Inverse scattering for shape and impedance revisited

Journal of Integral Equations and Applications

Volumn 30, Issue 2, 2018, Pages 293-311

  Kress, Rainer ^a   Rundell, William ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Boundary integral equations; Helmholtz equation; Inverse scattering; Regularized Newton iterations

Indexed keywords

EID: 85055005180     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/JIE-2018-30-2-293     Document Type: Article

References (15)

1. F. Cakoni, Y. Hu and R. Kress, Simultaneous reconstruction of shape and generalized impedance functions in electrostatic imaging, Inv. Prob. 30 (2014), 105009
2. F. Cakoni, R. Kress and C. Schuft, Simultaneous reconstruction of shape and impedance in corrosion detection, Meth. Appl. Anal. 17 (2010), 357-378
3. D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Springer, New York, 2012
4. F. Hettlich, 1995 Fréchet derivatives in inverse obstacle scattering, Inv. Prob. 11 (1995), 371-382; Erratum, Inv. Prob. 11, 209-210 (1995)
5. O. Ivanyshyn, R. Kress and P. Serranho, Huygens' principle and iterative methods in inverse obstacle scattering, Adv. Comp. Math. 33 (2010), 413-429
6. R. Kress, Linear integral equations, Springer, New York, 2013
7. R. Kress and W. Rundell, Inverse scattering for shape and impedance, Inv. Prob. 17 (2001), 1075-1085
8. R. Kress and W. Rundell, Nonlinear integral equations and the iterative solution for an inverse boundary value problem, Inv. Prob. 21 (2005), 1207-1223
9. J. Liu, G. Nakamura and M. Sini, Reconstruction of the shape and surface impedance from acoustic scattering data for an arbitrary cylinder, SIAM J. Appl. Math. 67 (2007), 1124-1146
10. J. Liu and M. Sini, On the accuracy of the numerical detection of complex obstacles from far field data using the probe method, SIAM J. Sci. Comp. 31 (2009), 2665-2687
11. J. Liu and H. Zhao, On the reconstruction of obstacle using MFS from the far field data, Inv. Prob. Sci. Engin. 21 (2013), 682-703
12. G. Nakamura and M. Sini, Obstacle and boundary determination from scattering data, SIAM J. Math. Anal. 39 (2007), 819-837
13. G. Nakamura and W. Wang, Reconstruction of an impedance cylinder at oblique incidence from the far-field data, SIAM J. Appl. Math. 75 (2015), 252-274
14. P. Serranho, A hybrid method for inverse scattering for shape and impedance, Inv. Prob. 22 (2006), 663-680
15. M. Simsek and N. Tezel, The reconstruction of shape and impedance exploit-ing space mapping with inverse difference method, IEEE Trans. Anten. Propag. 60 (2012), 1868-1877