A generalized formulation of the linear sampling method with exact characterization of targets in terms of farfield measurements

Inverse Problems

Volumn 30, Issue 3, 2014, Pages

  Audibert, Lorenzo ^a,b   Haddar, Houssem ^a  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b EDF R AND D   (France)

Author keywords

factorization Method; inverse scattering problems; linear sampling method; qualitative methods

Indexed keywords

EID: 84894550883     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/30/3/035011     Document Type: Article

References (18)

1. Arens T 2004 Why linear sampling works Inverse Problems 20 163-73
2. Arens T and Lechleiter A 2009 The linear sampling method revisited J. Integral Eqns Appl. 21 179-202
3. Boukari Y and Haddar H 2013 The factorization method applied to cracks with impedance boundary conditions Inverse Problems Imaging 7 1123-38
4. Cakoni F and Colton D 2006 Qualitative methods in inverse scattering theory Interaction of Mechanics and Mathematics (Berlin: Springer)
5. Chamaillard M, Chaulet N and Haddar H 2013 Analysis of the factorization method for a general class of boundary conditions J. Inverse Ill-posed Problems at press
6. Colton D, Haddar H and Piana M 2003 The linear sampling method in inverse electromagnetic scattering theory Inverse Problems 19 S105-37
7. Colton D and Kirsch A 1996 A simple method for solving inverse scattering problems in the resonance region Inverse Problems 12 383-93
8. Colton D and Kress R 2013 Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences vol 93) 3rd edn (New York: Springer)
9. Erhard K and Potthast R 2006 A numerical study of the probe method SIAM J. Sci. Comput. 28 1597-612
10. Haddar H 2013 Sampling 2d, Mars http://sourceforge.net/projects/ samplings-2d/
11. Ikehata M 2005 A new formulation of the probe method and related problems Inverse Problems 21 413-26
12. Kirsch A 1998 Characterization of the shape of a scattering obstacle using the spectral data of the far field operator Inverse Problems 14 1489-512
13. Kirsch A and Grinberg N 2008 The Factorization Method for Inverse Problems (Oxford Lecture Series in Mathematics and its Applications vol 36) (Oxford: Oxford University Press)
14. Nachman A I, Päivärinta L and Teirilä A 2007 On imaging obstacles inside inhomogeneous media J. Funct. Anal. 252 490-516
15. Rynne B P and Sleeman B D 1991 The interior transmission problem and inverse scattering from inhomogeneous media SIAM J. Math. Anal. 22 1755-62
16. Sorber L, Barel M and Lathauwer L 2012 Unconstrained optimization of real functions in complex variables SIAM J. Optim. 22 879-98
17. Sorber L, Barel M and Lathauwer L 2013 Complex optimization toolbox v1.0 http://esat.kuleuven.be/sista/cot/
18. Sylvester J 2012 Discreteness of transmission eigenvalues via upper triangular compact operators SIAM J. Math. Anal. 44 341-54