A Through-the-Wall Imaging Approach Based on a TSVD/Variable-Exponent Lebesgue-Space Method

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 me...

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Bibliographic Details
Published in:Remote sensing (Basel, Switzerland) Switzerland), 2021, Vol.13 (11), p.2028
Main Authors: Randazzo, Andrea, Ponti, Cristina, Fedeli, Alessandro, Estatico, Claudio, D’Atanasio, Paolo, Pastorino, Matteo, Schettini, Giuseppe
Format: Article
Language:English
Subjects:
Algorithms
Antennas
Approximation
Dielectric properties
Electric fields
electromagnetic problems
Fast Fourier transformations
Fourier transforms
Imaging
inverse scattering
Iterative methods
Localization
microwave imaging
Propagation
Reconstruction
Regularization
Singular value decomposition
through-wall radar
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Summary: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.
ISSN:2072-4292
2072-4292
DOI:10.3390/rs13112028