A note on the enclosure method for an inverse obstacle scattering problem with a single point source

Inverse Problems

Volumn 26, Issue 10, 2010, Pages

  Ikehata, Masaru ^a  

^a GUNMA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CONVEX HULL; ENCLOSURE METHOD; FAR-FIELD; LAYERED MEDIUM; LINEAR SAMPLING METHODS; OBSTACLE SCATTERING; OTHER APPLICATIONS; SINGLE POINT SOURCE; SUPPORT FUNCTIONS; TWO-DIMENSION;

HELMHOLTZ EQUATION;

ENCLOSURES;

EID: 78049420134     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/26/10/105006     Document Type: Article

References (31)

1. AlessandriniGandDiBenedetto E 1997 Determining 2-dimensional cracks in 3-dimensional bodies: uniqueness and stability Indiana Univ. Math. J. 46 1-82
2. Arens T 2004 Why linear sampling works Inverse Problems 20 163-73
3. Colton D and Kirsch A 1996 A simple method for solving inverse scattering problems in the resonance region Inverse Problems 12 383-93
4. Colton D and Kress R 1998 Inverse Acoustic and Electromagnetic Scattering Theory 2nd edn (Berlin: Springer)
5. Daniels D J, Gunton D J and Scott H F 1988 Introduction to subsurface radar IEE Proc. 135 278-320
6. Friedman A and Isakov V 1989 On the uniqueness in the inverse conductivity problem with one measurement Indiana Univ. Math. J. 38 563-79
7. Elschner J and Yamamoto M 2008 Uniqueness in determining polyhedral sound-hard obstacles with a single incoming wave Inverse Problems 24 035004
8. Hettlich F 1994 On the uniqueness of the inverse conductive scattering problem for the Helmholtz equation Inverse Problems 10 129-44
9. Ikehata M 1998 Reconstruction of an obstacle from the scattering amplitude at a fixed frequency Inverse Problems 14 949-54
10. Ikehata M 1999 Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data Inverse Problems 15 1231-41
11. Ikehata M 1999 Howto drawa picture of an unknown inclusion from boundary measurements. Two mathematical inversion algorithms J. Inverse Ill-Posed Problems 7 255-71
12. Ikehata M 2000 Reconstruction of the support function for inclusion from boundary measurements J. Inverse Ill-Posed Problems 8 367-78
13. Ikehata M 2000 On reconstruction in the inverse conductivity problem with one measurement Inverse Problems 16 785-93
14. Ikehata M 2002 A regularized extraction formula in the enclosure method Inverse Problems 18 435-40
15. Ikehata M 2003 Complex geometrical optics solutions and inverse crack problems Inverse Problems 19 1385-405
16. Ikehata M 2004 Inverse scattering problems and the enclosure method Inverse Problems 20 533-51
17. Ikehata M 2004 Mittag-Leffler's function and extracting from Cauchy data Inverse Problems and Spectral Theory (Contemp. Math. vol 348) ed H Isozaki (Providence, RI: AMS) pp 41-52
18. Ikehata M 2005 An inverse transmission scattering problem and the enclosure method Computing 75 133-56
19. Ikehata M 2005 The Herglotz wave function, the Vekua transform and the enclosure method Hiroshima Math. J. 35 485-506
20. Ikehata M and Itou H 2009 Extracting the support function of a cavity in an isotropic elastic body from a single set of boundary data Inverse Problems 25 105005
21. Ikehata M and Ohe T 2002 Numerical method for finding the convex hull of polygonal cavities using enclosure method Inverse Problems 18 111-24
22. Ikehata M and Ohe T 2002 A numerical method for finding the convex hull of inclusions using the enclosure method Elecromagnetic Nondestructive Evaluation (VI) (Studies in Applied Electromagnetics and Mechanics vol 23) ed F Kojima et al (Amsterdam: IOS Press) pp 21-8
23. Ikehata M and Ohe T 2008 The enclosure method for an inverse crack problem and the Mittag-Leffler function Inverse Problems 24 015006
24. Ikehata M and Siltanen S 2000 Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements Inverse Problems 16 1043-52
25. Ikehata M and Siltanen S 2004 Electrical impedance tomography and Mittag-Leffler's function Inverse Problems 20 1325-48
26. Liseno A and Pierri R 2003 Impossibility of recovering a scatterer's shape by the first version of the 'linear sampling method' Int. J. Electron. Commun. 57 70-3
27. Olver W J 1974 Asymptotics and Special Functions (New York: Academic)
28. Potthast R 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119-40
29. Potthast R 2000 Stability estimates and reconstructions in inverse scattering using singular sources J. Comput. Appl. Math. 114 247-74
30. Ramm A G 1986 Scattering by Obstacles (Dortrecht: Reidel)
31. Semenov S et al 1999 Three-dimensional microwave tomography: experimental prototype of the system and vector Born reconstruction method IEEE Trans. Biomed. Eng. 46 937-46