[Curvelets et Opérateurs Intégraux de Fourier]
Une série de récents articles ont introduit l'analyse en curvelets E. Candès, D. Donoho, in : (i) Curvelets – a surprisingly effective nonadaptive representation for objects with edges (A. Cohen, C. Rabut, L. Schumaker (Eds.)), Vanderbilt University Press, Nashville, 2000, pp. 105–120 ; (ii) http://www.acm.caltech.edu/~emmanuel/publications.html, 2002 : les curvelets offrent une représentation multi-échelle qui ouvre de nouvelles perspectives pour l'analyse de problèmes importants en théorie de l'approximation et en traitement de l'image. Cet article montre que les curvelets permettent une représentation optimale de la classe des opérateurs intégraux de Fourier. Par « optimale », nous entendons par exemple, la plus économe.
A recent body of work introduced new tight-frames of curvelets E. Candès, D. Donoho, in: (i) Curvelets – a suprisingly effective nonadaptive representation for objects with edges (A. Cohen, C. Rabut, L. Schumaker (Eds.)), Vanderbilt University Press, Nashville, 2000, pp. 105–120; (ii) http://www.acm.caltech.edu/~emmanuel/publications.html, 2002 to address key problems in approximation theory and image processing. This paper shows that curvelets essentially provide optimally sparse representations of Fourier Integral Operators.
Accepté le :
Publié le :
Emmanuel Candès 1 ; Laurent Demanet 1
@article{CRMATH_2003__336_5_395_0,
author = {Emmanuel Cand\`es and Laurent Demanet},
title = {Curvelets and {Fourier} {Integral} {Operators}},
journal = {Comptes Rendus. Math\'ematique},
pages = {395--398},
publisher = {Elsevier},
volume = {336},
number = {5},
year = {2003},
doi = {10.1016/S1631-073X(03)00095-5},
language = {en},
}
Emmanuel Candès; Laurent Demanet. Curvelets and Fourier Integral Operators. Comptes Rendus. Mathématique, Volume 336 (2003) no. 5, pp. 395-398. doi : 10.1016/S1631-073X(03)00095-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00095-5/
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