January 25 - 27, 2007

Decomposition methods for inverse obstacle scattering revisited

Rainer Kress (University of Göttingen)

The inverse obstacle scattering problem under consideration consists of the reconstruction of the boundary of an impenetrable obstacle from the knowledge of the far field pattern for scattering of time-harmonic acoustic waves. The so-called decomposition methods separate this inverse problem into an ill-posed linear problem to reconstruct the scattered wave from its far field pattern followed by a nonlinear problem that determinates the boundary shape of the scatterer from the boundary condition. We present recent modifications of a decomposition method due to Kirsch and K. (1987) that combines it with elements of Newton type iterations for inverse scattering problems and lead to considerable improvements of the reconstruction quality. The mathematical foundation of the new methods that rely on boundary integral equations will be discussed and numerical examples will be presented.

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