Inverse scattering for Schrödinger equation in the frequency domain via data-driven reduced order modeling

Abstract

In this paper we develop a numerical method for solving an inverse scattering problem of estimating the scattering potential in a Schrödinger equation from frequency domain measurements based on reduced order models (ROM). The ROM is a projection of Schrödinger operator onto a subspace spanned by its solution snapshots at certain wavenumbers. Provided the measurements are performed at these wavenumbers, the ROM can be constructed in a data-driven manner from the measurements on a surface surrounding the scatterers. Once the ROM is computed, the scattering potential can be estimated using non-linear optimization that minimizes the ROM misfit. Such an approach typically outperforms the conventional methods based on data misfit minimization. We develop two variants of ROM-based algorithms for inverse scattering and test them on a synthetic example in two spatial dimensions.

References in corpus (6)

• Full waveform inversion with nonlocal similarity and model-derivative domain adaptive sparsity-promoting regularization
• A model reduction approach to numerical inversion for a parabolic partial differential equation
• Direct, nonlinear inversion algorithm for hyperbolic problems via projection-based model reduction
• A nonlinear method for imaging with acoustic waves via reduced order model backprojection
• Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
• Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data