Mathematical Analysis of Microwave Tomography: The Reconstruction Problem of Malignant Tumor

Abstract

Early breast cancer detection is an emerging field of research as it can save many lives infected by malignant tumors. Microwave imaging is one of the main pillars in biomedical fields of comprehensive cancer care. The mathematical theory of microwave tomography involves solving an image reconstruction problem for Maxwell’s equations. In this research contribution, we analyze the potential of an image reconstruction model for the early detection of breast tumors from microwave tomography method. The detection of early-stage tumors within the breast by microwave tomography imaging is challenged by both the moderate endogenous dielectric contrast between healthy and malignant glandular tissues and the spatial resolution available from illumination at microwave frequencies. The formulation as a shape-reconstruction problem offers several advantages compared to more traditional pixel-based schemes, to mention, in particular, well defined boundaries and the incorporation of an intrinsic regularization that reduces the dimensionality of the inverse problem whereby at the same time stabilizing the reconstruction. We present in this paper a novel strategy that can detect very small tumors compared to the wavelength used for illuminating the breast. In addition, our algorithm can determine the sizes and the dielectric properties of the tumors with good accuracy.