We consider inverse medium problems for the Helmholtz equation. The time-harmonic inverse 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 velocity is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization, introducing regularization into the inversion and omitting standard Tikhonov-type regularization terms. Both analytic and numerical evidence underpins the accuracy of the Adaptive Eigenspace representation.
This is a joint work with M.J. Grote and U. Nahum from the University of Basel, Switzerland.
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