A method of solving the coefficient inverse problems of wave tomography

Abstract

In this paper, the problem of nonlinear wave tomography is formulated as a coefficient inverse problem for a hyperbolic equation in the time domain. Efficient methods for solving the inverse problems of wave tomography for the case of transparent boundary conditions are presented. The algorithms are designed for supercomputers. We prove the Fréchet differentiability theorem for the residual functional and derive an exact expression for the Fréchet derivative in the case of a transparent boundary in the direct and conjugate problems. The expression for the Fréchet derivative of the residual functional remains valid if the experimental data are provided for only a part of the boundary. The effectiveness of the proposed method is illustrated by the numerical solution of a model problem of low-frequency wave tomography. The model problem is tailored to apply to the differential diagnosis of breast cancer.