UNIverse - Public Research Portal
Project cover

Adaptive Spectral Decompositions for Inverse Medium Problems

Research Project
 | 
01.11.2018
 - 01.10.2023

Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all too often computationally prohibitive due to the high dimension of the search space. Adaptive spectral decompositions instead expand the unknown medium in a basis of eigenfunctions of a judicious elliptic operator, which depends itself on the medium. We combine the AS decomposition with standard inexact Newton-type methods for the solution of time-harmonic and time-dependent wave scattering problems. By repeatedly adapting both the eigenfunction basis and its dimension, the resulting adaptive spec- tral inversion (ASI) method substantially reduces the dimension of the search space during the nonlinear optimization. Rigorous estimates of the AS decomposition are proved for a general piecewise constant medium. Numerical results illustrate the accuracy and efficiency of the ASI method for time-harmonic inverse scattering problems, including realistic subsurface models from geophysics.

Members (3)

Profile Photo

Marcus J. Grote

Principal Investigator
MALE avatar

Yannik Gleichmann

Project Member
MALE avatar

Daniel Henri Baffet

Project Member