Solving the Inverse Electromagnetic Problem of Reconstructing Inhomogeneity in a Dielectric Body by Near-Field Measurements using the Two-Step Method

Background. The inverse electromagnetic problems of inhomogeneity reconstruction in a dielectric body by the near-field measurements arise, for example, in the early diagnosis of breast cancer by microwave tomography. The solution of such inverse problems is the basis for the development of a technique for detecting inhomogeneities using microwave devices. The efficiency of the technique depends on the inverse problem solution accuracy. Therefore, the development of new, more accurate methods for solving the inverse problem of microwave tomography is highly relevant. Aim. This study is aimed at the development of a method for solving the electromagnetic inverse problem of microwave tomography using near-field measurements, i.e., restoring the structure of an inhomogeneous dielectric body from values of an electromagnetic field outside this body using a measuring setup. Methods. The inverse problem is solved by a two-step method for determining the inhomogeneity of a body, in which the current function inside the body is first found and then the permittivity function is calculated. The method is non-iterative and does not require a good initial approximation. Results. A two-step method has been used to solve the inverse problem of microwave tomography. The numerical results are presented. Inhomogeneous bodies in the shape of a hemisphere have been investigated. Experimental results are presented. Conclusions. The efficiency of the proposed technique for detecting inhomogeneities in a dielectric body by microwave tomography is demonstrated. The calculation and experimental data are reported.