Document Type
Article
Version Deposited
Published Version
Publication Date
6-28-2023
Publication Title
Axioms
DOI
10.3390/axioms12070642
Abstract
This paper considers a 1D time-domain inverse scattering problem for the Helmholtz equation in which penetrable scatterers are to be determined from boundary measurements of the scattering data. It is formulated as a coefficient identification problem for a wave equation. Using the Laplace transform, the inverse problem is converted into an overdetermined nonlinear system of partial differential equations. To solve this system, a Carleman weighted objective functional, which is proved to be strictly convex in an arbitrary set in a Hilbert space, is constructed. An alternating minimization algorithm is used to minimize the Carleman weighted objective functional. Numerical results are presented to illustrate the performance of the proposed algorithm. © 2023 by the author.
Recommended Citation
Thành, N.T. Using Alternating Minimization and Convexified Carleman Weighted Objective Functional for a Time-Domain Inverse Scattering Problem. Axioms 2023, 12, 642. https://doi.org/10.3390/axioms12070642
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Comments
© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.