Numerical Analysis
Denoising using nonlinear multiscale representations
[Débruitage en utilisant les représentations multiéchelles non-linéaire]
Comptes Rendus. Mathématique, Tome 338 (2004) no. 8, pp. 647-652.

Le but de cet article est de présenter quelques résultats numériques pour le problème de débruitage monodimensionnel en utilisant les représentations multiéchelles non-linéaires. On propose des strategies modifiées de seuillage qui améliorent d'une manière significative les résultats existants pour le problème 1D de débruitage.

The goal of this paper is to present some numerical results for the one-dimensional denoising problem by using the nonlinear multiscale representations. We introduce modified thresholding strategies in this new context which give significant significant improvements for one-dimensional denoising problems.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.02.004
Matei, Basarab 1

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175, rue du Chevaleret, 75013 Paris, France
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Matei, Basarab. Denoising using nonlinear multiscale representations. Comptes Rendus. Mathématique, Tome 338 (2004) no. 8, pp. 647-652. doi : 10.1016/j.crma.2004.02.004. http://www.numdam.org/articles/10.1016/j.crma.2004.02.004/

[1] F. Arandiga, R. Donat, A class of nonlinear multiscale decomposition, Preprint, University of Valencia, 1999. Numer. Algorithms, in press

[2] Cohen, A. Wavelets in Numerical Analysis (Ciarlet, P.G.; Lions, J.L., eds.), Handbook of Numerical Analysis, vol. VII, Elsevier, Amsterdam, 1999

[3] Cohen, A.; Ryan, R. Wavelets and Multiscale Signal Processing, Chapman & Hall, London, 1995

[4] Cohen, A.; Dyn, N.; Matei, B. On the smoothness and stability of quasilinear subdivision schemes with application to ENO interpolation, Appl. Comp. Harm. Anal., Volume 15 (2003), pp. 89-116

[5] Cohen, A.; Matei, B. Nonlinear subdivisions schemes: applications to image processing (Iske, A.; Quack, E.; Floater, M., eds.), Tutorial on Multiresolution in Geometric Modelling, Springer, 2002

[6] R.R. Coifman, D. Donoho, Translation Invariant Denosing, Preprint, 1995

[7] Donoho, D.; Johnstone, I.; Kerkyacharian, G.; Picard, D. Wavelet shrinkage: Asymptotia?, J. Roy. Statist. Soc. Ser. B, Volume 57 (1994), pp. 301-369 (with discussion)

[8] Harten, A. Discrete multiresolution analysis and generalized wavelets, J. Appl. Numer. Math., Volume 12 (1993), pp. 153-193

[9] Harten, A. ENO schemes with subcell resolution, J. Comput. Phys., Volume 23 (1995), pp. 53-71

[10] Harten, A.; Enquist, B.; Osher, S.; Chakravarthy, S. Uniformly high order accurate essentially non-oscillatory schemes III, J. Comput. Phys., Volume 71 (1987), pp. 231-303

[11] B. Matei, Méthodes multi-échelles non-linéaires – Applications au traitemnt d'image, Ph.D. Thesis, Université Pierre et Marie Curie (Paris VI), 2002

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