Solution of electromagnetic inverse problem of inhomogeneity reconstruction in dielectric body by near-field measurements using two-step method

Background. The inverse electromagnetic problems of restoring inhomogeneity in a dielectric body from 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 technology for detecting inhomogeneities using microwave devices. The effectiveness of the corresponding technology depends on the accuracy of solving the inverse problem. Therefore, the development of new, more accurate methods for solving the inverse problem of microwave tomography is very relevant. Aim. The work is devoted to the development of a method for solving the electromagnetic inverse problem of microwave tomography using near-field measurements, that is, restoring the structure of an inhomogeneous dielectric body based on the values of the electromagnetic field outside this body using a measuring installation. Methods. The method of solving the inverse problem is a two-step one for determining the inhomogeneity of a body, which consists in first finding the current function inside the body, and then calculating the permittivity function. The method is not iterative and does not require knowledge of a «good» initial approximation. Results. A two-step method has been applied for the inverse problem of microwave tomography. Numerical results are presented. Inhomogeneous bodies in the shape of a hemisphere are considered. Experimental results are presented. Conclusion. The effectiveness of the proposed technology for detecting inhomogeneities in a dielectric body by microwave tomography is shown. The results of calculations and experimental data are presented.