An inverse problem of the determination of an initial condition in ahyperbolic equation from the lateral Cauchy data is considered. Thisproblem has applications to the thermoacoustic tomography, as wellas to linearized coefficient inverse problems of acoustics andelectromagnetics. A new version of the quasi-reversibility method isdescribed. This version requires a new Lipschitz stability estimate,which is obtained via the Carleman estimate. Numerical results arepresented.A new globally convergent numerical method is developed for a 1-Dand 2-D coefficient inverse problem for a hyperbolic partialdifferential equation (PDE). The back reflected data are used. Aversion of the quasi-reversibility method is proposed. A globalconvergence theorem is proven via a Carleman estimate. The resultsof numerical experiments are presented.