A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data
This work addresses the challenging problem of 3D coefficient inverse problems with limited data, offering a globally convergent alternative to local optimization methods for applications like explosive detection.
The paper develops a globally convergent numerical method for reconstructing 3D dielectric constants from multi-frequency scattered wave data using a single incident plane wave. The algorithm provides a good approximation of the exact coefficient without requiring a priori knowledge of the coefficient, demonstrated on both simulated and experimental data.
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated by only a single direction of the incident plane wave. To solve this inverse problem, a globally convergent algorithm is analytically developed. We prove that this algorithm provides a good approximation for the exact coefficient without any \textit{a priori} knowledge of any point in a small neighborhood of that coefficient. This is the main advantage of our method, compared with classical approaches using optimization schemes. Numerical results are presented for both computationally simulated data and experimental data. Potential applications of this problem are in detection and identification of explosive-like targets.