The problem of choosing initial approximations in inverse problems of ultrasound tomography

A. V. Goncharsky, S. Y. Romanov, S. Yu. Seryozhnikov

Lomonosov Moscow State University, Research Computing Center

Abstract: This paper is devoted to developing efficient iterative methods to solve nonlinear inverse problems of wave tomography. The iterative algorithms used to obtain an approximate solution of the inverse problem are based on an explicit representation of the gradient of the residual functional between the measured and computed wave fields. The choice of the initial approximation is of great importance for the convergence of the iterative process in a nonlinear inverse problem. The possibility of using an initial approximation to the sound speed obtained via solving the inverse problem in the ray approximation is studied. The efficiency of this approach is illustrated by solving model problems using a supercomputer. These model problems are designed for the ultrasound tomographic imaging of soft tissues in medicine.

Keywords: ultrasound tomography, wave equation, nonlinear coefficient inverse problem, iterative algorithms, initial approximation.

UDC: 519.6; 517.958:5

Received: 28.08.2017