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Regularized Reduced Order Lippman-Schwinger-Lanczos Method for Inverse Scattering Problems in the Frequency Domain
Justin Baker, Elena Cherkaev, Vladimir Druskin +2
Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) m…
Reduced order modeling inversion of mono static data in a multi-scattering environment
V. Druskin, S. Moskow, M. Zaslavsky
The data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of the inverse scattering problems with applications to seismic and sonar im…
Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky
Data-driven reduced order models (ROMs) are combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin p…
Reduced Order Model Approach to Inverse Scattering
Liliana Borcea, Vladimir Druskin, Alexander V. Mamonov +2
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (so…
Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data
Liliana Borcea, Vladimir Druskin, Alexander V. Mamonov +2
We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schrödinger equation in the spectral domain given boundary data at a few frequencie…
Fast finite-difference convolution for 3D problems in layered media
Vladimir Druskin, Mikhail Zaslavsky
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the gr…