Cakoni, F., and D. Colton (2006), Qualitative Methods in Inverse Scattering
Theory, Springer, Berlin.
Colton, D., and A. Kirsch (1996), A simple method for solving inverse
scattering problems in the resonance region, Inverse Probl., 12(4),
383–393, doi:10.1088/0266-5611/12/4/003.
Colton, D., and R. Kress (1998), Inverse Acoustic and Electromagnetic
Scattering Theory, Appl. Math. Sci., vol. 93, 2nd ed., Springer, Berlin.
Ikehata, M. (1998), Reconstruction of the shape of the inclusion by boundary
measurements, Commun. Partial Differ. Equations, 23, 1459–1474,
doi:10.1080/03605309808821390.
Kirsch, A. (1996), An Introduction to the Mathematical Theory of Inverse
Problems, Appl. Math. Sci., vol. 120, Springer, New York.
Kirsch, A. (1998), Characterization of the shape of a scattering obstacle
using the spectral data of the far field operator, Inverse Probl., 14(6),
1489–1512, doi:10.1088/0266-5611/14/6/009.
Kirsch, A., and N. Grinberg (2008), The Factorization Method for Inverse
Problems, Oxford Lect. Ser. Math. Its Appl., vol. 36, Oxford Univ. Press,
Oxford, U. K.
Kress, R. (1989), Linear Integral Equations, Springer, Berlin.
Lax, P. D., and R. S. Phillips (1967), Scattering Theory, Pure Appl. Math.,
vol. 26, Academic, New York.
Luke, D. R., and R. Potthast (2003), The no response test—A sampling
method for inverse scattering problems, SIAM J. Appl. Math., 63(4),
1292–1312, doi:10.1137/S0036139902406887.
Potthast, R. (1996), A fast new method to solve inverse scattering problems,
Inverse Probl., 12(5), 731–742, doi:10.1088/0266-5611/12/5/014.
Potthast, R. (1998), A point source method for inverse acoustic and electromagnetic
obstacle scattering problems, IMA J. Appl. Math., 61(2), 119–140, doi:10.1093/imamat/61.2.119.
Potthast, R. (2000), Stability estimates and reconstructions in inverse
acoustic scattering using singular sources, J. Comput. Appl. Math., 114(2),
247–274, doi:10.1016/S0377-0427(99)00201-0.
Potthast, R. (2001), Point Sources and Multipoles in Inverse Scattering
Theory, Res. Notes Math., vol. 427, Chapman and Hall, Boca Raton, Fla.
Potthast, R. (2004), A set‐handling approach for the no‐response test
and related methods, Math. Comput. Simul., 66, 281–295, doi:10.1016/
j.matcom.2004.02.012.
Potthast, R. (2006), A survey on sampling and probe methods for inverse
problems, Inverse Probl., 22(2), R1–R47, doi:10.1088/0266-5611/22/2/R01.
Potthast, R., and J. Schulz (2007), A multiwave range test for obstacle
reconstructions with unknown physical properties, J. Comput. Appl.
Math., 205, 53–71, doi:10.1016/j.cam.2006.04.040.
Potthast, R., J. Sylvester and S. Kusiak (2003), A range test for determining
scatterers with unknown physical properties, Inverse Probl., 19(3), 533–547,doi:10.1088/0266-5611/19/3/304.
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