Marie Kray, SLIM "Adaptive Eigenspace method for inverse scattering problems in the frequency domain" 12:30 pm, Rm 4133-2207 Main Mall

03/28

 

Marie Kray will discuss aspects of her work carried out at Department of Mathematics and Computer Science, University of Basel in collaboration with Marcus Grote and Uri Nahum.  For more information readers can refer to: Inverse Problems, Vol 3, No 2, publ Jan 9, 2017
http://iopscience.iop.org/article/10.1088/1361-6420/aa5250/meta

Abstract: A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion (AEI) method.
 

This lecture is part of the UBC SCAIM seminar series (Scientific Computing, Applied and Industrial Mathematics, for more information please see:

https://sites.google.com/site/ubcscaim/home