Vol. 38

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Behavior of the Regularized Sampling Inverse Scattering Method at Internal Resonance Frequencies

By Karl Warnick
Progress In Electromagnetics Research, Vol. 38, 29-45, 2002


The original proof of the Colton-Kirsch regularized sampling inverse scattering algorithm does not apply at frequencies which are eigenvalues of the interior Helmholtz problem. We explain numerical observations of the behavior of the method and show that useful information about scatterer shape can be obtained at internal resonance frequencies.


 (See works that cites this article)
Karl Warnick, "Behavior of the Regularized Sampling Inverse Scattering Method at Internal Resonance Frequencies," Progress In Electromagnetics Research, Vol. 38, 29-45, 2002.


    1. Colton, D. and A. Kirsch, "A simple method for solving inverse scattering problems in the resonance region," Inverse Problems, Vol. 12, 383-393, 1996.

    2. Colton, D., M. Piana, and R. Potthast, "A simple method using Morozov’s discrepancy principle for solving inverse scattering problems," Inverse Problems, Vol. 13, 1477-1493, 1997.

    3. Colton, D. and P. Monk, "A linear sampling method for the detection of leukemia using microwaves," SIAM J. Applied Math., Vol. 58, 926-941, 1998.

    4. Colton, D., K. Giebermann, and P. Monk, "A regularized sampling method for solving three dimensional inverse scattering problems," SIAM J. Sci. Comp., Vol. 21, No. 6, 2316-2330, 2000.

    5. Kress, R. and L. Kuhn, "Linear sampling methods for inverse boundary value problems in potential theory," Appl. Numer. Math., Vol. 43, 143-155, 2002.

    6. Kress, R., "A sampling method for an inverse boundary value problem for harmonic vector fields," III-Posed and Inverse Problems, S. I. Kabanikhin and V. G. Romanov (eds.), 243–262, VSP, Utrecht, 2002.

    7. Kirsch, A., "Characterization of the shape of the scattering obstacle using the spectral data," Inverse Problems, Vol. 14, 1489-1512, 1998.

    8. Brandfass, M., A. Lanterman, and K. Warnick, "A comparison of the Colton-Kirsch inverse scattering method with linearized tomographic inverse scattering," Inverse Problems, Vol. 17, 1797-1816, Dec. 2001.

    9. Colton, D. and R. Kress, Integral Equation Methods in Scattering Theory, John Wiley & Sons, 1983.

    10. Lax, P. and R. Phillips, Scattering Theory, Revised Edition, Academic Press, Inc., 1989.

    11. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Berlin, 1992.

    12. Kress, R., "Uniqueness in inverse obstacle scattering for electromagnetic wave," Proceedings of the URSI General Assembly, 2002.

    13. Warnick, K. F. and W. C. Chew, "Error analysis of surface integral equation methods," Fast and Efficient Algorithms in Computational Electromagnetic, W. C. Chew, J. Jin, E. Michielssen, and J. Song (eds.), 203–282, Artech House, Boston, MA, 2001.