Geometric methods for wavelet-based image compression

Michael Wakin, Justin Romberg, Hyeokho Choi, Richard Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Scopus citations


Natural images can be viewed as combinations of smooth regions, textures, and geometry. Wavelet-based image coders, such as the space-frequency quantization (SFQ) algorithm, provide reasonably efficient representations for smooth regions (using zerotrees, for example) and textures (using scalar quantization) but do not properly exploit the geometric regularity imposed on wavelet coefficients by features such as edges. In this paper, we develop a representation for wavelet coefficients in geometric regions based on the wedgelet dictionary, a collection of geometric atoms that construct piecewise-linear approximations to contours. Our wedgeprint representation implicitly models the coherency among geometric wavelet coefficients. We demonstrate that a simple compression algorithm combining wedgeprints with zerotrees and scalar quantization can achieve near-optimal rate-distortion performance D(R) ∼ (log R) 2/R 2 for the class of piecewise-smooth images containing smooth C 2 regions separated by smooth C 2 discontinuities. Finally, we extend this simple algorithm and propose a complete compression framework for natural images using a rate-distortion criterion to balance the three representations. Our Wedgelet-SFQ (WSFQ) coder outperforms SFQ in terms of visual quality and mean-square error.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsM.A. Unser, A. Aldroubi, A.F. Laine
Number of pages14
StatePublished - 2003
EventWavelets: Applications in Signal and Image Processing X - San Diego, CA, United States
Duration: Aug 4 2003Aug 8 2003


OtherWavelets: Applications in Signal and Image Processing X
Country/TerritoryUnited States
CitySan Diego, CA


  • Edges
  • Geometry
  • Image compression
  • Wavelets
  • Wedgelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics


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