### Wednesday, June 3

## IP6

Numerical Methods in Inverse Obstacle Scattering with Reduced Data

1:30 PM-2:15 PM

*Chair: John Berger, Colorado School of Mines*

*Room 246*

The inverse scattering problem consists of determining the shape of a scattering obstacle from a knowledge of the far field pattern of the scattered wave for time-harmonic plane wave incidence. Roughly speaking, one can distinguish between two different approaches for the approximate solution of this inverse problem. In a first group of methods, the inverse obstacle problem is separated into a linear ill-posed part for the reconstruction of the scattered wave from its far field pattern and a nonlinear well-posed part for finding the location of the boundary of the scatterer from the boundary condition for the total field. In a second group of methods, the inverse obstacle problem is either considered as an ill-posed nonlinear operator equation or reformulated as a nonlinear
optimization problem in an output least squares sense.

The speaker will present some mathematical foundations for methods of the second group such as regularized Newton iterations and provide some examples for the numerical implementation. He will present this for the basic problem to recover the scatterer from the far field pattern for one incident direction and all observation directions and for modifications with reduced data, i.e., reconstructions from limited angle observations, reconstructions from the modulus of the far field only or reconstructions from backscattering data.

**Rainer Kress**

*Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Germany*

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*tjf, 12/23/97*