A nonlinear integral equation method for the inverse scattering problem by sound-soft rough surfaces

References

• Chandler-Wilde SN, Zhang B. Electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate. Proc. R. Soc. Lond. A. 1998;454:519–542.
   Web of Science ®Google Scholar
• Chandler-Wilde SN, Ross CR. Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium. Inverse Prob. 1995;11:1063–1067.
   Web of Science ®Google Scholar
• Chandler-Wilde SN, Ross CR. Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane. Math. Methods Appl. Sci. 1996;19:959–976.
   Web of Science ®Google Scholar
• Chandler-Wilde SN, Ross CR, Zhang B. Scattering by infinite one-dimensional rough surfaces. Proc. R. Soc. Lond. A. 1999;455:3767–3787.
   Web of Science ®Google Scholar
• Chandler-Wilde SN, Zhang B. A uniqueness result for scattering by infinite rough surfaces. SIAM J. Appl. Math. 1998;58:1774–1790.
   Web of Science ®Google Scholar
• Zhang B, Chandler-Wilde SN. Integral equation methods for scattering by infinite rough surfaces. Math. Methods Appl. Sci. 2003;26:463–488.
   Web of Science ®Google Scholar
• Chandler-Wilde SN, Zhang B. On the solvability of a class of second kind integral equations on unbounded domains. J. Math. Anal. Appl. 1997;214:482–502.
   Web of Science ®Google Scholar
• Chandler-Wilde SN, Zhang B, Ross CR. On the solvability of second kind integral equations on the real line. J. Math. Anal. Appl. 2000;245:28–51.
   Web of Science ®Google Scholar
• Arens T, Chandler-Wilde SN, Haseloh KO. Solvability and spectral properties of integral equations on the real line: ∐. Lp-spaces and applications. J. Integral Equ. Appl. 2003;15:1–35.
   Google Scholar
• Meier A, Arens T, Chandler-Wilde SN, Kirsch A. A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces. J. Integral Equ. Appl. 2000;12:281–321.
   Google Scholar
• Burkard C, Potthast R. A multi-section approach for rough surface reconstruction via the Kirsch-Kress scheme. Inverse Prob. 2010;26:45007–45029.
   Web of Science ®Google Scholar
• Burkard C, Potthast R. A time-domain probe method for three-dimensional rough surface reconstructions. Inverse Prob. Imaging. 2009;3:259–274.
   Web of Science ®Google Scholar
• Lines C. Inverse scattering by unbounded rough surfaces [PhD thesis]. London: Department of Mathematics, Brunel University; 2003.
   Google Scholar
• Bao G, Lin J. Imaging of local surface displacement on an infinite ground plane: the multiple frequency case. SIAM J. Appl. Math. 2011;71:1733–1752.
   Web of Science ®Google Scholar
• Zhang H, Zhang B. A novel integral equation for scattering by locally rough surfaces and application to the inverse problem. SIAM J. Appl. Math. 2013;73:1811–1829.
   Web of Science ®Google Scholar
• Bao G, Li P. Inverse medium scattering problems for electromagnetic waves. SIAM J. Appl. Math. 2005;65:2049–2066.
   Web of Science ®Google Scholar
• Bao G, Li P. Near-field imaging of infinite rough surfaces. SIAM J. Appl. Math. 2013;73:2162–2187.
   Web of Science ®Google Scholar
• Bao G, Lin J, Triki F. A multi-frequency inverse source problem. J. Differ. Equ. 2010;249:3443–3465.
   Web of Science ®Google Scholar
• Chandler-Wilde SN, Potthast R. The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory. Proc. R. Soc. Lond. A. 2002;458:2967–3001.
   Web of Science ®Google Scholar
• Kress R, Rundell W. Nonlinear integral equations and the iterative solution for an inverse boundary value problem. Inverse Prob. 2005;21:1207–1223.
   Web of Science ®Google Scholar
• Ivanyshyn O, Johansson T. Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle. J. Integral Equ. Appl. 2007;19:289–308.
   Google Scholar
• Ivanyshyn O, Kress R. Inverse scattering for surface impedance from phase-less far field data. J. Comput. Phys. 2011;230:3443–3452.
   Web of Science ®Google Scholar
• Ivanyshyn O, Kress R. Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks. J. Integral Equ. Appl. 2006;18:13–38.
   Google Scholar
• Eckel H, Kress R. Nonlinear integral equations for the inverse electrical impedance problem. Inverse Prob. 2007;23:475–491.
   Web of Science ®Google Scholar
• Meier A. Numerical treatment of integral equations on the real line with application to acoustic scattering by unbounded rough surfaces [PhD thesis]. London: Department of Mathematical Sciences, Brunel University; 2001.
   Google Scholar
• Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 2nd ed. Berlin: Springer; 1998.
   Google Scholar
• Kress R. Linear integral equations. 2nd ed. Berlin: Springer Verlag; 1999.
   Google Scholar
• Lebedev NN. Special functions and their applications. New York (NY): Dover; 1972.
   Google Scholar
• Potthast R. Fréchet differentiability of boundary integral operators in inverse acoustic scattering. Inverse Prob. 1994;10:431–447.
   Web of Science ®Google Scholar