A Rapid Medical Microwave Tomography Based on Partial Differential Equations

The standard integral-based microwave tomography suffers from computational limitations associated with Green's function. Those limitations prevent the image reconstruction process from being fast, which is an important requirement for urgent medical applications such as stroke detection. To cope with these limitations, significant approximations are usually implemented within the integral equations. Those approximations include considering the imaging antennas as point sources, assuming homogeneity along one of the domain's coordinate axes, and necessitating a background matching medium. These approximations result in some undesirable effects in practice such as reconstructing merely 2-D images with limited accuracy, and manufacturing problems associated with selecting a suitable background matching medium with reasonable dielectric properties. To alleviate some of the above limitations and challenges, this paper introduces a partial differential equation framework for microwave tomography established on the wave and the third Maxwell equations. The proposed method is independent of Green's function and its corresponding limitations. Thus, it can reconstruct 3-D images in a faster manner, particularly in emergency scenarios such as stroke detection where time is life. To validate the proposed method, realistic biomedical head imaging problems are successfully solved, analyzed, and compared to the standard integral-based microwave tomography in terms of computational time and accuracy.