2019
DOI: 10.3390/electronics8090945
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Microwave Imaging by Means of Lebesgue-Space Inversion: An Overview

Abstract: An overview of the recent advancements in the development of microwave imaging procedures based on the exploitation of the regularization theory in Lebesgue spaces is reported in this paper. Such inversion schemes have been found to provide accurate results in several microwave imaging scenarios, thanks to the different geometrical properties that Lebesgue spaces can exhibit with respect to the more classical Hilbert ones. Moreover, the recent extension to the more general case of variable-exponent Lebesgue sp… Show more

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Cited by 35 publications
(24 citation statements)
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References 44 publications
(88 reference statements)
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“…is obtained, where ߜ , ∈ T is the unknown of the linearized problem, which is found by a truncated Landweber-type method in ‫ܮ‬ ሺ⋅ሻ spaces [35]. [36].…”
Section: Quantitative Inversion In Variable-exponent Settingmentioning
confidence: 99%
“…is obtained, where ߜ , ∈ T is the unknown of the linearized problem, which is found by a truncated Landweber-type method in ‫ܮ‬ ሺ⋅ሻ spaces [35]. [36].…”
Section: Quantitative Inversion In Variable-exponent Settingmentioning
confidence: 99%
“…In the framework of quantitative microwave tomography, an interesting class is represented by nonlinear Newton-based approaches [28]- [30], which have also been recently formulated in non-Hilbertian Lebesgue spaces with constant and nonconstant exponents [31]. The good performance of these methods has been proven in different case studies, with both single-and multifrequency data [32].…”
Section: Introductionmentioning
confidence: 99%
“…The good performance of these methods has been proven in different case studies, with both single-and multifrequency data [32]. So far, this kind of tomographic Newton-based techniques have been formulated by considering excitations from infinite linecurrent sources and ideal observation domains [31], [33] or with rectangular waveguide models of the radiating and receiving antenna elements [34]. However, there are several situations where the assumption of idealized or simplified probing elements does not lead to correct results.…”
Section: Introductionmentioning
confidence: 99%
“…While the goal of various quantitative microwave imaging techniques for GPR applications (including APEX and SPOT-GPR) is to detect, localize and characterize discrete buried objects, other approaches aim at an overall electromagnetic reconstruction of the underground structures, and more specifically at a qualitative or quantitative estimation of the geometrical distribution of the physical properties of media (dielectric permittivity, electric conductivity) in the subsurface [35,36]. Such methods are promising for the analysis of radargrams obtained in highly heterogeneous environments [37].…”
Section: Introductionmentioning
confidence: 99%