[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.
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@article{CRMATH_2003__336_5_395_0,
author = {Cand\`es, Emmanuel and Demanet, Laurent},
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},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00095-5/}
}
TY - JOUR AU - Candès, Emmanuel AU - Demanet, Laurent TI - Curvelets and Fourier Integral Operators JO - Comptes Rendus. Mathématique PY - 2003 SP - 395 EP - 398 VL - 336 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00095-5/ DO - 10.1016/S1631-073X(03)00095-5 LA - en ID - CRMATH_2003__336_5_395_0 ER -
%0 Journal Article %A Candès, Emmanuel %A Demanet, Laurent %T Curvelets and Fourier Integral Operators %J Comptes Rendus. Mathématique %D 2003 %P 395-398 %V 336 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00095-5/ %R 10.1016/S1631-073X(03)00095-5 %G en %F CRMATH_2003__336_5_395_0
Candès, Emmanuel; Demanet, Laurent. Curvelets and Fourier Integral Operators. Comptes Rendus. Mathématique, Tome 336 (2003) no. 5, pp. 395-398. doi : 10.1016/S1631-073X(03)00095-5. http://www.numdam.org/articles/10.1016/S1631-073X(03)00095-5/
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[3] Curvelets – a suprisingly effective nonadaptive representation for objects with edges (Cohen, A.; Rabut, C.; Schumaker, L., eds.), Curves and Surface Fitting: Saint-Malo 1999, Vanderbilt University Press, Nashville, 2000, pp. 105-120
[4] E. Candès, D. Donoho, New tight Frames of curvelets and optimal representations of objects with C2 singularities, submitted, http://www.acm.caltech.edu/~emmanuel/publications.html, 2002
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