An mrf-based approach to image reconstruction from few projections

The problem of image reconstruction from a small number of projections is ill-posed and the standard techniques are generally unable to compute suitable solutions. In these cases the use of regularization techniques allows us to incorporate available prior knowledge in the problem, and thus it can help in selecting a unique solution. However, such techniques often ignore image discontinuities, giving globally smooth solutions. In this paper a regularization approach is proposed which also exploits pre-existing knowledge on the image discontinuities. An image model based on a pair of Markov Random Fields (MRFs), associated with the intensity process and with the line process (discontinuities), respectively, is introduced. The Gibbs distribution is used to give probability densities to MRFs, allowing the problem to be treated in a Bayesian framework. The final solution is thus computed via a Maximum A Posteriori (MAP) estimate. In comparison with other techniques, such as Convolution Backprojection and ART, commonly adopted in X-ray Computed Tomography (X-ray CT), the proposed method is shown to give good solutions even when a . limited number of noisy projections are available. From a practical point of view, the method is attractive in all applications requiring a short exposure time, such as imaging of moving organs.