The operator factorization method in inverse obstacle scattering

Integral Equations and Operator Theory

Volumn 54, Issue 3, 2006, Pages 333-348

  Grinberg, N I ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Factorization method; Far field operator; Helmholtz operator; Inverse obstacle scattering problem

Indexed keywords

EID: 33144487493     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-004-1355-z     Document Type: Article

References (20)

1. D. Colton, H. Haddar, M. Piana, The linear sampling method in inverse electromagnetic scattering theory, Inverse problems 19 (2003), S105-S137.
2. D. Colton, A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems 12 (1996), 383-393.
3. D. Colton and R. Kress, Integral Equation Method in Scattering Theory, Wiley, New York, 1983.
4. D. Colton, P. Monk, The numerical solution of the three dimensional inverse scattering problem for time-harmonic acoustic waves, SIAM J. Sci. Stat. Comp. 8 (1987), 287-291.
5. H.W. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 1996.
6. N.I. Grinberg, Obstacle Localization in an Homogeneous Half-Space, Inverse Problems 17 (2001), 1113-1125.
7. N.I. Grinberg, On the inverse obstacle scattering problem with Robin or mixed boundary condition: application of the modified Kirsch factorization method, Preprintreihe der Fakultät für Mathematik, Universität Karlsruhe, Nr. 02/04, 2002.
8. N. Grinberg, A. Kirsch, The linear sampling method in inverse obstacle scattering for impedance boundary conditions, J. Inverse Ill-Posed Probl. 10 (2002), 171-185.
9. M. Hanke, F. Hettlich, O. Scherzer, The Landweber Iteration for the Inverse scattering Problem, in Proc. of the 1995 design engineering technical conference, Vol.3, Part C, K.-W. Wang et. al. (eds.), The American Society of Mechanical Engineers, New York, 1995, 909-915.
10. M. Ikehata, Reconstruction of an obstacle from the scattering amplitude at a fixed frequency, Inverse Problems 14 (1998), 949-954.
11. A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems 14 (1998), 1489-1512.
12. A. Kirsch, New Characterizations of Solutions in Inverse Scattering Theory, Applicable Analysis 76 (2000), 319-350.
13. A. Kirsch, The factorization method for a class of inverse elliptic problems, 2003, to appear in Mathematische Nachrichten.
14. A. Kirsch, R. Kress, An optimization method in inverse acoustic scattering in Boundary Elements IX, ed. Brebbia C.A., Springer, New York, 1987.
15. R. Kress, W. Rundell, A Quasi-Newton method in Inverse Obstacle Scattering, Inverse Problems 10 (1994), 1145-1157.
16. R. Kress, Integral equation method in inverse acoustic and electromagnetic scattering, in: Boundary Integral Formulations for Inverse Analysis, Ingham and Wrobel. eds. (Computational Mechanics Publications, Southampton), 1997, 67-92.
17. R. Luke, R. Potthast, The no responce test - a sampling method for inverse scattering problems, SIAM Journal of Applied Mathematics 63 (2003), 1291-1312.
18. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, 2000.
19. R. Potthast, J. Sylvester, S. Kusiak, A 'range test' for determining scatterers with unknown physical properties, Inverse Problems 19 (2003), 533-547.
20. A. Roger, Newton Kantorovich algorithm applied to an electromagnetic inverse problem, IEEE Trans. Ant. Prop. AP-29 (1981), 232-238.