Tomographic reconstruction from a small number of projections by an efficient sum-product reasoning method

Tomographic reconstruction from a small number of projections is still a challenging problem. In the paper, we formulate this problem as a statistical graphical model by the smooth assumption that the image has a structure where neighbor pixels have a larger probability to take a closer value. This Markov random filed framework allows easily integrating other prior information. Reasoning in the model can be solved using belief propagation algorithm. However, one projection line involves multiple pixels. This leads to high order cliques and exponential computation in the message passing procedure. A variable-change strategy is used to largely reduce the computation and forms an efficient sum-product reasoning algorithm. Numerical simulation examples show that the proposed method greatly surpasses traditional methods, such as FBP, EM and ART. Our method is suitable not only for the case of a very small amount of projection, but also for the multi-pixel-value case.