A novel differential inverse scattering methodology in biomedical imaging

An alternative differential framework for the existing integral-based electromagnetic inverse problems is proposed. This differential form, supplemented by the corresponding boundary conditions, overcomes the existing limitations of the integral-based inverse problems, i.e. considering the imaging antennas as point sources, the essential homogeneity along one axis, and the necessity of using a background matching medium. These limitations result in reconstructing two-dimensional images with certain level of error, and the practical problems associated with selecting suitable dielectric properties of the background medium. Thus, the ability of the proposed technique in reconstructing accurate three-dimensional images, including the dimensions and real structure of the imaging antennas and avoiding the essential use of matching medium, are unique advancements in solving inverse electromagnetic problems. To validate this proposed novel method, a biomedical inverse electromagnetic problem in head imaging is successfully solved.