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Gradient Methods in Inverse Acoustic and Electromagnetic Scattering

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Large-Scale Optimization with Applications

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 92))

Abstract

The problem of determining the complex permittivity or sound speed in a bounded inhomogeneity imbedded in a homogeneous medium from scattered field measurements exterior to the inhomogeneity is considered. A number of methods of attacking this problem, all based on minimizing the difference between an integral representation of the scattered field and the measured data, are described. These include Born, Newton-Kantorovich and distorted Born methods. The main part of the paper will be devoted to a description of a gradient type algorithm which is used to minimize a cost functional in which two objective functions are sought simultaneously. The error which is minimized is a bilinear form involving the product of two functions. This special form of the nonlinearity is retained in the algorithm. A number of numerical results will be presented which illustrate the effectiveness and limitations of the approach.

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Author information

Authors and Affiliations

  1. Laboratory of Electromagnetic Research, Faculty of Electrical Engineering, Delft University of Technology, P.O. Box 5031, Delft, 2600 GA, The Netherlands

    P. M. Van Den Berg

  2. Center for the Mathematics of Waves Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    R. E. Kleinman

Authors
  1. P. M. Van Den Berg
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  2. R. E. Kleinman
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Editor information

Editors and Affiliations

  1. Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Lorenz T. Biegler

  2. Computer Science Department, Cornell University, Ithaca, NY, 14853-0001, USA

    Thomas F. Coleman

  3. Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA

    Andrew R. Conn

  4. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Fadil N. Santosa

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© 1997 Springer Science+Business Media New York

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Van Den Berg, P.M., Kleinman, R.E. (1997). Gradient Methods in Inverse Acoustic and Electromagnetic Scattering. In: Biegler, L.T., Coleman, T.F., Conn, A.R., Santosa, F.N. (eds) Large-Scale Optimization with Applications. The IMA Volumes in Mathematics and its Applications, vol 92. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1962-0_10

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  • DOI: https://doi.org/10.1007/978-1-4612-1962-0_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7357-8

  • Online ISBN: 978-1-4612-1962-0

  • eBook Packages: Springer Book Archive

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