Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
arXiv:2101.12317 · doi:10.1088/1361-6420/abfca4
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.
References in corpus (7)
- 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
- Untangling the nonlinearity in inverse scattering with data-driven reduced order models
- A nonlinear method for imaging with acoustic waves via reduced order model backprojection
- Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models
- Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data
- Nonlinear inverse problem by T-matrix completion. I. Theory