A Mathematical Framework to Analyze the Achievable Resolution From Microwave Tomography

A mathematical framework is proposed to investigate how different parameters affect the achievable resolution from microwave tomography (MWT). This framework attempts to incorporate multiple scattering events within the object of interest (OI) into its analysis by taking into account the effect of the induced total field within the OI. To this end, a linearized operator, which maps the OI's permittivity profile to the measured data, is first constructed. The framework then revolves around the number of the right singular vectors of this operator, and their spatial frequency contents that can be utilized in reconstruction. Furthermore, this framework is used to introduce the “best” possible reconstruction that can be achieved in a given MWT system when imaging a typical OI. This concept can then provide some insights and guidelines for MWT system design.