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SUMMARY:Adaptive Spectral Decomposition for Inverse Scattering Problems
DTSTART;VALUE=DATE-TIME:20210923T123000Z
DTEND;VALUE=DATE-TIME:20210923T125000Z
DTSTAMP;VALUE=DATE-TIME:20211201T182426Z
UID:indico-contribution-847@conference2.aau.at
DESCRIPTION:Speakers: Yannik G. Gleichmann ()\nA nonlinear optimization me
thod is proposed for inverse scattering problems\, when the unknown medium
is characterized by one or several spatially varying parameters. The inve
rse medium problem is formulated as a PDE-constrained optimization problem
and solved by an inexact truncated Newton-type method. Instead of a grid-
based discrete representation\, each parameter is projected to a separate
fnite-dimensional subspace\, which is iteratively adapted during the optim
ization. Each subspace is spanned by the first few eigenfunctions of a lin
earized regularization penalty functional chosen a priori. The (small and
slowly increasing) finite number of eigenfunctions effectively introduces
regularization into the inversion and thus avoids the need for standard Ti
khonov-type regularization and\, in practice\, appears more robust to miss
ing data or added noise. Numerical results illustrate the accuracy and eff
iciency of the resulting adaptive spectral regularization for inverse scat
tering problems for the wave equation in time domain.\n\nhttps://conferenc
e2.aau.at/event/62/contributions/847/
LOCATION:Alpen-Adria-Universität Klagenfurt HS 1
URL:https://conference2.aau.at/event/62/contributions/847/
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