Image coding with geometric wavelets

Dror Alani*, Amir Averbuch, Shai Dekel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.

Original languageEnglish
Pages (from-to)69-77
Number of pages9
JournalIEEE Transactions on Image Processing
Issue number1
StatePublished - Feb 2007


  • Image coding
  • Nonlinear approximation
  • Piecewise polynomial approximation
  • Sparse geometric representations
  • Wavelets and multiresolution processing


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