We kindly invite you to the talk "Adaptive spectral decomposition for inverse medium problems" by Marcus J. Grote, March 30, 2:00pm Vienna Time.

This is part of the Joint Fudan - RICAM Seminar on Inverse Problems

The meeting is a hybrid meeting, come either in person to the meeting room 9 at Oskar-Morgenstern-Platz 1, 9th floor or
join the zoom meeting: https://zoom.us/join     Meeting-ID: 694 9293 2905     Password: SCMS

Abstract: Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations of a scattered wave field. Typically, they are formulated as PDE-constrained optimization problems and solved by an inexact Newton-like iteration. Clearly, standard grid-based representations are very general but often too expensive due to the resulting high-dimensional search space. Adaptive spectral inversion (ASI) instead expands the unknown medium in a basis of eigenfunctions of a judicious elliptic operator, which depends itself on the current iterate. Thus, instead of a grid-based discrete representation combined with standard Tikhonov regularization, the unknown medium is projected to a small finite-dimensional subspace, which is iteratively adapted using dynamic thresholding. Rigorous error estimates of the adaptive spectral decomposition (ASD) are proved for an arbitrary piecewise constant medium.