A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data

TL;DR

This paper introduces a new approximate mathematical model for a 3D coefficient inverse problem with backscattering data, demonstrating global convergence and including numerical results in heterogeneous media.

Contribution

It presents a novel approximate model that ensures global convergence for a hyperbolic inverse problem, with a unique tail function estimation method.

Findings

Successful numerical implementation in 2D and 3D cases

Effective handling of heterogeneous media

Convergence analysis incorporating tail function estimates

Abstract

An approximately globally convergent numerical method for a 3d Coefficient Inverse Problem for a hyperbolic equation with backscattering data is presented. A new approximate mathematical model is presented. An approximation is used only on the first iteration and amounts to the truncation of a certain asymptotic series. A significantly new element of the convergence analysis is that the so-called "tail functions" are estimated. Numerical results in 2d and 3d cases are presented, including the one for a quite heterogeneous medium.