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

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.