Iterative Multiscaling Approach Research Articles

Multiple Buried Target Reconstruction Using a Multiscale Hybrid of Diffraction Tomography and CMA-ES Optimization

In this article, a hierarchical stochastic optimization algorithm for profiling of multiple high-contrast buried objects in large investigation domains (IDs) is presented. As this problem is highly non-linear and ill-posed, a combination of different profiling modalities is required to tackle the challenges. First, an initialization step using qualitative diffraction tomography (DT) method is performed to not only limit the ID to scatterers’ locations but also obtain an approximation of their dielectric permittivity range. Then, an algorithm which combines the iterative multi-scaling approach (IMSA) with the reconstruction capabilities of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is implemented. IMSA is a multistep strategy, which starts with coarse meshes in lower frequencies, then, step by step, tightens the ID to the newly found domain of scatterers and uses finer meshes for partitioning them. This procedure enhances the resolution without increasing the number of unknowns. In each step, the inversion process is executed using the global optimization technique of CMA-ES. The proposed technique uses the full advantages of global optimization technique and at the same time, by executing it on a multi-scaling scheme, and using the initializing step, reduces the number of unknowns, the degree of freedom in the search space, and the required measured data. The Numerical assessments for various scenarios are performed that clearly shows an acceptable dielectric profile retrieval, even for inhomogeneous dielectric distributions or noisy measurements. Moreover, a comparison between CMA-ES and other global optimization algorithms is performed, which reveals the outperformance of CMA-ES in these scenarios.

2-D TM GPR Imaging Through a Multiscaling Multifrequency Approach in Lp Spaces

An iterative multiscaling approach for solving the electromagnetic inverse scattering problem related to the imaging of shallow subsurface targets with the ground-penetrating radar (GPR) is proposed. The approach combines the zooming properties of the multiscaling technique with the reconstruction capabilities of an Inexact-Newton (IN) method developed in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L^{p}$ </tex-math></inline-formula> spaces. It is based on multifrequency processing that allows one to face the ill-posedness of the inverse scattering problem by exploiting the regularization properties of a truncated Landweber (LW) method. Experimental data, extracted from radargrams obtained by the GPR in a real situation, are used for validation. The reconstruction results are also compared with those from competitive alternatives, such as a standard IN method or a state-of-the-art multifrequency Conjugate Gradient (CG)-based approach.

A multi-focusing contrast source Bayesian compressive method for solving inverse scattering problems

This work presents a novel inverse scattering (IS) methodology to deal wit.li the retrieval of the electromagnetic (EM) properties of unknown scat.t.erers. The proposed technique is based on the effective combination of a customized Bayesian compressive sensing (BCS) solver wit.li the iterative multi-scaling approach (IMSA). Accordingly, a-priori information on the class of imaged targets as well as progressively acquired information on their location and size is exploited to yield accurate and robust reconstructions. Moreover, a contrast source inversion (CSI) formulation is adopted in order to enable the retrieval of lion-Born scat.t.erers. Numerical results are shown to verify the effectiveness of the proposed IMSA-BCS-CSI method, as well as to compare it with state-of-the-art alternatives.

A Multiresolution Contraction Integral Equation Method for Solving Highly Nonlinear Inverse Scattering Problems

The solution of highly nonlinear inverse scattering problems is addressed. An innovative multiresolution microwave imaging technique, which leverages on the profitable integration of the contraction integral equation for inversion (CIE-I) and the iterative multiscaling approach (IMSA), is proposed. Thanks to the joint exploitation of the features of the CIE-I formulation and the IMSA, the arising IMSA-CIE-I inversion technique provides faithful reconstructions of complex-shaped strong scatterers with enhanced resolution and computational efficiency with respect to the state-of-the-art competitive alternatives. Numerical and experimental test cases verify the effectiveness and limitations of the proposed method.

Three-dimensional electromagnetic imaging of dielectric targets by means of the multiscaling inexact-Newton method.

A novel approach for three-dimensional electromagnetic imaging is presented. This technique is a combination of an iterative multiscaling approach with an inexact-Newton method. The multiscaling procedure allows one to iteratively focus the region of interest on the detected target, whereas the inexact-Newton method provides an efficient regularized solution of the nonlinear electromagnetic inverse scattering problem for each scaling step. The proposed method is validated against numerical data with different configuration settings. A preliminary experimental validation is also reported.

Multifrequency Particle Swarm Optimization for Enhanced Multiresolution GPR Microwave Imaging

An innovative inverse scattering (IS) technique for the simultaneous processing of multifrequency (MF) ground-penetrating radar (GPR) measurements is proposed. The nonlinear IS problem is solved by profitably integrating a customized MF version of the particle swarm optimizer (PSO) within the iterative multiscaling approach (IMSA) to jointly exploit the reduction of the ratio between unknowns and uncorrelated data with a pervasive exploration of the multidimensional search space for minimizing the probability that the solution is trapped into local minima corresponding to false solutions of the problem at hand. Both numerical and experimental test cases are reported to assess the reliability of the MF-IMSA-PSO method toward accurate GPR tomography as well as improvements with respect to the competitive state-of-the-art inversion approaches.

A computational method for the inversion of wide-band GPR measurements

An innovative method for the inversion of ground penetrating radar (GPR) measurements is presented. The proposed inverse scattering (IS) approach is based on the exploitation of wide-band data according to a multi-frequency (MF) strategy, and integrates a customized particle swarm optimizer (PSO) within the iterative multi-scaling approach (IMSA) to counteract the high non-linearity of the optimized cost function. If from the one hand the IMSA provides a reduction of the ratio between problem unknowns and informative data, on the other hand the stochastic nature of the PSO solver allows to "escape" from the high density of false solutions of the MF-IS subsurface problem. A set of representative numerical results verifies the effectiveness of the developed approach, as well as its superiority with respect to a deterministic implementation.

Advanced multi-frequency GPR data processing for non-linear deterministic imaging

In this paper, the quantitative imaging of the dielectric characteristics of unknown targets buried in a lossy half-space is performed by suitably processing wide-band ground penetrating radar (GPR) measurements. An innovative multi-frequency (MF) fully non-linear inverse scattering (IS) technique exploiting the integration of a conjugate-gradient (CG) solver within the iterative multi-scaling approach (IMSA) is proposed. Representative results from numerical test cases are presented to provide the interested readers with some indications on the effectiveness, as well as the current limitations, of the proposed approach when directly compared to a state-of-the-art frequency-hopping (FH) based method formulated in the same framework. Such a validation points out that if, on the one hand, the proposed MF strategy is computationally more efficient than the FH one, on the other hand, it turns out to be less reliable and accurate in several situations.

A comparative assessment of information-exploitation techniques for GPR data inversion

The inversion of Ground Penetrating Radar (GPR) data requires the development of suitable information-exploitation techniques that are able to extract as much as possible information on the unknown targets from the available measurements. An innovative singlefrequency (SF) inversion technique based on a deterministic conjugate-gradient (CG) minimization and the iterative multi-scaling approach (IMSA) is described. It is then shown how to improve the performances of the SF-IMSA-CG method by the introduction of an external frequency hopping (FH) iterative loop. On the one hand, the proposed FH-IMSA-CG method allows to exploit the intrinsic frequency diversity of wideband GPR measurements thanks to the FH strategy. On the other hand, the IMSA approach guarantees a significant reduction of the problem unknowns, providing an increased resolution within the identified regions of interest (RoIs). A numerical comparison shows the advantages of the FH-IMSA-CG over its single-frequency version. Moreover, the benefits of integrating the IMSA within the FH are verified by directly comparing the FH-IMSA-CG with its single-resolution (BARE) version (FH-BARE-CG).

Electromagnetic subsurface prospecting by a fully nonlinear multifocusing inexact Newton method

An electromagnetic inverse scattering procedure for the reconstruction of shallow buried objects in a homogeneous half-space is proposed. The approach is based on the numerical solution of the integral equations that model inverse scattering relationships, and it extends to strong scatterers the imaging capabilities of a previously proposed approach relying on approximated formulations. The inversion is based on the synergic application of a multifocusing strategy based on the iterative multiscaling approach along with an efficient regularization scheme based on the inexact Newton method. Numerical results corroborate the mathematical description to assess capabilities and current limitations of the proposed fully nonlinear technique.

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

In this paper the reconstruction of a shallow buried object is addressed by an electromagnetic inverse scattering method based on combining different imaging modalities. In particular, the proposed approach integrates the inexact Newton (IN) method with an iterative multiscaling approach. Moreover, the use of the second-order Born approximation is exploited. A numerical validation is provided concerning the potentialities arising by combining the regularization capabilities of the IN method and the effectiveness of the multifocusing strategy to mitigate the nonlinearity and ill-posedness of the inversion problem. Comparisons with the standard "bare" approach in terms of accuracy, robustness, noise levels, and computational efficiency are also included.

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

This paper is aimed at presenting a new time-domain imaging technique that combines the regularization properties of the Filtered FBTS method with an efficient information-acquisition strategy, namely the Iterative Multi-Scaling Approach (IMSA). The proposed time-domain approach is then validated by means of a set of preliminary numerical test cases aimed at pointing out its features and potentialities, as well.

A multi-resolution technique based on shape optimization for the reconstruction of homogeneous dielectric objects

In the framework of inverse scattering techniques, this paper presents the integration of a multi-resolution technique and the level-set method for qualitative microwave imaging. On the one hand, in order to effectively exploit the limited amount of information collectable from scattering measurements, the iterative multi-scaling approach (IMSA) is employed for enabling a detailed reconstruction only where needed without increasing the number of unknowns. On the other hand, the a priori information on the homogeneity of the unknown object is exploited by adopting a shape-based optimization and representing the support of the scatterer via a level-set function. Reliability and effectiveness of the proposed strategy are also assessed by processing both synthetic and experimental scattering data for simple and complex geometries.

MICROWAVE IMAGING FROM AMPLITUDE-ONLY DATA - ADVANTAGES AND OPEN PROBLEMS OF A TWO-STEP MULTI-RESOLUTION STRATEGY

In this report, a two step strategy for the inversion of amplitude-only data in microwave imaging applications is analyzed. At the first step of the proposed method, the illuminating source is synthesized according to a line sources model in order to compute the incident field in the investigation domain starting from the values available in the measurement domain. The second step is aimed at reconstructing the profile of the objects under test thanks to the iterative multi-scaling approach integrated with the Particle Swarm Optimizer, an effective evolutionary minimization technique. The reconstruction accuracy of the proposed phaseless retrieval strategy is analyzed using synthetic data concerned with a multiple scatterer configuration and successively further assessed inverting experimental data

Dealing With Multifrequency Scattering Data Through the IMSA

A set of representative results are presented that are obtained with two multiresolution strategies developed for dealing with multifrequency inverse scattering experiments starting from the iterative multiscaling approach previously studied for monochromatic illuminations. The first approach is concerned with the integration of the iterative multiscaling algorithm into a frequency-hopping reconstruction scheme, while the second one allows a multiresolution simultaneous processing of multifrequency data. The numerical and the experimental analysis are aimed at assessing both the reconstruction effectiveness and the required computational costs of the two- and three-dimensional implementations of the proposed inversion schemes in comparison with the monochromatic multistep process and to the single-step optimization strategy, as well.

On the effects of the electromagnetic source modeling in the iterative multiscaling method

The validation against experimental data is a fundamental step in the assessment of the effectiveness of a microwave imaging algorithm. It is aimed at pointing out the limitations of the numerical procedure for a successive application in a real environment. Towards this end, this paper evaluates the reconstruction capabilities of the Iterative Multiscaling Approach (IMSA) when dealing with experimental data by considering different numerical models of the illuminating setup. In fact, since the incident electromagnetic field is usually collected in a limited set of measurement points and inversion methods based on the use of the “state” equation require the knowledge of the radiated field in a finer grid of positions, an effective numerical procedure for the synthesis of the electromagnetic source is generally needed. Consequently, the performances of the inversion process may be strongly affected by the numerical model and, in such a case, a great care should be devoted to this key issue to guarantee suitable and reliable reconstructions.

Inversion of Phaseless Total Field Data Using a Two-Step Strategy Based on the Iterative Multiscaling Approach

In this paper, a new approach for the quantitative electromagnetic imaging of unknown scatterers located in free space from amplitude-only measurements of the total field is proposed and discussed. The reconstruction procedure splits the problem into two steps. The method is based on the use of an inverse source algorithm to first complete the scattering data by estimating the distribution of the radiated field in the investigation domain. The object's function profile is then retrieved from the phaseless data via an iterative multiresolution procedure integrated with an effective minimization technique based on the particle swarm algorithm. Numerical examples are provided to assess the effectiveness of the whole two-step strategy in the presence of synthetic noise-corrupted data as well as in dealing with experimental data sets. Comparisons with full-data and "bare" approaches are reported as well

Iterative image reconstruction of two-dimensional scatterers illuminated by TE waves

The iterative reconstruction of unknown objects from TE-measured scattered field data is presented. The paper investigates the performance of the iterative multiscaling approach (IMSA) in exploiting transverse electric (TE) illuminations. As a matter of fact, in these conditions, the problem turns out to be more complicated than the tranverse magnetic (TM) scalar one in terms of mathematical model as well as computational costs. However, it is expected that more information on the scenario under test can be drawn from scattered data. Therefore, this study is aimed at verifying whether the TE case can provide additional information on the scenario under test (compared to the TM illumination) and how such an enhancement can be suitably exploited by the IMSA for improving the reconstruction accuracy of the retrieval process. Such an analysis will be carried out by means of a set of numerical experiments concerned with dielectric and metallic targets in single- and multiple-objects configurations. Synthetic as well as experimental data will be dealt with.

Multi-resolution iterative inversion of real inhomogeneous targets

This paper presents a review of the reconstruction results obtained from the inversion of experimental data provided by the Institute Fresnel (Marseille, France) and concerned with inhomogeneous dielectric targets and hybrid configurations, where dielectric and metallic cylinders are present in the scenario under test. The iterative multi-scaling approach (IMSA) is applied for addressing the inversion of scattering data in order to effectively exploit the available information through a multi-step reconstruction procedure, which adaptively allocates a set of unknown coefficients, related to the dielectric distribution in the investigation area, on the basis of the information collected during the iterative process. The obtained results confirm the effectiveness of such an iterative multi-resolution strategy in dealing with complex scatterers already demonstrated in synthetic experiments.

An experimental study on the multiscaling iterative reconstruction of inhomogeneous targets

AbstractThis paper presents an experimental assessment of the iterative multiscaling approach (IMSA) in imaging inhomogeneous dielectric targets. The IMSA is used to address the inversion of scattering data provided by the Institute Fresnel in Marseille, France, in order to effectively exploit the available information. Since inversion methods based on the use of the “state” equation, as with the IMSA, require knowledge of the radiated field in the investigation area, different numerical models of the illuminating setup will be considered to evaluate the robustness of the inversion algorithm in case of an approximate knowledge of the incident field arising from a limited set of measured samples. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 47: 588–594, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21238