Reconstruction of a penetrable cavity and the external obstacle

References

• Jakubik P , Potthast R . Testing t he integrity of some cavity-the Cauchy problem and the range test. Appl Numer Math. 2008;58:899–914.
   Web of Science ®Google Scholar
• Ikehata M , Itou H . On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data. Inverse Prob. 2012;28:125003.
   Web of Science ®Google Scholar
• Qin HH , Liu X . The interior inverse scattering problem for cavities with an artificial obstacle. Appl Numer Math. 2015;88:18–30.
   Web of Science ®Google Scholar
• Zeng F , Cakoni F , Sun J . An inverse electromagnetic scattering problem for cavity. Inverse Prob. 2011;27:125002.
   Web of Science ®Google Scholar
• Qin HH , Colton D . The inverse scattering problem for cavities. J Appl Numer Math. 2012;62:699–708.
   Web of Science ®Google Scholar
• Qin HH , Colton D . The inverse scattering problem for cavities with impedance boundary condition. J Adv Comput Math. 2012;36:157–174.
   Web of Science ®Google Scholar
• Hu Y , Cakoni F , Liu J . The inverse scattering problem for a partially coated cavity with interior measurements. Appl Anal Int J. 2014;93:936–956.
   Web of Science ®Google Scholar
• Qin HH , Cakoni F . Nonlinear integral equations for shape reconstruction in the inverse interior scattering problem. Inverse Prob. 2011;27:035005.
   Web of Science ®Google Scholar
• Zeng F , Suarez P , Sun J . A decomposition method for an interior inverse scattering problem. Inverse Prob Imaging. 2013;7:291–303.
   Web of Science ®Google Scholar
• Liu X . The factorization method for cavities. Inverse Prob. 2014;30:015006.
   Web of Science ®Google Scholar
• Cakoni F , Colton D , Meng S . The inverse scattering problem for a penetrable cavity with internal measurements. AMS Contemp Math. 2014;615:71–88.
   Google Scholar
• Meng S , Haddar H , Cakoni F . The factorization method for a cavity in an inhomogeneous medium. Inverse Prob. 2014;30:045008.
   Web of Science ®Google Scholar
• Colton D , Kirsch A . A simple method for solving inverse scattering problems in the resonance region. Inverse Prob. 1996;12:383–393.
   Web of Science ®Google Scholar
• Kirsch A . Characterization of the shape of a scattering obstacle using the spectral data of the far-field operator. Inverse Prob. 1998;14:1489–1512.
   Web of Science ®Google Scholar
• Colton D , Kress R . Using fundamental solutions in inverse scattering. Inverse Prob. 2006;22:R49–R66.
   Web of Science ®Google Scholar
• Potthast R . A survey on sampling and probe methods for inverse problems. Inverse Prob. 2006;22:R1–R47.
   Web of Science ®Google Scholar
• Cakoni F , Colton D . Qualitative methods in inverse scattering theory. Berlin: Springer; 2006.
   Google Scholar
• Kirsch A , Grinberg N . The factorization method for inverse problems. Oxford lecture series in mathematics and its applications. Vol. 36. Oxford: Oxford University Press; 2008.
   Google Scholar
• Arens T , Lechleiter A . The linear sampling method revisited. J Integral Equ Appl. 2009;21:179–202.
   Web of Science ®Google Scholar
• Anagnostopoulos KA , Charalambopoulos A , Kleefeld A . The factorization method for the acoustic transmission problem. Inverse Prob. 2013;29:115015.
   Web of Science ®Google Scholar
• Yang J , Zhang B , Zhang H . The factorization method for reconstructing a penetrable obstacle with unknown buried objects. SIAM J Appl Math. 2013;73:617–635.
   Web of Science ®Google Scholar
• Kirsch A , Liu X . The factorization method for inverse acoustic scattering by a penetrable anisotropic obstacle. Math Methods Appl Sci. 2014;37:1159–1170.
   Web of Science ®Google Scholar
• Bondarenko O , Kirsch A , Liu X . The factorization method for inverse acoustic scattering in a layered medium. Inverse Prob. 2013;29:045010.
   Web of Science ®Google Scholar
• Liu X , Zhang B . Direct and inverse obstacle scattering problems in a piecewise homogeneous medium. SIAM J Appl Math. 2010;70:3105–3120.
   Web of Science ®Google Scholar
• Bonnet-BenDhia AS , Ciarlet P . Maria Zwolf C. Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J Comput Appl Math. 2010;234:1912–1919.
   Web of Science ®Google Scholar
• Colton D , Kress R . Inverse acoustic and electromagnetic scattering theory. 3rd ed. New York (NY): Springer; 2013.
   Google Scholar
• Mclean W . Strongly elliptic systems and boundary integral equations. Cambridge: Cambridge University Press; 2000.
   Google Scholar
• Grinberg N , Kirsch A . The linear sampling method in inverse obstacle scattering for impedance boundary conditions. J Inverse Ill-Posed Prob. 2002;10:171–185.
   Google Scholar