Exploiting sparsity and field conditioning in subsurface microwave imaging of nonweak buried targets

Abstract

An efficient inverse scattering strategy is proposed to achieve dielectric characterization of buried objects in lossy soils. The approach takes advantage of Virtual Experiments and Compressive Sensing to obtain quantitative reconstructions of nonweak targets which are nonsparse in the pixel representation basis, commonly adopted in microwave imaging. In addition, an original strategy is adopted to overcome the relevant information lack arising when data are gathered under aspect-limited configurations, such as in ground penetrating radar (GPR) surveys. The proposed strategy significantly outperforms the results achievable with the "state of the art" standard approaches since it allows to achieve nearly optimal reconstructions within a linear framework and without increasing the overall computational burden. Numerical examples with simulated data are given to show the feasibility of the proposed strategy.The last drawback can be circumvented, in principle, by adopting imaging recovery approaches based on the emerging framework of compressive sensing (CS) [Baraniuk, 2007;Donoho, 2006]. It offers a powerful framework to obtain satisfactory reconstructions of "sparse images," with the possibility to achieve nearly optimal reconstruction as well as superresolution. However, CS theory has been completely assessed only in the case of linear recovery problems [Baraniuk, 2007;Donoho, 2006] so that in subsurface microwave imaging,

Microwave Imaging by Means of Lebesgue-Space Inversion: An Overview

“…We recall that the Newton scheme is called "inexact" because each linear system is not solved exactly, but its solution is just iteratively approximated. It is interesting to notice that the outer-inner inexact Newton scheme (13)- (14) is an extension of the (single-step) Landweber iterative method (10). Indeed, if the inner iterations of (13) are always stopped at the very first iteration, that is, if the number of inner iteration is always fixed to k max ≡ 1 (which means that the linearized equation (11) is solved with a first, and very low, level of accuracy), then the two-steps scheme (13)- (14) coincides with the one-step scheme (10).…”

“…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.…”

Shape Reconstruction via Equivalence Principles,constrained Inverse Source Problems and Sparsity Promotion

“…CS is a very appealing tool for inverse problem in electromagnetism, as confirmed by the large number of papers published on relevant journals (see e.g., [21,[25][26][27][28][29][30][31][32]). In the proposed approach, an auxiliary variable is introduced to develop an ad hoc compressive sensing inspired inversion approach.…”

On the Orbital Angular Momentum Incident Fields in Linearized Microwave Imaging

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