Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems
V Druskin, S Moskow, M Zaslavsky
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.
Topics & Concepts
MathematicsInversion (geology)Inverse scattering problemLanczos resamplingInverse problemIntegral equationMathematical analysisGalerkin methodIterative methodNonlinear systemEmbeddingApplied mathematicsInverseProjection (relational algebra)AlgorithmLanczos algorithmScatteringRegularization (linguistics)Gravitational singularityProjection methodDomain (mathematical analysis)Time domainSpectral methodDomain decomposition methodsNumerical analysisInverse scattering transformInverse transform samplingSecond derivativeInverse theoryNoisy dataModel Reduction and Neural NetworksNumerical methods in inverse problemsMicrowave Imaging and Scattering Analysis