Tree Approximation and Optimal Encoding
Publication
, Journal Article
Cohen, A; Dahmen, W; Daubechies, I; Devore, R
Published in: Applied and Computational Harmonic Analysis
September 1, 2001
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.
Duke Scholars
Published In
Applied and Computational Harmonic Analysis
DOI
ISSN
1063-5203
Publication Date
September 1, 2001
Volume
11
Issue
2
Start / End Page
192 / 226
Related Subject Headings
- Numerical & Computational Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Cohen, A., Dahmen, W., Daubechies, I., & Devore, R. (2001). Tree Approximation and Optimal Encoding. Applied and Computational Harmonic Analysis, 11(2), 192–226. https://doi.org/10.1006/acha.2001.0336
Cohen, A., W. Dahmen, I. Daubechies, and R. Devore. “Tree Approximation and Optimal Encoding.” Applied and Computational Harmonic Analysis 11, no. 2 (September 1, 2001): 192–226. https://doi.org/10.1006/acha.2001.0336.
Cohen A, Dahmen W, Daubechies I, Devore R. Tree Approximation and Optimal Encoding. Applied and Computational Harmonic Analysis. 2001 Sep 1;11(2):192–226.
Cohen, A., et al. “Tree Approximation and Optimal Encoding.” Applied and Computational Harmonic Analysis, vol. 11, no. 2, Sept. 2001, pp. 192–226. Scopus, doi:10.1006/acha.2001.0336.
Cohen A, Dahmen W, Daubechies I, Devore R. Tree Approximation and Optimal Encoding. Applied and Computational Harmonic Analysis. 2001 Sep 1;11(2):192–226.
Published In
Applied and Computational Harmonic Analysis
DOI
ISSN
1063-5203
Publication Date
September 1, 2001
Volume
11
Issue
2
Start / End Page
192 / 226
Related Subject Headings
- Numerical & Computational Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics