Buried object detection by means of a L^p Banach‐space inversion procedure

Abstract

Electromagnetic inspection techniques are becoming powerful tools for buried object detection and subsurface prospection in several applicative fields, such as civil engineering and archeology. However, the nonlinearity and ill-posedness of the underlying inverse problem make the development of efficient imaging techniques a very challenging task. In the present paper, an algorithm based on a regularizing approach in L p Banach spaces is proposed for tackling such problems. The effectiveness of the approach is verified by means of numerical simulations in a noisy environment aimed at evaluating the reconstruction capabilities with respect to the choice of several model parameters. The reported results show that, for small targets, the use of L p Banach spaces with 1 < p < 2 allows to obtain a better localization of different buried scatterers.

Advanced Inversion Techniques for Ground Penetrating Radar

“…Consequently, sparse solutions (with respect to a properly selected basis) are obtained. Non-linear inversion algorithms performing a regularization in L p Banach spaces (with p greater than 1) have also been recently proposed in [49], [50]. Such methods have been found to be very effective in reconstructing small targets and in reducing over smoothing and background artifacts with respect to standard inversion in the Hilbert space (p = 2).…”

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

“…Recently, they have been developed also with reference to Lp Banach spaces [112,113], where the oversmoothing effects usually associated with regularization procedures developed in the common Hilbert space seem to be mitigated. It should be also noticed that sparsity concepts and compressive sensing can be successfully adopted [114,115].…”

A Multifrequency Inexact-Newton Method in <named-content content-type="math" xlink:type="simple"><inline-formula><tex-math notation="LaTeX">${L^p}$</tex-math></inline-formula> </named-content> Banach Spaces for Buried Objects Detection

“…By extending to multifrequency data the formulation in [25], [26], the problem solution can be written in an operator form as…”

“…Among them, the authors proposed in [24] a quite efficient iterative approach for inspecting strong scatterers in free space, based on an inexact-Newton strategy. The above method, extended to the framework of Banach spaces in [25], has also been applied to retrieve shallow buried objects [26], but its capabilities have been limited by the single frequency processing. In this paper, the improvements obtainable by using multifrequency input data with the inversion scheme are discussed by means of numerical simulations.…”