Abstract
A hybrid inversion scheme for through-the-wall imaging is proposed in this paper. The approach is based on a linearized model of the inverse-scattering problem, employing the Green’s function developed for a layered background. The reconstruction is obtained by means of a Landweber-like iterative method performing a regularization in the framework of variable-exponent Lebesgue spaces. Thanks to the non-conventional geometrical properties of such spaces, it is possible to enhance the reconstruction capabilities, e.g., by promoting sparseness and reducing over-smoothing. The exponent function defining the specific space adopted in the inversion procedure is adaptively obtained directly from the measured data, through a truncated-singular value decomposition method. In this way, it is possible to precompute and reuse in both steps, for a given scenario, all the matrices necessary in the inversion process, thus leading to a computationally efficient solving strategy. The effectiveness of the approach is evaluated by using experimental data obtained with a commercial GPR apparatus employing a pulsed source field. A fast Fourier transform is applied to the time-domain measurements to extract frequency-domain data at a set of frequencies in the source spectrum, which are fed in input to the imaging scheme. Very good reconstruction capabilities are obtained both with a single metallic target, as well as in a challenging two targets layout including both a metallic object and a low-permittivity target.
Highlights
A hybrid inversion scheme for through-the-wall imaging is proposed in this paper
Due to the presence of a wall that separates the radar antennas and the target, the complexity of this imaging problem is enhanced compared to classical microwave imaging of free-space targets, or of targets buried in the subsoil, as in ground penetrating radar (GPR) applications [2]
The obtained inverse problem is solved, in a regularized sense, by means of an iterative scheme developed in the context of the variableexponent Lebesgue spaces
Summary
In the considered imaging problem, one or more targets are located in an investigation area Ω behind a wall of thickness lw and complex dielectric permittivity ew. ) is the z-component of the scattered electr where to the targets, allowing to obtain an indication of their positions and shapes [22,50] It field and is a function depending on the the investigatio is worth remarking that (1) relies upon the use of dielectric the Green’sproperties function Gmlinside for a three-layer domain. Along non-standard directions, which are different from those of the anti-gradient used in standard inversion schemes in Hilbert spaces This allows a better exploitation of the geometrical properties of the Banach spaces, by properly tuning the values of the exponent function [53]. Higher regularization effects are obtained when p is higher, providing better reconstructions of parts with smooth dielectric variations
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