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 spaces is also addressed. Experimental results involving reference data are shown for supporting the theoretical description of the approaches.
Highlights
Microwave imaging is attracting an ever-growing interest in several applicative areas, ranging from non-destructive evaluation of civil and geophysical structures to biomedical diagnostics [1,2,3,4,5,6,7,8,9,10,11].Such an interest is due mainly to the attracting features of microwave techniques
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
They have been investigated in the context of Hilbert spaces, in most cases. In this case it is possible to use the spectral theory to analyze the convergence and regularization properties of the solving method. Despite this potential advantage that highly simplifies the mathematical study, regularization methods in Hilbert spaces in several cases lead to smoothed solutions, due to the filtering effects produced by regularization
Summary
Microwave imaging is attracting an ever-growing interest in several applicative areas, ranging from non-destructive evaluation of civil and geophysical structures to biomedical diagnostics [1,2,3,4,5,6,7,8,9,10,11]. Proper inversion procedures need to be devised, to consider both these theoretical problems To this end, several approaches have been proposed in the last years [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. Despite this potential advantage that highly simplifies the mathematical study, regularization methods in Hilbert spaces in several cases lead to smoothed solutions, due to the filtering effects produced by regularization This kind of behavior may be problematic in numerous imaging applications, especially when small targets needs to be retrieved. An overview of the imaging recent advancements in the development of Lebesgue-space inversion procedures for microwave is reported in this article.
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