Thermoacoustic tomography with an arbitrary elliptic operator

Abstract

Thermoacoustic tomography is a term for the inverse problem of determining of one of the initial conditions of a hyperbolic equation from boundary measurements. In past publications, both stability estimates and convergent numerical methods for this problem were obtained only under some restrictive conditions imposed on the principal part of the elliptic operator. In this paper, logarithmic stability estimates are obtained for an arbitrary variable principal part of that operator. Convergence of the quasi-reversibility method to the exact solution is also established for this case. Both complete and incomplete data collection cases are considered.