  In this article we study the inverse problem of recovering a space-dependent
coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the
trace of the solution on some open subset of the boundary. We obtain the
Lipschitz stability for this inverse problem, and we design a convergent
algorithm for the reconstruction of the unknown coefficient. The techniques
used are based on Carleman inequalities for wave equations and properties of
the MGT equation.
