  A new numerical method for X-ray tomography for a specific case of incomplete
Radon data is proposed. Potential applications are in checking out bulky
luggage in airports. This method is based on the analysis of the transport PDE
governing the X-ray tomography rather than on the conventional integral
formulation. The quasi-reversibility method is applied. Convergence analysis is
performed using a new Carleman estimate. Numerical results are presented and
compared with the inversion of the Radon transform using the well-known
filtered back projection algorithm. In addition, it is shown how to use our
method to study the inversion of the attenuated X-ray transform for the same
case of incomplete data.
