On the multi-frequency obstacle reconstruction via the linear sampling method

Inverse Problems

Volumn 26, Issue 12, 2010, Pages

  Guzina, Bojan B ^a   Cakoni, Fioralba ^b   Bellis, Cédric ^a,c  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF DELAWARE   (United States)

^c LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE SOLUTION; CONTINUOUS FREQUENCY; COUNTABLE SET; DIRICHLET; EIGEN-VALUE; EIGENVALUES; EXPERIMENTAL OBSERVATION; FAR-FIELD; FREQUENCY DOMAINS; FREQUENCY SAMPLING; INDICATOR FUNCTIONS; ISOLATED EIGENVALUE; LINEAR SAMPLING; LINEAR SAMPLING METHODS; MULTI FREQUENCY; NATURAL EXTENSION; NEAR-FIELD; NUMERICAL RESULTS; PERTURBATION ANALYSIS; SCATTERED FIELD; SCATTERING CONFIGURATION; SPACE-FREQUENCY; THEORETICAL RESULT; TIME DOMAIN; ZERO FREQUENCY;

ACOUSTIC WAVE SCATTERING; FREQUENCY BANDS; MONOCHROMATORS; TIME DOMAIN ANALYSIS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 78649769233     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/26/12/125005     Document Type: Conference Paper

References (39)

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 Equ. Appl. 21 179-202
3. Bellis C and Guzina B 2010 On the existence and uniqueness of a solution to the interior transmission problem for piecewise-homogeneous solids J. Elast. 101 29-57
4. Bonnet M 2008 Inverse acoustic scattering by small-obstacle expansion of misfit function Inverse Problems 24 35022
5. Cakoni F and Colton D 2003 Combined far field operators in electromagnetic inverse scattering theory Math. Methods Appl. Sci. 26 413-429
6. Cakoni F and Colton D 2003 On the mathematical basis of the linear sampling method Georgian Math. J. 10 911-925
7. Cakoni F and Colton D 2006 Qualitative Methods in Inverse Scattering Theory (Berlin: Springer)
8. Cakoni F, Colton D and Gintides D 2010 The interior transmission eigenvalue problem SIAM J. Math. Anal. to appear
9. Cakoni F, Colton D and Haddar H 2002 The linear sampling method for anisotropic media J. Comput. Appl. Math. 146 285-299
10. Cakoni F, Colton D and Haddar H 2010 On the determination of dirichlet and transmission eigenvalues from far field data C. R. Acad. Sci. Paris, Ser. I 348 379-383
11. Cakoni F, Colton D andMonk P 2007 On the use of transmission eigenvalues to estimate the index of refraction from far field data Inverse Problems 23 507-522
12. Cakoni F, Colton D, Monk P and Sun J 2010 The inverse electromagnetic scattering problem for anisotropic media Inverse Problems 26 74004
13. Cakoni F, Gintides D and Haddar H 2010 The existence of an infinite discrete set of transmission eigenvalues SIAM J. Math. Anal. 42 237-255
14. Cakoni F and Kirsch A 2010 On the interior transmission eigenvalue problem Int. J. Comput. Sci. Math. 3 142-167
15. Chen Q, Haddar H, Lechleiter A and Monk P 2010 A sampling method for inverse scattering in the time domain Inverse Problems 26 85001
16. Collino F, Fares M and Haddar H 2003 A linear sampling method for the inverse transmission problem in near-field elastodynamics Inverse Problems 19 1279-1298
17. Colton D, Coyle J and Monk P 2000 Recent developments in inverse acoustic scattering theory SIAM Rev. 42 369-414
18. Colton D and Kirsch A 1996 A simple method for solving inverse scattering problems in the resonance region Inverse Problems 12 383-393
19. Colton D and Kress R 1992 Inverse Acoustic and Electromagnetic Scattering Theory (Berlin: Springer)
20. Colton D, Paivarinta L and Sylvester J 2006 The interior transmission problem Inverse Probl. Imaging 1 13-28
21. Colton D and Sleeman B D 2001 An approximation property of importance in inverse scattering theory Proc. Edinburgh Math. Soc. 44 449-454 (Pubitemid 33771850)
22. Guzina B B and Bonnet M 2006 Small-inclusion asymptotic for inverse problems in acoustics Inverse Problems 22 1761-1785
23. Guzina B B and Madyarov A I 2007 A linear sampling approach to inverse elastic scattering in piecewisehomogeneous domains Inverse Problems 23 1467-1493
24. Kato T 1995 Perturbation Theory for Linear Operators (Berlin: Springer)
25. Kirsch A 1998 Characterization of the shape of a scattering obstacle using the spectral data of the far field operator Inverse Problems 14 1489-1512
26. Kirsch A 2002 The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media Inverse Problems 18 1025-1040
27. Kirsch A 2009 On the existence of transmission eigenvalues Inverse Problems Imaging 3 155-172
28. Kirsch A and Grinberg N 2008 The Factorization Method for Inverse Problems (New York: Oxford University Press)
29. Lines C D and Chandler-Wilde S N 2005 A time domain point source method for inverse scattering by rough surfaces Computing 75 157-180
30. Luke D R 2004 Multifrequency inverse obstacle scattering: the point source method and generalized filtered backprojection Math. Comput. Simul. 66 297-314
31. Luke D R and Potthast R 2006 The point source method for inverse scattering in the time domain Math.Methods Appl. Sci. 29 1501-1521
32. Malcolm A and Guzina B B 2008 On the topological sensitivity of transient acoustic fields Wave Motion 45 821-834
33. McLeanW2000 Strongly Elliptic Systems and Boundary Integral Equations (Cambridge: Cambridge University Press)
34. Paivarinta L and Sylvester J 2008 Transmission eigenvalues SIAM J. Math. Anal. 40 738-753
35. Petrovskii I G 1967 Partial Differential Equations (London: Iliffe Books)
36. 2u = 0 and deren auftreten in diemathematischen physik Z. Math. Phys. 37 100-5
37. Porat B 1996 A Course in Digitial Signal Processing (New York: Wiley)
38. Potthast R 2001 Point Sources and Multipoles in Inverse Scattering Theory (Research Notes in Mathematics, no. 427) (London: Chapman and Hall/CRC)
39. Rynne B P and Sleeman BD1991 The interior transmission problem and inverse scattering from inhomogeneous media SIAM J. Math. Anal. 22 1755-1762