Regularization in microwave tomography

Microwave tomography is a promising method for the breast cancer imaging. Dielectric properties of the healthy tissue and the tumor have a high contrast under microwave investigation. To determine the dielectric properties from antenna measurements it is necessary to solve the inverse electromagnetic problem. This inverse problem is ill-posed, its solution is not stable. Regularization is used to achieve stability. Ordinary Tikhonov regularization usually makes the solution too smooth. Edge-preserving regularization is investigated to obtain a stable solution without oversmoothing the solution. Tikhonov and Edge-preserving regularizations are compared. It is found that edge-preserving regularization decreases the smoothness of the reconstruction but has the same robustness against the noise compared to Tikhonov regularization