Tree Approximation and Optimal Encoding Academic Article uri icon


  • Tree approximation is a new form of nonlinear approximation which appears naturally in some applications such as image processing and adaptive numerical methods. It is somewhat more restrictive than the usual n-term approximation. We show that the restrictions of tree approximation cost little in terms of rates of approximation. We then use that result to design encoders for compression. These encoders are universal (they apply to general functions) and progressive (increasing accuracy is obtained by sending bit stream increments). We show optimality of the encoders in the sense that they provide upper estimates for the Kolmogorov entropy of Besov balls. 2001 Academic Press.

published proceedings

  • Applied and Computational Harmonic Analysis

author list (cited authors)

  • Cohen, A., Dahmen, W., Daubechies, I., & DeVore, R.

citation count

  • 96

complete list of authors

  • Cohen, Albert||Dahmen, Wolfgang||Daubechies, Ingrid||DeVore, Ronald

publication date

  • January 2001