University Proceedings. Volga Region. Physical and Mathematical Sciences

Abstract

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.

Keywords

• numerical methods
• integral equation
• helmholtz equation
• neural network