The linear sampling method revisited

Journal of Integral Equations and Applications

Volumn 21, Issue 2, 2009, Pages 179-202

  Arens, Tilo ^a   Lechleiter, Armin ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b INRIA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 74349116964     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/JIE-2009-21-2-179     Document Type: Article

References (14)

1. H. Ammari,M. S. Vogelius, and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations, J. Math. Pures Appl., 80, (2001), pp. 769-814.
2. P. Anselone and J. Davis, Collectively compact operator approximation theory and applications to integral equations, Prentice-Hall, (1971).
3. T. Arens, Why linear sampling works, Inverse Problems, 20, (2004), pp. 163- 173.
4. F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory: An Introduction, Springer, Berlin, (2006).
5. D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, 12, (1996), pp. 383-393.
6. D. Colton, M. Piana, and R. Potthast, A simple method using Morozov's discrepancy principle for solving inverse scattering problems, Inverse Problems, 13 (1997), pp. 1477-1493.
7. D. L. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Springer, 2nd ed., (1998).
8. P. Hähner, An inverse problem in electrostatics, Inverse Problems, 15, (1999), pp. 961-975.
9. T. Kato, Perturbation theory for linear operators, Springer, repr. of the 1980 ed., (1995).
10. A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), pp. 1489-1512.
11. A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford Lecture Series in Mathematics and its Applications 36, Oxford University Press, (2008).
12. A. Lechleiter, A regularization technique for the factorization method, Inverse Problems, 22, (2006), pp. 1605-1625.
13. G. Vainikko, The discrepancy principle for a class of regularization methods, U.S.S.R. Comput. Maths. Math. Phys., 21, (1982), pp. 1-19.
14. M. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter, M2AN, 79 (2000), pp. 723-748.