| Pierre Maréchal Professeur Institut de Mathématiques de Toulouse Université Paul Sabatier 31 062 Toulouse Cedex 9 France Téléphone: 05 61 55 76 60 Courrier électronique: cliquez ici |  | Pierre Maréchal Professor Mathematical Institute of Toulouse Université Paul Sabatier 31 062 Toulouse Cedex 9 France Phone: +33 561 557 660 E-mail: click here |
| - Domaines de recherche - 1. Problèmes inverses. Mots-Clés: problèmes mal-posés, régularisation, robustesse, méthodes d'entropie, analyse de Fourier, transformations de Radon. Applications: tomographie d'émission (TEMP, TEP), tomographie thermo-acoustique (TTA) , IRM, synthèse d'ouverture, résonance magnétique nucléaire. 2. Optimisation, analyse variationnelle et applications. Mots-Clés: optimisation non linéaire, analyse convexe, dualité, fonctions spectrales, analyse non lisse. Applications: problèmes inverses, pricing d'options, méthodes d'entropie, optimisation du conditionnement, etc. | - Research interests - 1. Inverse problems. Keywords: ill-posed problems, regularization, robustness, entropy methods, Fourier analysis, Radon transformations. Applications: emission tomography (SPECT, PET), thermoacoustic tomography (TAT), MRI, aperture synthesis, nuclear magnetic resonance. 2. Optimization, variational analysis ans applications. Keywords: nonlinear programming, convex analysis,, duality, spectral functions, nonsmooth analysis. Applications: inverse problems, option pricing, entropy methods, conditioning optimization, etc. |
- Quelques séminaires / Selected talks - Generalized perspective and applications Optimizing condition numbers Fourier synthesis |
- Publications - P. Maréchal & J. Ye, Optimizing condition numbers, SIAM Journal of Optimization, 20(2) (2009) 935-947.P. Maréchal & A. Rondepierre, A proximal approach to the inversion of illconditioned matrices, Comptes Rendus de l’Académie des Sciences, Paris, Serie I, 347 (2009) 1435-1438. N. Alibaud, X. Bonnefond & P. Maréchal, Analyse asymptotique de la régularisation par mollification, Actes du colloque: Mathématiques pour l’image, Presses Universitaires d’Orléans (2009). X. Bonnefond & P. Maréchal, A variational approach to the inversion of some compact operators, Pacific Journal of Optimization, 5(1) (2009) 97-110. N. Alibaud, P. Maréchal & Y. Saesor, A variational approach to the inversion of truncated Fourier operators, Inverse Problems 25 (2009). P. Maréchal & D. Wallach, Fourier synthesis via partially finite convex programming, Mathematical and Computer Modelling, 49 (2009) 2206-2212. B. Dacorogna & P. Maréchal, The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity, Journal of Convex Analysis, 15(2), (2008), 271-284. D. Mariano-Goulart, P. Maréchal, L. Giraud, S. Gratton & M. Fourcade, A priori selection of the regularization parameters in emission tomography by Fourier synthesis, Computerized Medical Imaging and Graphics, 31 (2007) 502-509. B. Dacorogna & P. Maréchal, Convex SO(N) × SO(n)-invariant functions and refinements of Von Neumann’s inequality, Annales de la Faculté des Sciences de Toulouse, XVI(1) (2007) 71-89. B. Dacorogna & P. Maréchal, A Note on Spectrally Defined Polyconvex Functions, Proceedings of the workshop: New developments in the Calculus of Variations, Edizioni Scientifiche Italiane (2006) 259-274. P. Maréchal, On a class of convex sets and functions, Set Valued Analysis, 13(2) (2005) 197-212. P. Maréchal, On a functional operation generating convex functions. Part II : algebraic properties, Journal of Optimization Theory and Applications, 126(2) (2005) 357-366. P. Maréchal, On a functional operation generating convex functions. Part I : duality, Journal of Optimization Theory and Applications, 126(1) (2005) 175-189. J.M. Borwein, R. Choksi & P. Maréchal, Probability distributions of assets inferred from option prices via the principle of maximum entropy, SIAM J. Optim., 14(2) (2003) 464-478. P. Maréchal, On the convexity of the multiplicative potential and penalty functions and related topics, Mathematical Programming, Series A, 89 (2001) 505-516. P. Maréchal, A note on entropy optimization, in M. Lassonde (Editeur), Approximation, Optimization and Mathematical Economics, Physica-Verlag (2001) 205-211. P. Maréchal, On the principle of Maximum Entropy as a methodology for solving linear inverse problems, in B. Grigelionis et al. (Editeurs), Probability Theory and Mathematical Statistics, VPS/TEV (1999) 481-492. J. M. Borwein, P. Maréchal and D. Naugler, Convex dual approach to the computation of NMR complex spectra, Mathematical Methods of Operations Research, 51(1) (2000) 91-102. D. Borwein, J. M. Borwein and P. Maréchal, Surprise Maximization, the American Mathematical Monthly, 107(6) (2000) 517-527. P. Maréchal, D. Togane and A. Celler, A new reconstruction methodology for Computerized Tomography : FRECT (Fourier Regularized Computed Tomography), IEEE, Transactions on Nuclear Science, 47 (2000) 1595-1601. P. Maréchal, D. Togane, A. Celler and J. M. Borwein, Computation and stability analysis for regularized tomographic reconstructions, IEEE, Transactions on Nuclear Science, 46 (1999) 2177-2184. A. Lannes, E. Anterrieu and P. Maréchal, Clean and Wipe, Astronomy and Astrophysics, Suppl. Series, 123 (1997) 183-198. P. Maréchal & A. Lannes, Unification of some deterministic and probabilistic methodologies for the solution of linear inverse problems via the principle of maximum entropy on the mean, Inverse Problems, 13 (1997) 135-151. |
| - Notes de cours / Lecture notes - Introduction to Inverse Problems of Fourier Synthesis Eléments d'Analyse Convexe |