DETERMINATION OF PARAMETERS OF BODY INHOMOGENEITY BY MEASUREMENT SCALAR FIELD IN THE MICROWAVE TOMOGRAPHY PROBLEM 

Alyona D. Barysheva, Student of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: allyprofit@gmail.com
Inna V. Eliseeva, Student of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: innaeliseeva2003@mail.ru
Aleksey V. Medvedev, Student of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mdl-studio@yandex.ru
Mikhail Yu. Medvedik, Candidate of physical and mathematical sciences, associate professor of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: _medv@mail.ru 

Background. The purpose of the work is the use of neural network technologies in the problems of restoring the parameters of inhomogeneities within the body. This problem occurs in acoustics, electrodynamics, flaw detection, as well as in medicine. Materials and methods. The process of propagating an acoustic wave inside various objects is described using the Helmholtz equation. After setting the boundary problem, the transition to the Lippmann-Schwinger integral equation is performed. To solve the reverse problem, a two-step method was used. Results. The problem is solved numerically. The order of the matrix obtained in the calculation is about 10,000 elements. Graphic illustrations of the recovery of the function of inhomogeneities within the body are presented. An experiment was conducted demonstrating the peculiarities of restoring body parameters when using neural networks. Conclusions. Proposed and implemented is software complex for determination of parameters of inhomogeneities inside body. The advantages of using neural networks as a method are shown. 

numerical methods, integral equation, Helmholtz equation, neural network 

Barysheva A.D., Eliseeva I.V., Medvedev A.V., Medvedik M.Yu. Determination of parameters of body inhomogeneity by measurement scalar field in the microwave tomography problem. Modeli, sistemy, seti v ekonomike, tekhnike, prirode i obshchestve = Models, systems, networks in economics, technology, nature and society. 2024;(1):94–106. (In Russ.). doi: 10.21685/2227-8486-2024-1-7