Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set

Inverse Problems

Volumn 14, Issue 3, 1998, Pages 685-706

  Litman, A ^a,c   Lesselier, D ^a   Santosa, F ^b  

^a CNRS   (France)

^b UNIVERSITY OF MINNESOTA   (United States)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000386587     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/14/3/018     Document Type: Article

References (37)

1. Angell T S, Jiang X and Kleinman R E 1997 A distributed source method for inverse acoustic scattering Inverse Problems 13 531-46
2. Angell T S, Kleinman R E and Roach F G 1987 An inverse transmission problem for the Helmholtz equation Inverse Problems 3 149-80
3. Belkebir K and Tijhuis A G 1996 Using multiple frequency information in the iterative solution of a two-dimensional nonlinear inverse problem Proc. PIERS 96: Progress in Electromagnetics Research Symposium (Innsbruck, Austria) p 353
4. Caselles V, Catté F, Coll T and Dibos F 1993 A geometric model for active contours in image processing Num. Math. 66 1-31
5. Céa J 1976 Une méthode numérique pour 1a recherche d'un domaine optimal Publication IMAN Université de Nice
6. Charalambopoulos A 1995 On the Fréchet-differentiability of boundary integral operators in the inverse elastic scattering problem Inverse Problems 11 1137-62
7. Colton D and Kress R 1992 Inverse Acoustic and Electromagnetic Scattering Theory (Berlin: Springer)
8. Colton D and Monk P 1994 The detection and monitoring of leukemia using electromagnetic waves: mathematical modelling Inverse Problems 10 1235-52
9. de Oliveira Bohbot O, Lesselier D and Duchêne B 1996 Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints J. Electromagn. Waves Applic. 10 983-1004
10. Delfour M C and Zolésio J P 1992 Structure of shape derivatives for nonsmooth domains J. Funct. Anal. 104 1-33
11. Germain P 1973 Cours de Mécanique des Milieux Continus (Paris: Masson)
12. Ghosh Roy D N, Couchman L and Warner J 1997 Scattering and inverse scattering of sound-hard obstacles via shape deformation Inverse Problems 13 585-606
13. Haas M, Rieger W, Rucker W and Lehner G 1997 Inverse 2D electromagnetic obstacle scattering for multiple scatterers using an iterative adaptation technique Proc. IEEE Antennas and Propagation Soc. Int. Symp. 1997 (Montreal, Canada) pp 1722-5
14. Haug E J and Céa J 1981 Optimization of Distributed Parameter Structures (The Netherlands: Sijthoff and Noordhoff)
15. Hettlich F 1995 Fréchet derivatives in inverse obstacle scattering Inverse Problems 11 371-82
16. Heulich F and Rundell W 1996 Iterative methods of the reconstruction of an inverse potential problem Inverse Problems 12 251-66
17. Kirsch A 1993 The domain derivative and two applications in inverse scattering theory Inverse Problems 9 81-96
18. Kirsch A and Kress R 1993 Uniqueness in inverse obstacle scattering Inverse Problems 9 285-99
19. Kleinman R E and van den Berg P M 1992 A modified gradient method for two-dimensional problems in tomography J. Comput. Appl. Math. 42 17-35
20. Kress R and Zinn A 1992 On the numerical solution of the three-dimensional inverse obstacle scattering problem J. Comput. Appl. Math. 42 49-61
21. Lesselier D and Duchêne B 1996 Wavefield inversion of objects in stratified environments. From backpropagation schemes to full solution Review of Radio Science 1993-1996 ed R Stone et al (Oxford: Oxford University Press) pp 235-68
22. Litman A 1997 Deux méthodes d'inversion pour la caractérisation électromagnétique ou acoustique d'objets enfouis: transformée de Fourier-Laplace inverse et déformation d'ensembles de niveaux Thèse de Doctorat en Sciences Université Paris XI Orsay
23. Litman A, Lesselier D and Santosa F 1997 A level-set approach for eddy current imaging of defects in a conductive half-space Inverse Problems of Wave Propagation and Diffraction ed G Chavent and P C Sabatier (Berlin: Springer) pp 250-62
24. Malladi R, Sethian J A and Vemuri B C 1995 Shape modelling with front propagation: a level set approach IEEE Trans. Pattern Anal. Machine Intell. 17 158-75
25. Masmoudi M 1987 Outils pour la conception optimale de formes Thèse d'Etat en Sciences Mathématiques Université de Nice
26. Murat F and Simon J 1976 Sur le contrôle par un domaine géométrique Publications du Laboratoire d'Analyse Numérique Université Paris VI
27. Osher S and Sethian J A 1988 Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations J. Comput. Phys. 79 12-49
28. Peng Z Q and Tijhuis A G 1993 Transient scattering by a lossy dielectric cylinder: marching-on-in-frequency approach J. Electromagn. Waves Applic. 7 739-63
29. Potthast R 1996 Fréchet differentiability of the solution to the acoustic neumann scattering problem with respect to the domain J. Inverse Ill-Posed Problems 4 67-84
30. Rozier C, Lesselier D, Angell T and Kleinman R E 1997 Shape retrieval of an obstacle immersed in shallow water from single frequency fields using a complete family method Inverse Problems 13 487-508
31. Santosa F 1996 A level-set approach for inverse problems involving obstacles ESAIM: COCV 1 17-33
32. Sethian J A 1990 Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws J. Diff. Geom. 31 131-61
33. Sethian J A and Strain J 1992 Crystal growth and dendritic solidification J. Comput. Phys. 98 231-53
34. Sokolowski J and Zolésio J P 1992 Introduction to Shape Optimization. Shape Sensitivity Analysis (Heidelberg: Springer)
35. Sounau L, Duchêne B, Lesselier D and Kleinman R E 1996 A modified gradient approach to inverse scattering for binary objects in stratified media Inverse Problems 12 463-81
36. Vincent P, Saillard M and Bonnard S 1997 Cross-borehole inverse scattering using a conjugate gradient algorithm Proc. PIERS 97: Progress in Electromagnetics Research Symp. (Boston, USA) p 553
37. Zolésio J P 1979 Identification de domaines par déformations Thèse d'Etat en Mathématiques Université de Nice