Abstract
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 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.
Highlights
We are interested in this paper in the inverse problem of recovering the spatially distributed dielectric constant of the Helmholtz equation from a single boundary measurement of its solution
The goal of this paper is to develop a new GCM for a Coefficient Inverse Problem (CIP) for the Helmholtz equation in R3 with a single measurement of multi-frequency data
We develop the theory of our numerical method for this CIP
Summary
We are interested in this paper in the inverse problem of recovering the spatially distributed dielectric constant of the Helmholtz equation from a single boundary measurement of its solution. This inverse problem is called a coefficient inverse problem with a single measurement data (CIP). CIPs are both ill-posed and highly nonlinear. An important and challenging question to address in a numerical treatment of a CIP is: How to obtain at least one point in a sufficiently small neighborhood of the exact coefficient without any advanced knowledge of this neighborhood? As soon as this point is obtained, one can refine.
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