Convexification Numerical Method for Imaging of Moving Targets
Numerical Analysis
2025-12-23 v1 Numerical Analysis
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.
Cite
@article{arxiv.2512.18361,
title = {Convexification Numerical Method for Imaging of Moving Targets},
author = {Michael V. Klibanov and Jingzhi Li and Vladimir G. Romanov and Zhipeng Yang},
journal= {arXiv preprint arXiv:2512.18361},
year = {2025}
}