Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Necmi Serkan Tezel: A Second Order Newton Method for Shape Reconstruction of the Sound-soft Obstacle Buried in a Dielectric Cylinder of Arbitrary Shape

Thu, 23 July, 2009, 17:15-18:15, Foyer

A new second order Newton method for reconstructing the shape of a sound-soft scatterer
buried in an arbitrary shaped dielectric cylinder from the measured far-field pattern is
presented. This method extends a hybrid between regularized Newton iterations and
decomposition. The main idea of our iterative method is to use Huygen's principle, i.e.,
represent the scattered field as a single-layer potential by using Green's fuction of
domain containing dielectric cylinder. Given an approximation for the boundary of the
scatterer, this leads to an ill-posed integral equation of the first kind that is solved via
Tikhonov regularization. Then, in a second order Taylor expansion, the so sound-soft
boundary condition is employed to update the boundary approximation. In an iterative
procedure, these two steps are alternated until some stopping criterium is satisfied. We
describe the method in detail and illustrate its feasibility through examples with exact and
noisy data.

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