Adaptive multivariate piecewise polynomial approximation

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5207, Issue 1, 2003, Pages 125-133

  Dekel, Shai ^a   Leviatan, Dany ^b  

^a RealTimeImage   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Multivariate polynomial approximation; Nonlinear approximation; Piecewise polynomial approximation

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; FUNCTIONS; IMAGE COMPRESSION; OSCILLATIONS; SIGNAL PROCESSING; TRIANGULATION;

MULTIVARIATE POLYNOMIAL APPROXIMATION; NONLINEAR APPROXIMATION; PIECEWISE POLYNOMIAL APPROXIMATION;

POLYNOMIAL APPROXIMATION;

EID: 1242330927     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.503961     Document Type: Conference Paper

References (16)

1. R. Adams, Sobolev Spaces, Academic Press, 1975.
2. S. C. Brenner and L. R. Scott, The mathematical theory of finite elements methods, Springer-Verlag, 1994.
3. A. Cohen and B. Matei, "Compact representation of images by edge adapted multiscale transforms", preprint, 2001.
4. S. Dekel and D. Leviatan, "The Bramble-Hilbert lemma for convex domains", preprint, 2002.
5. S. Dekel and D. Leviatan, "On local and piecewise multivariate polynomial approximation", preprint, 2003.
6. S. Dekel, D. Leviatan and M. Sharir, "On bivariate smoothness spaces associated with nonlinear approximation", Constructive Approximation, to appear.
7. R. DeVore, "Nonlinear approximation", Acta Numerica 7 (1998), 51-150.
8. p, 0 < p < 1", Constructive Approximation 11 (1995), 67-83.
9. M. N. Do, P. L. Dragotti, R. Shukla and M. Vetterli, "On the compression of two-dimensional piecewise smooth functions", Proc. of IEEE International Conference on Image Processing (ICIP), Greece, 2001.
10. Fritz John, "Extremum problems with inequalities as subsidiary conditions", in Studies and Essays Presented to R. Courant on his 60th Birthday, Interscience Publishers (1948), 187-204.
11. B. Karaivanov and P. Petrushev, "Nonlinear piecewise polynomial approximation beyond Besov spaces", Industrial Mathematics Institute, University of South Carolina, technical report 01:13, 2001.
12. D. Mumford and J. Shah, "Optimal Approximations of Piecewise Smooth Functions and Associated Variational Problems", Comm. in Pure and Appl. Math. 42 (1989), 577-685.
13. E. Pennec and S. Mallat, "Image compression with geometrical wavelets", preprint, 2001.
14. P. Petrushev, "Nonlinear n - term approximation from hierarchical spline bases", Industrial Mathematics Institute, University of South Carolina, technical report 02:21, 2002.
15. P. Prandoni and M. Vetterli. "Approximation and compression of piecewise-smooth functions", Phil. Trans. R. Soc. Lond. A. 357 (1999), 2573-2591.
16. R. Shukla, P. L. Dragotti, M. N. Do and M. Vetterli, "Rate-distortion optimized tree structured compression algorithms for piecewise smooth images", preprint, 2003.