Reconstruction of the object inhomogeneity parameters
from near-field measurements in microwave tomography problem using neural networks 

Aleksey V. Medvedev, Master’s degree student, 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, associate professor of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia) E-mail: _medv@mail.ru

The article proposes a method for reconstruction inhomogeneity parameters based on the results of near-field measurements in medical diagnostic problems. The process of wave propagation inside various objects is described using the Helmholtz equation. The field is induced by a point source located outside the body. The problem posed is re- duced to the Lippmann-Schwinger integral equation. A two-step algorithm is used to search for inhomogeneity. A neural network approach was used to filter the values obtained after a two-step algorithm. This problem arises in acoustics, electrodynamics, flaw detection, as well as in medical diagnostics. When solving the problem numerically, the order of the matrix obtained in the calculation is about 25,000 elements. Graphic illustrations of the restoration of the function of inhomogeneities within an object are presented. An experiment was conducted demonstrating the features of restoring object parameters using neural networks. The results show the effectiveness of the autoencoder filtering the calculated data. Conclusions. A software package for determining the parameters of inhomogeneities inside an object has been proposed and implemented..

numerical methods, integral equation, Helmholtz equation, neural network

Medvedev A.V., Medvedik M.Yu. Reconstruction of the object inhomogeneity parameters from near-field measurements in microwave tomography problem using neural networks. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2024;(4):53–66. (In Russ.). doi: 10.21685/2072-3040-2024-4-5