Wavelets and Functions with Bounded Variation from Image Processing to Pure Mathematics

Yves Meyer

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: S1, page 77-105
  • ISSN: 1120-6330

Abstract

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JPEG-2000 has the potential to be the most significant advance in still image compression since the introduction of JPEG over a decade ago. JPEG-2000 is a wavelet based algorithm and it relies on new estimates on wavelet coefficients of functions of bounded variation. These new estimates have far reaching implications in pure mathematics.

How to cite

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Meyer, Yves. "Wavelets and Functions with Bounded Variation from Image Processing to Pure Mathematics." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.S1 (2000): 77-105. <http://eudml.org/doc/289670>.

@article{Meyer2000,
abstract = {JPEG-2000 has the potential to be the most significant advance in still image compression since the introduction of JPEG over a decade ago. JPEG-2000 is a wavelet based algorithm and it relies on new estimates on wavelet coefficients of functions of bounded variation. These new estimates have far reaching implications in pure mathematics.},
author = {Meyer, Yves},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
language = {eng},
month = {12},
number = {S1},
pages = {77-105},
publisher = {Accademia Nazionale dei Lincei},
title = {Wavelets and Functions with Bounded Variation from Image Processing to Pure Mathematics},
url = {http://eudml.org/doc/289670},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Meyer, Yves
TI - Wavelets and Functions with Bounded Variation from Image Processing to Pure Mathematics
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/12//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - S1
SP - 77
EP - 105
AB - JPEG-2000 has the potential to be the most significant advance in still image compression since the introduction of JPEG over a decade ago. JPEG-2000 is a wavelet based algorithm and it relies on new estimates on wavelet coefficients of functions of bounded variation. These new estimates have far reaching implications in pure mathematics.
LA - eng
UR - http://eudml.org/doc/289670
ER -

References

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  14. MOREL, J.-M., Filtres itératifs des images et équations aux dérivées partielles. Notes de cours du centre Emile Borel, 1998. 
  15. MOREL, J.-M. - SOLIMINI, S., Variational methods in image segmentation. Birkhäuser, Boston1995. 
  16. MUMFORD, D., Book reviews on [12]. Bulletin of the American Mathematical Society, vol. 33, n. 2, April 1996. 
  17. MUMFORD, D. - SHAH, J., Boundary detection by minimizing functionals. Proc. IEEE Conf. Comp. Vis. Pattern Recognition, 1985. 
  18. ORU, F., Le rôle des oscillations dans quelques problèmes d'analyse non-linéaire. Thèse, CMLA, Ecole Norm. Sup. de Cachan, 9 Juin 1998. 
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