Celebratio Mathematica — Daubechies

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Works connected to Wolfgang A. Dahmen

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A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore: “Tree approximation and optimal encoding,” Appl. Comput. Harmon. Anal. 11 : 2 (2001), pp. 192–226. MR 1848303 Zbl 0992.65151 article

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.

Albert Cohen	Related
Ronald Alvin DeVore	Related
Wolfgang A. Dahmen	Related

A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore: “Harmonic analysis of the space BV,” Rev. Mat. Iberoamericana 19 : 1 (2003), pp. 235–263. MR 1993422 Zbl 1044.42028 article

Albert Cohen	Related
Ronald Alvin DeVore	Related
Wolfgang A. Dahmen	Related