On the reconstruction of surface impedance from the far-field data in inverse scattering problems

References

• Cheng , J , Liu , JJ and Nakamura , G . 2003 . Recovery of the shape of an obstacle and the boundary impedance from the far-field pattern . J. Math. Kyoto Univ. , 43 ( 1 ) : 165 – 186 .
   Web of Science ®Google Scholar
• Cheng , J , Liu , JJ , Nakamura , G and Wang , SG . 2009 . Recovery of multiple obstacles by probe method . Quart. Appl. Math. , 67 ( 2 ) : 221 – 247 .
   Web of Science ®Google Scholar
• Cakoni , F and Colton , D . 2006 . Qualitative Methods in Inverse Scattering Theory , Berlin : Springer-Verlag .
   Google Scholar
• Colton , D and Kress , R . 1998 . Inverse Acoustic and Electromagnetic Scattering Theory , Berlin : Springer-Verlag .
   Google Scholar
• Ikehata , M . 1999 . Reconstruction of obstacle from boundary measurements . Wave Motion , 30 ( 3 ) : 205 – 223 .
   Web of Science ®Google Scholar
• Ikehata , M . 1998 . Reconstruction of an obstacle from the scattering amplitude at a fixed frequency . Inverse Probl. , 14 ( 4 ) : 949 – 954 .
   Web of Science ®Google Scholar
• Liu , JJ , Nakamura , G and Sini , M . 2007 . Reconstruction of the shape and surface impedance for acoustic scattering data for an arbitrary cylinder . SIAM J. Appl. Math. , 67 ( 4 ) : 1124 – 1146 .
   Web of Science ®Google Scholar
• Liu , JJ and Sini , M . 2009 . On the accuracy of the numerical detection of complex obstacles from far-field data using the probe method . SIAM J. Sci. Comput. , 31 ( 4 ) : 2665 – 2687 .
   Web of Science ®Google Scholar
• Nakamura , G and Sini , M . 2007 . Obstacle and boundary determination from scattering data . SIAM J. Math. Anal. , 39 ( 3 ) : 819 – 837 .
   Web of Science ®Google Scholar
• Potthast , R . 2001 . Point Sources and Multipoles in Inverse Scattering Theory , London : Chapman & Hall/CRC .
   Google Scholar
• Akduman , I and Kress , R . 2003 . Direct and inverse scattering problems for inhomogeneous impedance cylinders of arbitrary shape . Radio Sci. , 38 ( 3 ) : 1055
   Web of Science ®Google Scholar
• Cakoni , F and Colton , D . 2004 . The determination of the surface impedance of a partially coated obstacle from far field data . SIAM J. Appl. Math. , 64 ( 2 ) : 709 – 723 .
   Web of Science ®Google Scholar
• Cakoni , F , Colton , D and Monk , P . 2010 . The determination of boundary coefficients from far field measurements . J. Int. Eqns Appl. , 42 ( 2 ) : 167 – 191 .
   Web of Science ®Google Scholar
• Godin , YA and Vaingerg , B . 2010 . On the determination of the boundary impedance from the far-field pattern . SIAM J. Appl. Math. , 70 ( 7 ) : 2273 – 2280 .
   Web of Science ®Google Scholar
• Kress , R , Yaman , F , Yapar , A and Akduman , I . 2009 . Inverse scattering for an impedance cylinder buried in a dielectric cylinder . Inverse Probl. Sci. Eng. , 17 ( 4 ) : 473 – 488 .
   Web of Science ®Google Scholar
• Labreuche , C . 1999 . Stability of the recovery of surface impedances in inverse scattering . J. Math. Anal. Appl. , 231 ( 1 ) : 161 – 176 .
   Web of Science ®Google Scholar
• Liu , JJ , Cheng , J and Nakamura , G . 2002 . Reconstruction and uniqueness of an inverse scattering problem with impedance boundary . Sci. China, Ser. A , 45 ( 11 ) : 1408 – 1419 .
   Google Scholar
• Sincich , E . 2006 . Stable determination of the surface impedance of an obstacle by far-field measurements . SIAM J. Math. Anal. , 38 ( 2 ) : 434 – 451 .
   Web of Science ®Google Scholar
• Sini , M . 2011 . On uniqueness and reconstruction of rough and complex obstacles from acoustic scattering data . Comput. Methods Appl. Math. , 11 ( 1 ) : 83 – 104 .
   Google Scholar
• Colton , D and Kress , R . 1983 . Integral Equation Methods in Scattering Theory , New York : Wiley & Sons .
   Google Scholar
• Colton , D and Kress , R . 1995 . Eigenvalue of the far field operator for the Helmholtz equation in an absorbing medium . SIAM J. Appl. Math. , 55 ( 6 ) : 1724 – 1735 .
   Web of Science ®Google Scholar
• Ammari , H and Kang , H . 2007 . Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory , New York : Springer-Verlag .
   Google Scholar
• Martin , PA . 2006 . Multiple Scattering , Cambridge , , UK : Cambridge University Press .
   Google Scholar
• Kenig , CE . Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, CBMS Regional Conference Series in Mathematics, Vol. 83, American Mathematical Society, Providence, RI, 1994
   Google Scholar
• Kress , R . 1989 . Linear Integral Equations , Berlin, Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Kress , R . 1995 . On the numerical solution of a hypersingular integral equation in scattering theory . J. Comput. Appl. Math. , 61 ( 3 ) : 345 – 360 .
   Web of Science ®Google Scholar