Variable-exponent Lebesgue-space inversion for brain stroke microwave imaging

This article describes a microwave tomographic approach for the quantitative imaging of brain stroke inside the human head. For the acquisition of the scattered-field information, a prototype of multistatic system is adopted. An array of custom antennas is placed in contact with the head, and a switching matrix is used to measure the scattering parameters for each pair of probes. The collected data are processed by an inversion method based on a variable-exponent Lebesgue-space regularization technique, whose outcome is a map of dielectric properties of a slice of the head. With respect to previous approaches, this kind of inversion procedure performs an adaptive update of the Lebesgue-space exponents on the basis of the results at each inexact-Newton iteration and exploits stepped frequency data. This allows for an automatic setting of the regularization level, which becomes variable and target-dependent inside the whole investigation domain. The proposed approach is validated by means of FDTD synthetic simulations with a realistic 3-D forward scattering model of the human head, as well as by using real experimental cylindrical test phantoms filled with saline and glycerin/water mixtures.