Emanuele Tavanti

A numerical study concerning brain stroke detection by microwave imaging systems

In this paper, a numerical study devoted to evaluate the application of a microwave imaging method for brain stroke detection is described. First of all, suitable operating conditions for the imaging system are defined by solving the forward electromagnetic scattering problem with respect to simplified configurations and analyzing the interactions between an illuminating electromagnetic wave at microwave frequencies and the biological tissues inside the head. Then, preliminary inversion results are obtained by applying an imaging procedure based on an iterative Gauss-Newton scheme to a realistic model of the human head. The proposed imaging algorithm is able to deal with the nonlinear and ill-posed problem associated to the integral equations describing the inverse scattering problem. The aim of the inversion procedure is related to the determination of the presence of a hemorrhagic brain stroke by retrieving the distributions of the dielectric parameters of the human tissues inside a slice of the head model.

Brain stroke detection by microwave imaging systems: Preliminary two-dimensional numerical simulations

In this paper, a microwave imaging method is proposed for brain stroke detection. In particular, the developed imaging procedure is based on an iterative Gauss-Newton scheme and it is aimed at determining the presence of a hemorrhagic brain stroke. Interrogating microwaves are used in a multistatic and multiview arrangement. Preliminary numerical results concerning the reconstruction of a simulated stroke inside a two-dimensional slice of the human head are reported. A numerical model is used to obtain the synthetic data used in the inversion process through the solution of a forward electromagnetic scattering problem, which is performed under transverse magnetic conditions.

Application of EMFs at microwave frequencies for brain stroke detection: Preliminary results

An approach for microwave imaging of brain strokes is presented. Numerical simulations show the potentialities of this technique in retrieving the dielectric properties of biological tissues inside the head. An efficient iterative two-loop method is used to face the ill-posedness of the considered inverse scattering problem, which is formulated in terms of integral equations.

A three-dimensional microwave imaging approach based on a L p Banach space inversion procedure

A three-dimensional microwave imaging inversion algorithm is proposed in this paper. The developed approach is based on an efficient procedure, performing a regularization in the framework of the Lp functional Banach spaces. In order to increase the computational efficiency of the method, two specific speed-up strategies have been developed. The performances of the method have been preliminarily assessed by means of numerical simulations.

Microwave imaging systems: Three-dimensional reconstructions of dielectric targets

A full-wave three-dimensional microwave imaging approach is proposed in this paper. The method is based on the inversion of the full non-linear scattering equations that relate the measured scattered electric field data to the dielectric properties of the inspected volume. In particular, a Gauss-Newton scheme is employed, where the inner linearized problem is solved by using an iterative algorithm performing a regularization in the framework of the Lp Banach spaces. The capabilities of the method have been tested with noisy simulated data. The obtained results, although preliminary, confirm that the developed procedure is able to correctly retrieve the considered dielectric profiles.

Phaseless tomographic inverse scattering in Banach spaces

In conventional microwave imaging, a hidden dielectric object under test is illuminated by microwave incident waves and the field it scatters is measured in magnitude and phase in order to retrieve the dielectric properties by solving the related non-homogenous Helmholtz equation or its Lippmann-Schwinger integral formulation. Since the measurement of the phase of electromagnetic waves can be still considered expensive in real applications, in this paper only the magnitude of the scattering wave fields is measured in order to allow a reduction of the cost of the measurement apparatus. In this respect, we firstly analyse the properties of the phaseless scattering nonlinear forward modelling operator in its integral form and we provide an analytical expression for computing its Frechet derivative. Then, we propose an inexact Newton method to solve the associated nonlinear inverse problems, where any linearized step is solved by a Lp Banach space iterative regularization method which acts on the dual space Lp* . Indeed, it is well known that regularization in special Banach spaces, such us Lp with 1 < p < 2, allows to promote sparsity and to reduce Gibbs phenomena and over-smoothness. Preliminary results concerning numerically computed field data are shown.

A Banach-space multifrequency imaging approach for electromagnetic subsurface sensing

An approach for electromagnetic subsurface sensing is proposed in this contribution. The inverse scattering problem arising from the full-wave electromagnetic formulation is solved by using an efficient regularization method developed in the framework of Lp Banach spaces. Such approach has been found to enhance the reconstruction quality with respect to standard regularization techniques in Hilbert spaces, allowing a reduction of the ringing and over-smoothing effects in the reconstructed images and providing a better identification of small and sparse targets. Multi-frequency data are also exploited in order to increase the available information. Some numerical simulations showing the capabilities of the developed approach will be presented.

Nonlinear electromagnetic inverse scattering in via Frozen or Broyden update of the Fréchet derivative

Microwave imaging methods are useful for non-destructive inspection of dielectric targets. In this work, a numerical technique for solving the 3D Lippmann-Schwinger integral equation of the inverse scattering problem via Gauss-Newton linearization in Banach spaces is analysed. More specifically, two different approximations of the Frechet derivative are proposed in order to speed up the computation. Indeed it is well known that the computation of the Frechet derivative is generally quite expensive in three dimensional restorations. Numerical tests show that the approximations give a faster restoration without loosing accuracy.