Calculation of Triple Integrals of Rapidly Oscillating Functions of General Form Using Data Along Lines

Mathematical modeling in digital image processing is of great relevance given the rapid growth in the volume of digital data and the need for its rapidand reliable analysis. Modern technologies in computer vision, artificial intelligence, remote sensing, medical diagnostics and robotics require effective mathematical models for image reconstruction, filtering, recognition and interpretation. Methods of mathematical modelling are of particular importance, as they enable greater processing accuracy, reduced computational costs and ensure the reliability of results even in the presence of noise, incomplete or distorted data. An important task in digital image processing is the numerical integration of rapidly oscillating functions of several variables. Due to the complexity of numerically integrating such functions, there is a need to apply efficient numerical methods. Currently, methods of integration developed using information operators are of particular interest; these reconstruct intermediate values of quantities based on a given set of known values of a multivariable function at points, on lines, in planes, and so on. Based on such operators, cubature formulas are derived for the approximate calculation of multidimensional integrals, including integrals of rapidly oscillating functions of general form. The aim of this article is toanalyse the accuracy of the computation of triple integrals of rapidly oscillating functions of general form using a cubature formula based on interlineation operators. The method is based on data specified along the lines for both phase and amplitude. To evaluate the accuracy of the numerical integration method, a series of numerical experiments was carried out, during which the influence of the oscillation parameter and the partitioning parameter on the accuracy of the integral approximation was analysed.