Power Balance Regularization of the Microwave Inverse Scattering Problem

The incorporation of a priori information is required to regularize the ill-posed microwave scattering problem associated with microwave tomography (MWT). A new physics-informed regularization technique using electromagnetic power balance is introduced. The method does not require the ad hoc specification of the regularization parameter. The technique is demonstrated on in silico synthetic data, as well as previously reported measurements for simple lossless dielectrics in free space, and in vivo measurements of human forearms in a lossy matching medium. In the lossless imaging scenario, the power balance regularization (PBR) technique produces similar results to the well-known truncated conjugate gradient (TCG) and total variation multiplicative regularizer (TVMR). However, for biomedical measurements, the results are markedly different with the reconstructed images demonstrating significantly higher contrast, more accurate property estimation for high contrast inclusions, and successful resolution of inclusions in the imaginary permittivity. The PBR technique can be easily added to conventional microwave imaging algorithms and suggests other physics-informed regularization schemes could be used in future work.