Gabriele Franceschini

An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems

The application of a multiscale strategy integrated with a stochastic technique to the solution of nonlinear inverse scattering problems is presented. The approach allows the explicit and effective handling of many difficulties associated with such problems ranging from ill-conditioning to nonlinearity and false solutions drawback. The choice of a finite dimensional representation for the unknowns, due to the upper bound to the essential dimension of the data, is iteratively accomplished by means of an adaptive multiresolution model, which offers a considerable flexibility for the use of the information on the scattering domain acquired during the iterative steps of the multiscaling process. Even though a suitable representation of the unknowns could limit the local minima problem, the multiresolution strategy is integrated with a customized stochastic optimizer based on the behavior of a particle swarm, which prevents the solution from being trapped into false solutions without a large increasing of the overall computational burden. Selected examples concerned with a two-dimensional microwave imaging problem are presented for illustrating the key features of the integrated stochastic multiscaling strategy.

Parallel GA-based approach for microwave imaging applications

Genetic algorithms (GAs) are well-known optimization strategies able to deal with nonlinear functions as those arising in inverse scattering problems. However, they are computationally expensive, thus offering poor performances in terms of general efficiency when compared with inversion techniques based on deterministic optimization methods. In this paper, a parallel implementation of an inverse scattering procedure based on a suitable hybrid genetic algorithm is presented. The proposed strategy is aimed at reducing the overall clock time in order to make the approach competitive with gradient-based methods in terms of runtime, but preserving the capabilities of escaping from local minima. This result is achieved by exploiting the natural parallelism of evolutionary techniques and the searching capabilities of the hybrid approach . The effectiveness of the proposed implementation is demonstrated by considering a selected numerical benchmark related to two-dimensional scattering geometries.

A Numerical Assessment of the Reconstruction Effectiveness of the Integrated GA-Based Multicrack Strategy

This letter is aimed at presenting a numerical study on the reconstruction accuracy (quantitative imaging) of the integrated genetic algorithm (GA)-based multicrack strategy, thus completing the assessment previously carried out and limited to verifying the accuracy of the qualitative imaging (i.e., crack detection, location, and size estimation). The obtained results prove an acceptable reliability and accuracy of the GA-based integrated strategy also in reconstructing multiple defective regions even though the resulting performances degrade in comparison with those achieved by the same approach when used for qualitative imaging purposes.

Effective exploitation of the a priori information through a microwave imaging procedure based on the SMW for NDE/NDT applications

This paper presents an innovative microwave technique, which is suitable for the detection of defects in nondestructive-test and nondestructive-evaluation (NDT/NDE) applications where a lot of a priori information is available. The proposed approach is based on the equations of the inverse scattering problem, which are solved by means of a minimization procedure based on a genetic algorithm. To reduce the number of problem unknowns, the available a priori information is efficiently exploited by introducing an updating procedure for the electric field computation based on the Sherman-Morrison-Woodbury formula. The results of a representative set of numerical experiments as well as comparisons with state-of-the-art methods are reported. They confirm the effectiveness, feasibility, and robustness of the proposed approach, which shows some interesting features by a computational point of view as well.

Full-vectorial three-dimensional microwave imaging through the iterative multiscaling strategy-a preliminary assessment

In this letter, a multiscaling strategy for full-vectorial three-dimensional inverse scattering problems is presented. The approach is fully iterative, and it avoids solving any forward problem at each step. Thanks to the adaptive multiresolution model, which offers considerable flexibility for the inclusion of the a priori knowledge and of the knowledge acquired during the iterative steps of the multiscaling process, the overall computational burden as well as the dimension of the search-space is considerably reduced. This allows to balance effectively the tradeoff between computational costs and achievable resolution accuracy. The effectiveness of the proposed approach is demonstrated through a selected set of preliminary experiments using homogeneous dielectric scatterers in a noisy synthetic environment.

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.

Improving the effectiveness of GA-based approaches to microwave imaging through an innovative parabolic crossover

Several studies have shown that evolutionary-based approaches are efficient, effective, and are robust optimization methods for microwave imaging. However, the convergence rate of such techniques still does not meet all the requirements for online real applications and attempting to speed up the optimization is needed. In this paper, a new local search operator, the fitness-based parabolic crossover, is proposed and embedded into a real-coded genetic algorithm. Such a modification enables the imaging method to achieve a better tradeoff between convergence rate and robustness to false solutions. By exploiting the relationship between the crossover operation and the local quadratic behavior of the functional, it is possible to increase the convergence rate of the genetic algorithm and, thereby, to obtain an acceptable solution with a smaller number of fitness function evaluations. The effectiveness of the modified genetic-algorithm-based imaging method is assessed by considering some synthetic test cases in different dimensions and noisy conditions. The obtained numerical results provide an empirical evidence of the efficiency and reliability of the proposed modified evolutionary algorithm.

A Comparative Assessment among Iterative Linear Solvers Dealing with Electromagnetic Integral Equations in 3D Inhomogeneous Anisotropic Media

This paper deals with full-vectorial, three-dimensional, electromagnetic scattering problems formulated in terms of integral scattering equations. The weak formulation is applied in order to effectively deal with inhomogeneous anisotropic media and the arising set of algebraic linear equations is solved through some of the most recent and effective iterative linear solvers for allowing a detailed assessment of their performances when facing with three-dimensional complex scenarios.

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

Effective Exploitation of Multi-View Data through the Iterative Multi-Scaling Method - An Experimental Assessment

The reconstruction capabilities of a microwave imaging algorithm can be enhanced by exploiting a multi-view measurement set-up. In the past, different researches have proved that collecting scattering data by probing the unknown scenario from different incidence angles, it allows to acquire more information on the scenario when the Iterative Multi-Scaling Approach (IMSA) is used to fully exploit multi-view data. In fact, unlike synthetic data, in real enviroment more measurements introduce larger systematic errors that could affect the physical constraints used in the inversion procedure and, consequently, the reconstruction process. Thus, the analysis is carried out by considering a set of experimental data concerning different scattering configurations involving single and multiple dielectric scatterers.