The Quasi-Reversibility Method for the Thermoacoustic Tomography and a Coefficient Inverse Problem

TL;DR

This paper introduces a new quasi-reversibility method for solving inverse problems in thermoacoustic tomography, utilizing a Lipschitz stability estimate derived from Carleman estimates, with supporting numerical results.

Contribution

A novel quasi-reversibility approach for hyperbolic inverse problems, incorporating a new stability estimate based on Carleman inequalities.

Findings

The method achieves Lipschitz stability for the inverse problem.

Numerical experiments demonstrate the effectiveness of the approach.

Abstract

An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient inverse problems of acoustics and electromagnetics. A new version of the quasi-reversibility method is described. This version requires a new Lipschitz stability estimate, which is obtained via the Carleman estimate. Numerical results are presented.