PDE-based numerical method for a limited angle X-ray tomography
This work addresses the problem of incomplete Radon data in X-ray tomography, which is relevant for airport baggage screening, but the improvement over existing methods is incremental.
The paper proposes a PDE-based numerical method for limited angle X-ray tomography, demonstrating convergence via a new Carleman estimate and showing improved reconstruction over filtered back projection in numerical experiments.
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.