Brain Stroke Microwave Imaging by Means of a Newton-Conjugate-Gradient Method in <inline-formula> <tex-math notation="LaTeX">$L^{p}$ </tex-math> </inline-formula> Banach Spaces

Abstract

A conjugate-gradient-based regularization technique in L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> Banach spaces, in conjunction with an inexact-Newton solving scheme, is presented in this paper. The proposed method is applied to obtain the reconstruction of the dielectric properties of human tissues in hemorrhagic brain stroke microwave imaging. The dielectric reconstruction is obtained by solving a nonlinear inverse problem, starting from a set of scattered-field measurements. The presented numerical simulations with 2-D and 3-D anatomically realistic phantoms, as well as the preliminary experimental results, show that this method can be useful for retrieving the dielectric properties of the human head with a reduced over-smoothing effect in the final images.