Collection of papers, dedicated to 85-th birthday of academician Vladimir Gavrilovich Romanov (Editors: S.I. Kabanikhin, M.A. Shishlenin)

On the numerical reconstruction of the three-dimensional density of the medium in the acoustic system of equations

D. V. Klyuchinskiy, N. S. Novikov, M. A. Shishlenin

Institute of Computational Mathematics and Mathematical Geophysics, 630090, Novosibirsk, Russia

Abstract: In the article it is considered a gradient method for solving a 3D coefficient inverse problem of determining the density of a medium for a hyperbolic acoustic system using a finite number of measurements. The inverse problem is reduced to minimizing the cost functional by the gradient method. A numerical algorithm for solving the coefficient inverse problem is implemented and the gradient of the residual functional is obtained by solving the corresponding conjugate problem. Within the framework of a model experiment simulating ultrasound tomography of human tissues, the results of restoring the three-dimensional density coefficient of the medium are presented.

Keywords: 3D ultrasound tomography, gradient method, optimization, 3D coefficient inverse problem, hyperbolic acoustics system, Godunov method.

UDC: 519.63

MSC: 65M32

Received November 1, 2023, published December 31, 2024

Language: English

DOI: 10.33048/semi.2024.21.A05