On the importance of combining wavelet-based nonlinear approximation with coding strategies

Journal Article (Journal Article)

This paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory. Contrasting linear and nonlinear approximation spaces, we show that there are interesting classes of functions/random processes which are much more compactly represented by wavelet-based nonlinear approximation. These classes include locally smooth signals that have singularities, and provide a model for many signals encountered in practice, in particular for images. However, we also show that nonlinear approximation results do not always translate to efficient compression strategies in a rate-distortion sense. Based on this observation, we construct compression techniques and formulate the family of functions/stochastic processes for which they provide efficient descriptions in a rate-distortion sense. We show that this family invariably leads to Besov spaces, yielding a natural relationship among Besov smoothness, linear/nonlinear approximation order, and compression performance in a rate-distortion sense. The designed compression techniques show similarities to modern high-performance transform codecs, allowing us to establish relevant rate-distortion estimates and identify performance limits.

Full Text

Duke Authors

Cited Authors

  • Cohen, A; Daubechies, I; Guleryuz, OG; Orchard, MT

Published Date

  • July 1, 2002

Published In

Volume / Issue

  • 48 / 7

Start / End Page

  • 1895 - 1921

International Standard Serial Number (ISSN)

  • 0018-9448

Digital Object Identifier (DOI)

  • 10.1109/TIT.2002.1013132

Citation Source

  • Scopus