A Visualization Method for Breast Cancer Detection Using Microwaves

Abstract

This paper proposes a qualitative approach to the inverse scattering problem of microwave tomography for breast cancer detection. In a two-dimensional framework, the tumor inside the breast is regarded as an unknown scatterer placed inside an inhomogeneous and lossy background formed by skin and fat. We first present in detail the mathematical formulation of the method, which is based on the reciprocity gap functional: in particular, the physical and geometrical properties of the healthy breast are coded into the Green's function of the corresponding scattering equation, while any other object outside the array of receiving antennas can be neglected. Then, we propose a “no-sampling” implementation of the method, which allows a very fast visualization of the breast slices (the computational time is around 1s). Finally, we test the resulting algorithm against synthetic but realistic and noisy scattering data, by considering different plausible clinical situations.