Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

Inverse Problems and Imaging

Volumn 2, Issue 3, 2008, Pages 355-372

  Gebauer, Bastian ^a   Hyvönen, Nuutti ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b AALTO UNIVERSITY   (Finland)

Author keywords

Factorization method; Inclusions; Inverse elliptic boundary value problems

Indexed keywords

EID: 70350256666     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2008.2.355     Document Type: Article

References (23)

1. S. R. Arridge, Optical tomography in medical imaging, Inverse Problems, 15 (1999), R41–R93.
2. S. R. Arridge and W. R. B. Lionheart, Nonuniqueness in diffusion-based optical tomography, Opt. Lett., 23 (1998), 882–884.
3. K. Astala and L. Päivärinta, Calderon’s inverse conductivity problem in the plane, Ann. of Math., 163 (2006), 265–299.
4. G. Bal, Reconstructions in impedance and optical tomography with singular interfaces, Inverse Problems, 21 (2005), 113–131.
5. M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography, Inverse Problems, 16 (2000), 1029–1042.
6. M. Brühl, Explicit characterization of inclusions in electrical impedance tomography, SIAM J. Math. Anal., 32 (2001), 1327–1341.
7. J. Diestel and J. J. Uhl, “Vector Measures,” vol. 15 of Mathematical Surveys, American Mathematical Society, Providence, Rhode Island, 1977.
8. H. W. Engl, M. Hanke and A. Neubauer, “Regularization of Inverse Problems,” vol. 375 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, 1996.
9. F. Frühauf, B. Gebauer and O. Scherzer, Detecting interfaces in a parabolic-elliptic problem from surface measurements, SIAM J. Numer. Anal., 45 (2007), 810–836.
10. B. Gebauer, M. Hanke, A. Kirsch, W. Muniz and C. Schneider, A sampling method for detecting buried objects using electromagnetic scattering, Inverse Problems, 21 (2005), 2035-2050.
11. B. Gebauer, The factorization method for real elliptic problems, Z. Anal. Anwend., 25 (2006), 81–102.
12. B. Gebauer and N. Hyvönen, Factorization method and irregular inclusions in electrical impedance tomography, Inverse Problems, 23 (2007), 2159–2170.
13. M. Hanke and M. Brühl, Recent progress in electrical impedance tomography, Inverse Problems, 19 (2003), S65–S90.
14. J. Heino and E. Somersalo, Estimation of optical absorption in anisotropic background, Inverse Problems, 18 (2002), 559–573.
15. N. Hyvönen, Characterizing inclusions in optical tomography, Inverse Problems, 20 (2004), 737–751.
16. N. Hyvönen, Application of a weaker formulation of the factorization method to the charac- terization of absorbing inclusions in optical tomography, Inverse Problems, 21 (2005), 1331-1343.
17. N. Hyvönen, Application of the factorization method to the characterization of weak inclu- sions in electrical impedance tomography, Adv. in Appl. Math., 39 (2007), 197–221.
18. N. Hyvönen, Locating transparent regions in optical absorption and scattering tomography, SIAM J. Appl. Math., 67 (2007), 1101–1123.
19. 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.
20. A. Kirsch, The factorization method for a class of inverse elliptic problems, Math. Nachr., 278 (2005), 258–277.
21. S. Kusiak and J. Sylvester, The scattering support, Comm. Pure Appl. Math., 56 (2003), 1525–1548.
22. A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math., 143 (1996), 71–96.
23. J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125 (1987), 153–169.