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Applied and Computational Math Seminar

The Lippmann Schwinger Lanczos algorithm for inverse scattering problems

Shari Moskow (Drexel University)

Location:  Hill 525
Date & time: Tuesday, 07 November 2023 at 11:00AM - 12:00PM

We combine data-driven reduced order models with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding into the continuous problem, a data-driven internal solution is produced. This internal solution is then used in the Lippmann-Schwinger equation, in a direct or iterative framework. The approach allows us to process more general transfer functions than the earlier versions of the ROM based inversion algorithms.  We give examples of its use for spectral domain MIMO problems and in the time domain given mono static data, targeting synthetic aperture radar. Authors: Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky

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