deposit_your_work

Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets

Files in this item

Files Size Format View
Cha2006Mar1Representa.PDF 793.8Kb application/pdf Thumbnail

Show full item record

Item Metadata

Title: Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets
Author: Chandrasekaran, Venkat; Wakin, Michael; Baron, Dror; Baraniuk, Richard G.
Type: Journal Paper
Keywords: source coding; image compression; video compression; wavelets; wedgelets; geometry
Citation: V. Chandrasekaran, M. Wakin, D. Baron and R. G. Baraniuk, "Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets," None, 2006.
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.
Date Published: 2006-03-01

This item appears in the following Collection(s)

  • ECE Publications [1028 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.