I am an associate professor since 2008 at the Université de Bretagne Sud in Vannes (France). I am interested in harmonic analysis, multrifractal theory, wavelet analysis and in their applications in Image processing.
Contact
Email : beatrice.vedel[AT]univ-ubs.fr
(change [AT] in @)
Phone : +33 2 97 01 71 51
LMBA
Centre Yves Coppens
Campus de Tohannic
56017 Vannes Cedex
FRANCE
Research interests
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Harmonic analysis, wavelet theory, Besov and Triebel-Lizorkhin spaces
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Anisotropy and hyperbolic wavelet analysis
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Multifractal analysis
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anisotropic stochastic processes
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Image processing : classification and denoising, dictionaries and frames, parcimony, patches methods, tomography, CNNs, Diffusion models.
Preprint
- C. Esser and B. Vedel. Counter-examples to multifractal formalisms.
- C. Esser, C. Launay, L. Loosveldt, B. Vedel. Weighted tensorized fractional brownian textures.
- C. Vazia, A. Bousse, J. Froment, B. Vedel, F. Vermet, Z. Wang, T. Dassow, J.P. Tasu, D. Visvikis. Spectral CT Two-step and One-step Material Decomposition using Diffusion Posterior Sampling.
Journal Papers
- C. Esser, S. Jaffard and B. Vedel. Regulartiy properties of random wavelet series, To appear in Theory of Probability and Mathematical Statistics.
- Z. Wang, A. Bousse, F. Vermet, J. Froment, B. Vedel, A. Perelli, J.P. Tasu, D. Visvikis. Uconnect: Synergistic Spectral CT Reconstruction with U-Nets Connecting the Energy bins, IEEE Transactions on Radiation and Malsma Medical Sciences, 2023.
- M. Schäfer, T. Ullrich, B. Vedel. Hyperbolic wavelet analysis of classical isotropic and anisotropic Besov-Sobolev spaces. In J. Fourier Anal. Appl., 27:51, 2021
- P. Abry, S. G. Roux, H. Wendt, P. Messier, A. G. Klein, N. Tremblay, P. Borgnat, S. Jaffard, B. Vedel, J. Coddington, L. Daffner, "Multiscale Anisotropic Texture Analysis and Classification of Photographic Prints: Art scholarship meets image processing algorithms," IEEE Signal Proces. Mag., vol. 32, no. 4, pp. 18-27, July 2015.
- P. Abry, M. Clausel, S. Jaffard, S.G. Roux, and B.Vedel. "The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic textures." In Revista Matematica Iberoamericana, 1:1--36, 2015.
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S.G. Roux, M. Clausel, B. Vedel, S. Jaffard, and P. Abry. "Self-similar anisotropic texture analysis: the hyperbolic wavelet transform contribution." In Transaction on Image Processing, 22(11):4353 -- 4363, 2013.
- M. Clausel, B. Vedel, Explicit constructions of operator scaling Gaussian fields, Fractals, vol 19 (1), pp 101-111 (2011)
- H. Wendt, P. Abry, S.G. Roux, S. Jaffard, B. Vedel. Analyse multifractale d'image: l'apport des coefficients dominants, Traitement du Signal, vol. 25, no. 4-5 (2009) (journal national)
- B. Vedel. Wavelet bases with pseudo-polynomials and orthonormal basis for confinement of the infrared divergence. J. Four. Anal. Appl. Vol 15, n1 (2009) 101-123
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B. Vedel. Flat wavelet bases adapted to the homogeneous Sobolev spaces. Math. Nachrichten. Vol 282, Issue I (2009) 104-124
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B. Vedel. Besov Characteristic of a distribution. Revista Matematica Complutense, vol. 20, num2, 407-421. (2007)
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B. Vedel. Confinement of the infrared divergence of the Mumford Process. Appl. and Comp. Harm. Anal., 2006, 21, pp 305-323.
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B. Vedel. Bases d'ondelettes adaptées au règlement de la divergence infra-rouge (Wavelet bases
adapted to the settlement of infrared divergence),
C.R. Acad. Sci. Paris, Ser. l 341 (2005)
Book chapters
- M. Clausel, B. Vedel, An optimality results about sample paths properties of Operator Scaling Gaussian Random Fields in anisotropic Besov spaces. Annals of the University of Bucharest (mathematical series), Proceedings of the "XIème Colloque Franco-Roumain de Math\'ematiques Appliqu\'ees" 4 (LXII), pp 375-409 (2013).
- S. Jaffard, P. Abry, S.G. Roux, B. Vedel, H. Wendt. The contribution of wavelets in multifractal analysis, in Wavelet Methods in Mathematical Analysis and Engineering, A. Damlamian, S. Jaffard, Eds., Series in contemporary applied mathematics, Vol. 14, pp. 55-98, World scientific publishing, (2010).
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B. Vedel, H. Wendt, P. Abry, S. Jaffard, On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time," in Dependence in Probability and Statistics, P. Doukhan, G. Lang, D. Surgailis, Eds., Lecture Notes in Statistics, Vol. 200, pp. 71-102, Springer, (Oct. 2010).
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P. Abry, S. Jaffard, S.G. Roux, B. Vedel, H. Wendt. Wavelet decomposition of measures: Application to multifractal analysis of images, in Unexploded Ordnance Detection and Mitigation: Proceedings of the NATO Advanced Study Institute on Unexploded Ordnance Detection and Mitigation, J. Byrnes, Ed., pp. 1-20, Springer, (2009).
Conferences : papers and posters
- Z. C. Vazia, A. Bousse, B. Vedel, F. Vermet, Z. Wang, T. Dassow, J. Froment, J.P. Tasu, D. Visvikis, J. Froment. Spectral Diffusion Posterior Sampling for Synergistic Reconstruction in Spectral Computed Tomography. Accepted to ISBI 2024, Athens
- Z. Wang, A. Bousse, F. Vermet, N. Pinton, J. Froment, B. Vedel, J.P. Tassu, D. Visvikis. Synergestic Multi-Energy Reconstruction with a Deep Penalty "Connecting the Energies". IEEE Nuclear Science Symposium Medical Imaging Conference and Room Temperature Semiconductor Conference} (2022)
- J. Mifdal, B. Coll, N. Courty, J. Froment, B. Vedel Hyperspectral and Multispectral Wasserstein barycenter for image fusion, IGARSS 2017, Jul 2017, Houston, United States.
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J. Mifdal, B. Coll, N. Courty, J. Froment, B. Vedel, Hyperspectral and multispectral image fusion based on optimal transport, Workshop SIGMA'2016 : SIGNAL, IMAGE, GEOMETRY, MODELLING, APPROXIMATION, Oct 2016, Marseille, France. (Poster session)
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S.G. Roux, P. Abry, B. Vedel, S. Jaffard, H. Wendt, "Hyperbolic wavelet leaders for anisotropic multifractal texture analysis," IEEE Int. Conf. Image Proces. (ICIP), Phoenix, AZ, USA, Sept. 2016.
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S. Postec, J. Froment, B. Vedel, Non-Local means est un algorithme de débruitage local, XXIVe Colloque GRETSI - Traitement du Signal et des Images, Sep 2013, Brest, France. pp.ID107, 2013
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S. Postec, J. Froment, B. Vedel, Un algorithme de débruitage Non-Local means espace-fréquence, XXIVe Colloque GRETSI - Traitement du Signal et des Images, Sep 2013, Brest, France. pp.ID181, 2013
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S.G. Roux, B. Vedel, S. Jaffard, and P. Abry. "Coefficients dominants de la transformée hyperbolique en ondelettes 2d: Application à l'analyse de textures invariantes d'échelle, multifractales et anisotropes." In proceedings of the XXIV colloque sur le Traitement du Signal et des Images GRETSI, Brest, France, 2013.
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S. G. Roux, M. Clausel, B. Vedel, S. Jaffard and P. Abry. "Transformée hyperbolique en ondelettes 2D pour la caractérisation des images autosimilaires anisotropes." In proceedings of the XXIII ième colloque GRETSI, Bordeaux, France, 2011.
Main co-authors
Please visit their webpages !
PhD Students and postdoc
Corentin Vazia : PhD Student (co-advisor with J. Froment, A. Bousse, F. Vermet)
Christelle Davezac : PhD student (co-advisor with J. Froment)
Anne-Charlotte Philippe : post-doctoral researcher, Oct. 2018 - 2020 (project with industrial partners)
Stéphanie Le Garrec : PhD Student (co-advisor with J. Froment)
Kim Phuc Tran : post-doctoral researcher, Dec 2017- Sept. 2018 (project with industrial partners)
Teaching
I tought a mini-course 'Introduction à l'analyse en ondelettes' at the Journées du GdR Analyse Fonctionnelle, Harmonique et Probabilités en 2016
Master degrees courses : Fourier Analysis and distributions, PDE's, Image processing
Other courses : Topology, probabilities, numeric simulations, basics.