A nonlinear optimization method is proposed for inverse scattering problems in the frequency domain, when the unknown medium is characterized by one or several spatially varying parameters. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type method combined with frequency stepping. Instead of a grid-based discrete representation combined with standard Tikhonov-type regularization, each parameter is projected to a (small and slowly increasing) finite-dimensional subspace, which is iteratively adapted during the optimization.

This presentation is part of Contributed Presentation “CP7 - Contributed session 7”

Authors:

Marcus Grote (University of Basel)

Uri Nahum (University of Basel)

Keywords:

inverse problems, nonlinear optimization, partial differential equation models, regularization