Sommaire 4.1 La méthode de Descente de gradient (DG), p.78 ,
Sommaire 9.1 Le Gradient Topologique (GT), p.138 ,
162 10.1.2 Algorithme de segmentation d'image, p.164 ,
On Second Order Shape Optimization Methods for Electrical Impedance Tomography, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1556-1590 ,
DOI : 10.1137/070687438
URL : https://hal.archives-ouvertes.fr/hal-00140211
The calibration method for the Mumford-Shah functional and free-discontinuity problems, Calculus of Variations and Partial Differential Equations, vol.16, issue.3, pp.299-333, 2003. ,
DOI : 10.1007/s005260100152
URL : https://hal.archives-ouvertes.fr/hal-01283208
Shape optimization by the homogenization method, 2001. ,
Shape optimization by the homogenization method, Numerische Mathematik, vol.76, issue.1, pp.27-68, 1997. ,
DOI : 10.1007/s002110050253
Optimal design for minimum weight and compliance in plane stress using extremal microstructures, Europ. J. Mech. A/Solids, vol.12, issue.6, pp.839-878, 1993. ,
Structural Optimization with FreeFem++, R.I. 586, Ecole Polytechnique, 2005. ,
Analyse numérique et optimisation -Une introductionàintroductionà la modélisation mathématique etàetà la simulation numérique, 2009. ,
Damage evolution in brittle materials by shape and topological sensitivity analysis, 2010. ,
A level-set method for shape optimization, Comptes Rendus Mathematique, vol.334, issue.12, pp.1125-1130, 2002. ,
DOI : 10.1016/S1631-073X(02)02412-3
URL : https://hal.archives-ouvertes.fr/hal-01336301
Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004. ,
DOI : 10.1016/j.jcp.2003.09.032
Conception optimale de structures, Cours detroisì eme année MAP562, Ecole Polytechnique, 2004. ,
Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics, vol.1846, 2004. ,
DOI : 10.1007/b98245
Polarization and Moment Tensors : with Applications to Inverse Problems and Effective Medium Theory, Applied Mathematical Sciences Series, vol.162, 2007. ,
An Introduction to Mathematics of Emerging Biomedical Imaging, Mathématiques et Applications, vol.62, 2008. ,
The three dimensional inverse scattering problem for acoustic waves, Journal of Differential Equations, vol.46, issue.1, pp.46-58, 1982. ,
DOI : 10.1016/0022-0396(82)90108-5
A constructive method for identification of an impenetrable scatterer, Wave Motion, vol.11, issue.2, pp.185-200, 1989. ,
DOI : 10.1016/0165-2125(89)90036-X
Why linear sampling works, Inverse Problems, vol.20, issue.1, pp.163-173, 2004. ,
DOI : 10.1088/0266-5611/20/1/010
Image Restoration and Classification by Topological Asymptotic Expansion. Variational Formulations in Mechanics : Theory And Applications, 2006. ,
Identification par Imagerie Laser d'un Objet Dissimulé, 2011. ,
Qualitative Methods for Inverse Scattering in Solid Mechanics, Thèse, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01323219
Methods for optimization of structural topology, shape and material, 1995. ,
Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.197-224, 1988. ,
DOI : 10.1016/0045-7825(88)90086-2
Topology Optimization. Theory, Methods, and Applications, 2003. ,
Mathematical Methods for Wave Phenomena, 1984. ,
Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework, Journal of Computational Physics, vol.228, issue.2, pp.294-311, 2009. ,
DOI : 10.1016/j.jcp.2008.09.009
URL : https://hal.archives-ouvertes.fr/hal-00320517
Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems, Engineering Analysis with Boundary Elements, pp.35-223, 2011. ,
Inverse acoustic scattering by small-obstacle expansion of misfit function, Inverse Problems, pp.24-035022, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00128911
Recent convexity arguments in the calculus of variations, lecture notes from the 3rd Int. Summer School on the Calculus of Variations, 1998. ,
On simultaneous identification of a scatterer and its generalized impedance boundary condition, Inria ,
A fully no-sampling formulation of the linear sampling method for three-dimensional inverse electromagnetic scattering problems, Inverse Problems, vol.25, issue.1, p.15014, 2009. ,
DOI : 10.1088/0266-5611/25/1/015014
A framework for the construction of level set methods for shape optimization and reconstruction, Interfaces and Free Boundaries, pp.301-329, 2003. ,
On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.65-73, 1980. ,
Qualitative Methods in Inverse Scattering Theory, 2006. ,
Conception optimale ou identification de formes, calcul rapide de la d??riv??e directionnelle de la fonction co??t, ESAIM: Mathematical Modelling and Numerical Analysis, vol.20, issue.3, pp.371-402, 1986. ,
DOI : 10.1051/m2an/1986200303711
The shape and topological optimizations connection, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.4, pp.713-726, 1998. ,
DOI : 10.1016/S0045-7825(99)00357-6
Waves and Fields in Inhomogeneous Media, 1990. ,
A Linear Sampling Method for the Detection of Leukemia Using Microwaves II, SIAM Journal on Applied Mathematics, vol.60, issue.1, pp.60-241, 1999. ,
DOI : 10.1137/S003613999834426X
A Novel Method for Solving the Inverse Scattering Problem for Time-Harmonic Acoustic Waves in the Resonance Region, SIAM Journal on Applied Mathematics, vol.45, issue.6, pp.1039-1053, 1985. ,
DOI : 10.1137/0145064
A Novel Method for Solving the Inverse Scattering Problem for Time-Harmonic Acoustic Waves in the Resonance Region II, SIAM Journal on Applied Mathematics, vol.46, issue.3, pp.506-523, 1986. ,
DOI : 10.1137/0146034
The Numerical Solution of the Three-Dimensional Inverse Scattering Problem for Time Harmonic Acoustic Waves, SIAM Journal on Scientific and Statistical Computing, vol.8, issue.3, pp.278-291, 1987. ,
DOI : 10.1137/0908035
Inverse Acoustic And Electromagnetic Scattering Theory, 1997. ,
DOI : 10.1007/978-1-4614-4942-3
Integral Equation Methods in Scattering Theory, 1983. ,
DOI : 10.1137/1.9781611973167
The linear sampling method in inverse electromagnetic scattering theory, Inverse Problems, vol.19, issue.6, pp.105-138, 2003. ,
DOI : 10.1088/0266-5611/19/6/057
URL : https://hal.archives-ouvertes.fr/hal-00744163
A simple method using Morozov's discrepancy principle for solving inverse scattering problems, Inverse Problems, vol.13, issue.6, pp.1477-1493, 1997. ,
DOI : 10.1088/0266-5611/13/6/005
A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, vol.12, issue.4, pp.383-393, 1996. ,
DOI : 10.1088/0266-5611/12/4/003
La tomographie sismique comme méthode de reconnaissance détaillé du sous-sol, Rev. Franç, Géotech, vol.36, pp.47-53, 1986. ,
Variational Methods for Structural Optimization, 2000. ,
DOI : 10.1007/978-1-4612-1188-4
On variations of the shape of Hessian and sufficient conditions for the stability of critical shapes, RACSAM, pp.95-121, 2002. ,
About stability of equilibrium shapes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, issue.4, pp.811-834, 2000. ,
DOI : 10.1051/m2an:2000105
Acoustic tomography, Inverse Problems of Acoustic and Elastic Waves (Santosa et al, pp.250-273, 1984. ,
Bubble method for topology and shape optimization of structures, Structural Optimization, pp.42-51, 1994. ,
Practical Methods of Optimization, 1987. ,
DOI : 10.1002/9781118723203
The Topological Asymptotic for PDE Systems: The Elasticity Case, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1756-1778, 2001. ,
DOI : 10.1137/S0363012900369538
A sampling method for detecting buried objects using electromagnetic scattering, Inverse Problmes, pp.2035-2050, 2005. ,
DOI : 10.1088/0266-5611/21/6/015
On the multi-frequency obstacle reconstruction via the linear sampling method, Inverse Problems, vol.26, issue.12 ,
DOI : 10.1088/0266-5611/26/12/125005
Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics, Inverse Problems, vol.22, issue.5, pp.1761-1785, 2006. ,
DOI : 10.1088/0266-5611/22/5/014
URL : https://hal.archives-ouvertes.fr/hal-00111266
Méthode de variations defrontì eres etprobì eme de diffraction inverse, 2008. ,
The linear sampling method for solving the electromagnetic inverse scattering problem, In SIAM J. Sci. Comp. v, vol.24, issue.3, pp.719-731, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00744171
The linear sampling method for solving the electromagnetic inverse medium problem, Inverse Problems, vol.18, issue.3, pp.891-906, 2002. ,
DOI : 10.1088/0266-5611/18/3/323
URL : https://hal.archives-ouvertes.fr/hal-00744180
Why linear sampling really seems to work, Inverse Problems and Imaging, vol.2, issue.3, pp.373-395, 2008. ,
DOI : 10.3934/ipi.2008.2.373
Variation et optimisation de formes, Math et App, vol.48, 2005. ,
DOI : 10.1007/3-540-37689-5
A Second Order Shape Optimization Approach for Image Segmentation, SIAM Journal on Applied Mathematics, vol.64, issue.2, pp.442-467 ,
DOI : 10.1137/S0036139902403901
The two-dimensional inverse scattering problem, IEEE Transactions on Antennas and Propagation, vol.18, issue.5, pp.633-642, 1970. ,
DOI : 10.1109/TAP.1970.1139769
On uniqueness in th invese transmission scattering problem, Communications in Partial Differential Equations, vol.125, issue.4, pp.1565-1587, 1990. ,
DOI : 10.1080/03605309908820737
Acoustic and Electromgnetic Waves, 1986. ,
Stability and resolution analysis for a topological derivative based imaging functional ,
URL : https://hal.archives-ouvertes.fr/hal-00695667
Topological optimum design using genetic algorithms, Control and Cybernetics, vol.25, pp.1059-1088, 1996. ,
Generalized Boundary Value and Control Problems for the Helmholtz Equation, 1984. ,
Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, vol.14, issue.6, pp.1489-1512, 1998. ,
DOI : 10.1088/0266-5611/14/6/009
The factorization Method for Inverse Problems, OUP Oxford, vol.216, 2007. ,
DOI : 10.1093/acprof:oso/9780199213535.001.0001
On an Integral Equation of the first Kind in Inverse Acoustic Scattering, Inverse Problems (Cannon and Hornung, ads). ISNM, pp.93-102, 1986. ,
DOI : 10.1007/978-3-0348-7014-6_6
A NUMERICAL METHOD FOR AN INVERSE SCATTERING PROBLEM, Inverse Problems (Engl and Groetsch, pp.279-290, 1987. ,
DOI : 10.1016/B978-0-12-239040-1.50022-3
An optimization method in inverse acoustic scattering Fluid Flow and Potentiel Applications, In : Boundary elements IX, vol.3, pp.3-18, 1987. ,
Inverse problems for acoustic waves using the penalised likelihood method, Inverse Problems, vol.2, issue.4, pp.461-479, 1986. ,
DOI : 10.1088/0266-5611/2/4/011
Applied inverse problems for acoustic, electromagnetic and elastic wave scattering, Basic Methods of Tomography and Inverse Problems ,
The topological asymptotic expansion for the Maxwell equations and some applications, Inverse Problems, vol.21, issue.2, pp.547-564, 2005. ,
DOI : 10.1088/0266-5611/21/2/008
On the solution of functional equations by the method or regularization, Soviet Math. Doklady, vol.7, pp.414-417, 1966. ,
Choice of parameter for the solution of functional equations by the regularisation method, Soviet Math. Doklady, vol.8, pp.1000-1003, 1967. ,
Linear Acoustic Theory, In : Encyclopedia of PhysicsFlugge, pp.1-128, 1961. ,
DOI : 10.1007/978-3-642-45956-6_1
Zur mathematischen Theorie elektromagnetischer Schwingungen, Abh. deutsch. Akad. Wiss. Berlin, vol.346, pp.5-56, 1945. ,
Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989. ,
DOI : 10.1002/cpa.3160420503
Sur le contrôle par un domaine géométrique, Internal report No 76015, Laboratoire d'Analyse Numérique de l'université Paris, 1976. ,
Etude de problemes d'optimal design, Lecture Notes in Computer Science, vol.41, pp.54-62, 1976. ,
DOI : 10.1007/3-540-07623-9_279
Reconstructions From Boundary Measurements, The Annals of Mathematics, vol.128, issue.3, pp.531-576, 1988. ,
DOI : 10.2307/1971435
Acoustic and electromagnetic equations : Integral representations for harmonic problems, Appl. Math. Sc, vol.144, 2001. ,
A linear sampling method for near-field inverse problmes in elastodynamics, Inverse Problems, vol.20, pp.713-736, 2004. ,
Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Functional Analysis and Its Applications, vol.38, issue.3, pp.263-272, 1988. ,
DOI : 10.1007/BF01077418
Newton's method in shape optimisation : a three-dimensional case, Bit Numerical Mathematics, vol.40, issue.1, pp.102-120, 2000. ,
DOI : 10.1023/A:1022370419231
Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, vol.153, 2003. ,
DOI : 10.1115/1.1760520
URL : http://dx.doi.org/10.1016/s0898-1221(03)90179-9
Level Set Methods for Optimization Problems Involving Geometry and Constraints, Journal of Computational Physics, vol.171, issue.1, pp.272-288, 2001. ,
DOI : 10.1006/jcph.2001.6789
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
Sensibilit?? de l'??quation de la chaleur aux sauts de conductivit??, Comptes Rendus Mathematique, vol.341, issue.5, pp.333-337, 2005. ,
DOI : 10.1016/j.crma.2005.07.005
Scattering theory for hyperbolic operators, Mathematics and its Applications, 1989. ,
An algorithm for minimizing the Mumford-Shah functional, 2009 IEEE 12th International Conference on Computer Vision, 2009. ,
DOI : 10.1109/ICCV.2009.5459348
Optimal shape design for elliptic systems, 1984. ,
Recovery of the potential from fixed-energy scattering data, Inverse Problems, vol.4, issue.3, pp.877-886, 1988. ,
DOI : 10.1088/0266-5611/4/3/020
Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem, IEEE Transactions on Antennas and Propagation, vol.29, issue.2, pp.232-238, 1981. ,
DOI : 10.1109/TAP.1981.1142588
Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, vol.163, issue.2, pp.489-528, 2000. ,
DOI : 10.1006/jcph.2000.6581
Level-Set Methods and fast marching methods : evolving interfaces in computational geometry, fluid mechanics, computer vision and materials science, 1999. ,
Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, vol.163, issue.2, pp.489-528, 2000. ,
DOI : 10.1006/jcph.2000.6581
Second variation for domain optimization problems, Control and estimation of distributed parameter systems, pp.361-378, 1989. ,
Differentiation with Respect to the Domain in Boundary Value Problems, Numerical Functional Analysis and Optimization, vol.24, issue.7-8, pp.649-687, 1980. ,
DOI : 10.1016/0045-7825(78)90024-5
Introduction to shape optimization. Shape sensitivity analysis, 1992. ,
On the Topological Derivative in Shape Optimization, SIAM Journal on Control and Optimization, vol.37, issue.4, pp.1251-1272, 1999. ,
DOI : 10.1137/S0363012997323230
Topological Derivatives of Shape Functionals for Elasticity Systems, Mech. Structures Mach, vol.29, issue.3, pp.331-349, 2001. ,
DOI : 10.1007/978-3-0348-8148-7_19
On the solution of incorrectly formulated problems and the regularization method, Soviet Math. Doklady, vol.4, pp.1035-1038, 1963. ,
Regularization of incorrectly posed problems, Soviet Math. Doklady, vol.4, pp.1624-1627, 1963. ,
A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.1-2, pp.227-246, 2003. ,
DOI : 10.1016/S0045-7825(02)00559-5
Structural shape and topology optimization in a level set based implicit moving boundary framework ,
Zur mathematischen theorie akustischer Wellenfelder, Archive for Rational Mechanics and Analysis, vol.21, issue.1, pp.231-260, 1961. ,
DOI : 10.1007/BF00276164