Sergey I. Kabanikhin & Abdigany D. Satybaev 
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems [PDF ebook] 

The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel’fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.