Bayesian reconstruction in SPECT with entropy prior and iterative statistical regularization

When reconstructing SPECT data using the maximum a posteriori algorithm with entropy-based prior (MAP-ENT), the effectiveness of the algorithm depends strongly upon the choice of regularization parameter. The problem of choosing an optimal parameter remains still an open question in SPECT. Convergence properties of the MAP-ENT algorithm depending on a regularization parameter are investigated in this paper. The main goal was to study the effect of iteratively adjusting the regularization parameter on stability of the reconstruction process. Numerical tests have shown that there is a tradeoff between the resolution and noise level of the image that changes with iterations. It entails the choice of an appropriate regularization parameter at each iteration step. The iterative regularization was performed in the following way: the "best" regularization parameter was selected at each iteration step by using the adaptive chi-square criterion. A comparison with the maximum-likelihood-based OS-EM algorithm has shown that both (OS-EM and MAP-ENT) algorithms rather confidently lead the solution to a \´feasible\´ image in a few iterations. Then, as the iteration number increases, the OS-EM solution passes the feasibility area and produces images that begin to deteriorate. The MAP-ENT algorithm retains the solution within the interval due to the dynamic choice of an appropriate regularization parameter.