Abstract
A survey is given of the linear sampling method for solving the inverse scattering problem of determing the support of an inhomogeneous medium from a knowledge of the far field pattern of the scattered field. An application is given to the problem of detecting leukemia in the human body.
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Colton, D. and Kirsch, A., A simple method for solving inverse scattering problems in the resonance region, Inverse Problems 12(1966), 383–393.
Colton, D., Kirsch, A. and Päivärinta, A., Far field patterns for acoustic waves in an inhomogeneous medium, SIAM J. Math. Anal. 20 (1989), 1472–1483.
Colton, D. and Kress, R., Eigenvalues of the far field operator for the Helmholtz equation in an absorbing medium, SIAM J. Appl Math. 55 (1995), 1724–1735.
Colton, D. and Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory, Second Ed., Springer-Verlag, New York, 1998.
Colton, D. and Monk, P., A linear sampling method for the detection of leukemia using microwaves, SIAM J. Appl. Math. 58 (1998), 926–941.
Colton, D. and Monk, P., Mathematical problems in microwave medical imaging, in Computational Radiology and Imaging: Therapy and Diagnostics, C. Börgers and F. Natterer, eds., Springer-Verlag, New York, 1999, 137–156.
Colton, D. and Monk, P., A linear sampling method for the detection of leukemia using microwaves II, submitted for publication.
Colton, D., Piana, M. and Potthast, R., A simple method using Morozov’s discrepancy principle for solving inverse scattering problems, Inverse Problems 13 (1997), 1477–1493.
Coyle, J., Direct and Inverse Problems in Electromagnetic Scattering from Anisotropic Objects, Ph.D. Thesis, University of Delaware, Newark, 1998.
Harrington, R. and Mautz, J., An impedance sheet approximation for thin dielectric shells, IEEE Trans. Antennas and Propagation 23 (1975), 531–534.
Kirsch, A., An Introduction to the Mathematical Theory of Inverse Problems, Springer-Verlag, New York, 1996.
Kirsch, A., Characterization of the shape of the scattering obstacle by the spectral data of the far field operator, Inverse Problems 14 (1998), 1489–1512.
Kirsch, A., Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory, Inverse Problems, to appear.
Langenberg, K. J., Applied inverse problems for acoustic, electromagnetic and elastic wave scattering, in Basic Methods of Tomography and Inverse Problems, P.C. Sabatier, ed., Adam Hilger, Bristol, 1987, 125–467.
Potthast, R., On a concept of uniqueness in inverse scattering for a finite number of incident waves, SIAM J. Appl. Math. 58 (1998), 666–682.
Ringrose, J. R., Compact, Non-Self-Adjoint Operators, Van Nostrand Rein-hold Co., London, 1971.
Sun, Z. and Uhlmann, G., Recovery of singularities for formally determined inverse problems, Comm. Math. Physics 153 (1993), 431–445.
Tikhonov, A. N., Goncharsky, A. V., Stepanov, V. V. and Yagola, A. G., Numerical Methods for the Solution of Ill-Posed Problems, Kluwer, Dordrecht, 1995.
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Colton, D., Kirsch, A., Monk, P. (2000). The Linear Sampling Method in Inverse Scattering Theory. In: Colton, D., Engl, H.W., Louis, A.K., McLaughlin, J.R., Rundell, W. (eds) Surveys on Solution Methods for Inverse Problems. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6296-5_6
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DOI: https://doi.org/10.1007/978-3-7091-6296-5_6
Publisher Name: Springer, Vienna
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