Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems. (15th June 2021)

• Record Type: Journal Article
• Authors: Druskin, V; Moskow, S; Zaslavsky, M
• Is Part Of: Inverse problems. Volume 37:Number 7(2021)
• Publication Date: 2021-06-15
• Subjects: inverse scattering -- reduced order models -- Lippman–Schwinger -- Galerkin projection; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abfca4
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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 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, thus making further iterative updates unnecessary. We show numerical experiments for spectral domain domain data for which our inversion is far superior to the Born inversion and works as well as when the true internal solution is known.