Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data
Numerical Analysis
2022-03-23 v1 Numerical Analysis
Analysis of PDEs
Abstract
It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the corresponding numerical method is established. Numerical studies for both computationally simulated and experimentally collected data are presented. The experimental part is concerned with the problem of computing dielectric constants of explosive-like targets in the standoff mode using severely underdetermined data.
Cite
@article{arxiv.2109.11098,
title = {Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data},
author = {Thuy T. Le and Michael V. Klibanov and Loc H. Nguyen and Anders Sullivan and Lam Nguyen},
journal= {arXiv preprint arXiv:2109.11098},
year = {2022}
}