A Gibbs random field‐based active electromagnetic method for noninvasive diagnostics in biomedical applications

Abstract

A new approach to the reconstruction of dielectric properties of unknown biological bodies is proposed, which is developed starting from an integral equation formulation of the electromagnetic inverse scattering problem. A Gibbs Random Field model is used to develop a stochastic approach based on the Bayes theorem. An iterative solution is obtained by the simulated annealing technique. The method integrates the important features of the spatial domain method with the possibility of taking into account a priori information on the scatterers under test. No large ill‐conditioned matrix inversions are required. A two‐dimensional formulation is considered, involving cylindrical scatterers illuminated by transverse magnetic‐wave incident fields. A multi‐illumination multiview reconstruction process is also performed. Some results on the reconstruction of strong scatterers are reported.

A model-driven approach to microwave diagnostics in biomedical applications

“…Once the problem has been defined in this way, the solution can be obtained by one of the various inversion methods recently proposed in the literature. In particular, in the present work, we apply the reconstruction technique previously developed by us [17], [21].…”

“…In [21], we proposed an iterative method based on a probabilistic approach with extensive use of a priori information. As compared with other techniques, this method allowed larger discretizations (on the order of 10 000 cells).…”

An iterative numerical method for inverse scattering problems

“…ficulty. Algorithms based on the Newton-Kantorovich [Franchois and Pichot, 1997] or the distorted Born iterative method [Chew and Wang, 1990] have also been implemented and applied to microwave imaging of biological tissues [Joachimowicz et al, 1991]. Furthermore, Kleinman and van den Berg [1992] have proposed a modified conjugate gradient optimization technique, which does not require the exact solution of the direct scattering problem during each iteration.…”

“…Furthermore, Kleinman and van den Berg [1992] have proposed a modified conjugate gradient optimization technique, which does not require the exact solution of the direct scattering problem during each iteration. In addition, a stochastic approach based on the application of the Gibbs random fields has been developed by Caorsi et al [ 1995].…”

Inverse‐scattering method for dielectric objects based on the reconstruction of the nonmeasurable equivalent current density

“…In order to overcome this drawback, it seems mandatory to resort to nonlinear modeling, as is suggested by recent literature on inverse scattering and microwave imaging [Chew et al, 1996]. For example, a nonlinear stochastic algorithm that proved useful in imaging strongly scattering cylinders was recently proposed [Caorsi et al, 1994[Caorsi et al, , 1995. Such an algorithm is based on a Markov random field model of the problem and makes use of simulated annealing [Caorsi et al, 1 Also at Department of Biophysical and Electronic Engineer- [1994], where also the problem of nonradiating (or invisible) currents is discussed in great detail and the problems that arise when such currents are not properly considered are focused on.…”