Microwave tomography employing an adjoint network based sensitivity matrix

A reconstruction algorithm for two- and three-dimensional microwave imaging is proposed. The present effort is focused on the reconstruction of conductivity (σ) and permittivity (ε_r) distributions aiming at a technique serving medical imaging, while permeability imaging can be easily incorporated to serve geophysical geophysical prospecting as well. This work constitutes the most recent one within the effort of extending our Modified Perturbation Method (MPM) from static to high and now microwave frequencies. MPM is an approximate method based on an exact Sensitivity or Jacobian matrix for an iterative update of an initial (σ,ε_r) guess until convergence. This method is proved almost immune of the problem inherent illposedness, but its robustness is actually gained by paying a penalty of compromised accuracy in the final achieved image. However, this image can be fine tuned by formulating and solving an exact inverse problem. Regarding the involved Jacobian matrix, this is evaluated through closed form expressions obtained through an Adjoint Network Theorem in conjuction with the electromagnetics reciprocity theorem. The field distributions required for its evaluation are readily available from the always required forward problem solutions on the assumed (σ,ε_r) distributions. Herein, the finite element method along with absorbing boundary conditions are employed for the forward problem electromagnetic simulation.