Electromagnetic imaging within the contrast-source formulation by means of the multiscaling inexact Newton method

Abstract

We introduce a new imaging technique that integrates the inexact Newton method into a multifocusing scheme within the contrast-source formulation of the inverse scattering problem. Representative results from an extensive validation concerned with both synthetic and experimental scattering data are reported to assess, also through comparisons, advantages and limitations of the proposed approach in terms of accuracy, robustness, and computational efficiency.

Electromagnetic subsurface prospecting by a multifocusing inexact Newton method within the second-order Born approximation

“…In most cases, an empty domain is used as the initial guess. As mentioned in Section 1, the effectiveness of an integrated procedure that profitably exploits the regularization capabilities of the IN method and the capability of the IMSA [54] to reduce the occurrence of local minima has been already assessed in [48,49] for free-space imaging. Issues such as numerical instabilities caused by the presence of noise on measured data, as well as the ill-conditioned and nonlinear nature of the inversion problem, are thus jointly addressed throughout the synergetic combination of both techniques.…”

“…In [49] the importance of defining an efficient stopping criterion for the IMSA-IN-SOBA when no a priori information on the object under test is available has been pointed out. To monitor the evolution of the reconstruction residual, a parameter is introduced, which is defined at each IN iteration i as the discrepancy between measured and retrieved scattered field at M measurement locations:…”

“…Stochastic approaches can efficiently overcome the above limitation, but they exhibit a significantly higher computational cost [41,42]. Among deterministic approaches, inexact Newton (IN) methods [28,29,[43][44][45][46][47][48][49] have been proven to be effective as linearization and regularization tools for solving inversescattering problems, both numerically and experimentally [44]. Basically, these methods provide a linearization of the imaging equations by means of a Newton's expansion through the Fréchet derivative, and solve them in an approximate way [29].…”

“…The synergetic integration of a direct regularization technique, such as the IN method, and the iterative multiscaling approach (IMSA) [54] has been shown to effectively tackle both the nonlinearity and the ill-posedness/ ill-conditioning of microwave imaging problems by exploiting the best properties of the two strategies and mutually overcoming their intrinsic limitations in tomographic imaging [47][48][49]. As a matter of fact, the exploitation of such an approach leads to a strong simplification of the problem, thanks its capability to enforce a higher resolution only in the so-called regions of interest (RoIs) [54].…”

A Multi-Scaling Forward-Backward Time-Stepping Method for microwave imaging

“…By reviewing the state-of-the-art literature, several techniques have been successfully developed in the frequency domain under the assumption of monochromatic illuminations [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Despite their success, such inversion methods often present some limitations since only a reduced amount of information is actually retrievable from a single frequency measurement [30] and the exploitation of higher frequencies to enhance the spatial resolution [30,31] generally causes an increase of the complexity of the measurement system [31].…”