduce the multiscale surflet representation for sparse piecewise approximation of these functions. We propose a compression algorithm using surflets that achieves the optimal asymptotic rate-distortion performance for Horizon functions. This algorithm can be implemented using knowledge of only the N-dimensional function, without explicitly estimating the (N-1)-dimensional discontinuity.
Date Published: 2004-07-01

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  • ECE Publications [1082 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.