Tree Approximation and Optimal Encoding

Applied and Computational Harmonic Analysis

Volumn 11, Issue 2, 2001, Pages 192-226

  Cohen, Albert ^a   Dahmen, Wolfgang ^b   Daubechies, Ingrid ^c   Devore, Ronald ^d  

^a SORBONNE UNIVERSITÉ   (France)

^b RWTH AACHEN UNIVERSITY   (Germany)

^c PRINCETON UNIVERSITY   (United States)

^d UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Compression; Encoding; Kolmogorov entropy; N term approximation

Indexed keywords

EID: 0035447035     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.2001.0336     Document Type: Article

References (23)

1. Adams R. A. Sobolev Spaces. 1975;Academic Press, San Diego.
2. Birgé L., Massard P. An adaptive compression algorithm in Besov spaces. Constr. Approx. 16:2000;1-36.
3. p. Mat. Sb. 73:1967;295-317.
4. Candès E., Donoho D. Curvelets - A surprisingly effective nonadaptive representation for objects with edges. Cohen A., Babut C., Schumaker L. Curve and Surface Fihing, Saint Malo 1999. 2000;Vanderbilt Univ. Press.
5. Cohen A., Daubechies I., Feauveau J.-C. Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45:1992;485-560.
6. A. Cohen, I. Daubechies, O. Guleryuz, and, M. Orchard, On the importance of combining wavelet based non-linear approximation in coding strategies, IEEE Trans. Inf. Th, in press.
7. Cohen A., DeVore R., Hochmuth R. Restricted approximation. Constr. Approx. 16:2000;85-113.
8. Dahlke S., Dahmen W., DeVore R. Nonlinear approximation and adaptive techniques for solving elliptic equations. Dahmen W., Kurdila A., Oswald P. Multiscale Techniques for PDEs. 1997;237-284 Academic Press, San Diego.
9. Dahlke S., Dahmen W., Hochmuth R., Schneider R. Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23:1997;21-47.
10. Daubechies I. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41:1988;909-996.
11. Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics. 1992;SIAM, Philadelphia.
12. DeVore R. A. Nonlinear approximation. Acta Numer. 7:1998;51-150.
13. DeVore R. A., Jawerth B., Popov V. Compression of wavelet decompositions. Amer. J. Math. 114:1992;737-785.
14. DeVore R. A., Johnson L. S., Pan C., Sharpley R. C. Optimal entropy encoders for mining multiply resolved data. Ebecken N., Brebbia C. A. Data Mining II. 2000;73-82 MIT Press, Boston.
15. DeVore R. A., Lorentz G. G. Constructive Approximation. Grundlehren. 303:1993;Springer-Verlag, Berlin/New York.
16. DeVore R. A., Sharpley R. C. Maximal Functions Measuring Smoothness. Memoirs of the American Mathematical Society. 293:1984;Am. Math. Soc. Providence.
17. Donoho D. Unconditional bases and bit-level compression. Appl. Comput. Harmon. Anal. 3:1996;388-392.
18. Mallat S., Falzon F. Analysis of low bit rate transform coding. IEEE Trans. Signal Process. 46:1998;1027-1042.
19. Güntürk C. Harmonic Analysis of Two Problems in Signal Analysis and Compression. 2000;Princeton University, Princeton.
20. Lorentz G. G., von Golitschek M., Makovoz Ju. Constructive Approximation: Advanced Problems. 1996;Springer-Verlag, Berlin/New York.
21. Said A., Pearlman W. A. An image multyresolution representation for lossless and lossy compression. IEEE Trans. Image Process. 5:1996;1303-1310.
22. Shapiro J. Embedded image coding using zero-trees of wavelet coefficients. IEEE Trans. Signal Process. 41:1993;3445-3462.
23. Temlyakov V. Best m-term approximation and greedy algorithms. Adv. Comput. Math. 8:1998;249-265.