Abstract:Background. The work is devoted to the implementation of a two-step method for solving a vector three-dimensional inverse diffraction problem on an inhomogeneous dielectric scatterer in the form of a hemisphere characterized by inhomogeneous permittivity. The main area of application of the results of this article is the early diagnosis of breast cancer by microwave tomography. Materials and methods. The two-step method for solving the vector inverse problem of hemisphere diffraction is applied. Unlike traditional approaches, the two-step method of solving the inverse problem is non-iterative and does not require knowledge of a good initial approximation. Accordingly, there are no problems related to the convergence of the numerical method. Results and conclusions. The boundary value problem for the Maxwell system of equations is reduced to a system of integro-differential equations. An integral formulation of the vector inverse diffraction problem is proposed. A detailed description of the collocation method for solving an integro-differential equation of the first kind in special classes of functions is presented. The results of calculations of approximate solutions to the inverse problem are presented. It is shown that the two-step method is an effective approach to solving vector problems of near-field tomography.
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