A modified contrast source inversion method for microwave tomographic imaging of Debye dispersive media

Abstract

The Debye empirical formulas are often used for the description of the dispersion characteristics of common media, such as biological tissues, water, and soil. In order to reconstruct their frequency-related electrical properties, a multi-frequency contrast source inversion (CSI) method is modified from the direct estimation of the contrast between Debye scatterers and background medium, into the reconstruction of three kinds of Debye model parameters, namely, the optical relative permittivity, relative permittivity difference, and static conductivity. Through three two-dimensional (2D) benchmark numerical experiments, detailed comparisons between the results by the improved CSI method, and those by the frequency hopping (FH) technique, single frequency subspace-based optimization method (SOM) with deep learning (DL), multi frequency (MF) dispersive SOM, and time-domain inverse scattering (TDIS) approach, show preliminarily that the modified CSI (M-CSI) method is feasible and robust, and that it exhibits acceptable compromise performance by the comprehensive consideration of convergence characteristics, positioning accuracy, reconstruction errors, and computational efficiency. Also, the M-CSI method has been successfully applied to quantitatively reconstruct the internal breast composition in a 2D cancerous phantom extracted from a realistic numerical breast, dielectrically and anatomically.