Convexification Numerical Method for Imaging of Moving Targets

TL;DR

This paper develops a globally convergent convexification numerical method, based on Carleman estimates, for imaging moving targets modeled as a coefficient inverse problem for hyperbolic equations, with demonstrated stability and numerical results.

Contribution

It introduces a new convexification approach with convergence analysis for imaging moving targets in hyperbolic equations.

Findings

Lipschitz stability estimate established

Convexification method demonstrated to be globally convergent

Numerical experiments confirm effectiveness

Abstract

The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running along a straight line is used. Lateral Cauchy data are known for each position of the point source. A truncated Fourier series with respect to a special orthonormal basis is used. First, Lipschitz stability estimate is obtained. Next, a globally convergent numerical method, the so-called convexification method, is developed and its convergence analysis is carried out. The convexification method is based on a Carleman estimate. Results of numerical experiments are presented.