Shape reconstruction of acoustic obstacles from the modulus of the far field pattern

Inverse Problems and Imaging

Volumn 1, Issue 4, 2007, Pages 609-622

  Ivanyshyn, Olha ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Acoustic scattering; Inverse problem; Modulus of far field; Nonlinear integral equations

Indexed keywords

EID: 46749102084     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2007.1.609     Document Type: Article

References (8)

1. D. Colton and R. Kress, “Inverse Acoustic and Electromagnetic Scattering Theory”, Springer-Verlag, Berlin, second edition, 1998.
2. O. Ivanyshyn and R. Kress, Nonlinear integral equations in inverse obstacle scattering, in “Mathematical Methods in Scattering Theory and Biomedical Engineering” (Fotiatis, Massalas, eds), (2006), 39–50.
3. R. Kress, On the numerical solution of a hypersingular integral equation in scattering theory, J. Comput. Appl. Math., 61 (1995), 345–360.
4. R. Kress and W. Rundell, Inverse obstacle scattering with modulus of the far field pattern as data, in “Inverse Problems in Medical Imaging and Nondestructive Testing” (Oberwolfach, 1996), (1997), 75–92.
5. R. Kress and W. Rundell. Nonlinear integral equations and the iterative solution for an inverse boundary value problem, Inverse Problems, 21 (2005), 1207–1223.
6. K.-M. Lee, Inverse scattering via nonlinear integral equations for a Neumann crack, Inverse Problems, 22 (2006), 1989–2000.
7. J. Liu and J. Seo, On stability for a translated obstacle with impedance boundary condition, Nonlinear Anal., 59 (2004), 731–744.
8. R. Potthast, Fréchet differentiability of boundary integral operators in inverse acoustic scattering, Inverse Problems, 10 (1994), 431–447.