Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data. (1st April 2022)

• Record Type: Journal Article
• Authors: Le, Thuy T; Klibanov, Michael V; Nguyen, Loc H; Sullivan, Anders; Nguyen, Lam
• Is Part Of: Inverse problems. Volume 38:Number 4(2022)
• Publication Date: 2022-04-01
• Subjects: one-dimensional wave equation -- Carleman estimate -- iterative method -- contraction principle -- numerical solution -- experimental data -- global convergence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac50b8
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: It is demonstrated 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.