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

Abstract

An electromagnetic inverse scattering approach for imaging of shallow subsurface objects is reported. It extends to multifrequency processing an efficient method previously developed for single frequency imaging. The considered approach is an iterative procedure based on an inexact-Newton method developed in L p Banach spaces, which exhibits effective regularization capabilities and reduced over-smoothing effects. The approach is validated by using numerical simulations in which cylindrical scatterers are reconstructed in a homogeneous lossy medium. Results are compared with those obtained by using standard single frequency operating conditions. Index Terms-Electromagnetic scattering inverse problems, Buried object detection, Newton method, Banach spaces.

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

“…, F. Subsequently, a subscript ω is added to the frequency-dependent functions and operators to specify at which frequency they refer. However, since the contrast function depends upon the frequency, it is necessary to modify the problem formulation [31,41]. To explain, let us assume that the dielectric permittivity and the electric conductivity do not depend on the frequency (i.e., dispersion is neglected).…”

“…Compressive sensing strategies, which allow to retrieve sparse solutions, have been proposed recently to mitigate this drawback. More recently, regularization methods developed in the framework of the regularization theory in the more general Banach spaces also have been introduced in the mathematical literature [27][28][29] and investigated for microwave imaging applications [30][31][32][33].…”

“…imaging applications [30][31][32][33]. Due to the geometrical properties of specific Banach spaces, these regularization methods allow one to obtain solutions endowed with lower over-smoothness and ringing effects, which results in a better localization of targets and restoration of the discontinuities between different media.…”

Time-Domain Electromagnetic Scattering by Buried Dielectric Objects with the Cylindrical-Wave Approach for GPR Modelling

“…This may be accomplished, for example, through a direct comparison of simulated data with measured radargrams [5]. Otherwise, numerical results may be used as input data in of inversion and imaging algorithms, to assess the validity of the reconstruction scheme [6][7][8][9].…”

Performance Evaluation of Group Sparse Reconstruction and Total Variation Minimization for Target Imaging in Stratified Subsurface Media

“…Effective and reliable imaging of targets embedded in stratified subsurface media is highly desirable in ground penetrating radar (GPR) applications [1][2][3][4][5][6][7][8][9][10][11][12][13]. Regularization methods based on L p (1 < p < 2) spaces framework have shown promise for microwave imaging of buried targets [14][15][16]. The sparse nature of targets has also been successfully exploited in GPR image recovery through sparse reconstruction approaches [4,[17][18][19][20][21].…”