Maximum a posteriori (MAP) algorithm with iterative statistical regularization

The problem of image reconstruction in SPECT is considered in the general context of statistical regularization of ill-posed problems. The MAP algorithm with the prior information based on the maximum entropy (MEENT) concept is presented in this work. The MENT method is known as a powerful tool for solving tomography problems. Introduction of prior information entails the necessity of choosing an appropriate regularization parameter. The effectiveness of a reconstruction method depends strongly on the choice of a good parameter. In practice optimal regularization parameters are often found empirically: one needs to test a large number of parameters in order to find a reasonable good one. This paper intends to make some further contribution to the subject in developing some practical regularization parameter choice strategies in SPECT. The method for selecting an optimal regularization parameter based on the theory of a ´laminar ensemble´ is studied. This statistical method has an excellent theoretical basis. Numerical tests have shown, that there is a tradeoff between the resolution and noise level of the image that changes with iteration. The regularization parameter enables us to operate the tradeoff. This nice property seems especially useful and important in real applications as it provides a feasible and stable numerical resolution. The optimal regularization parameter was defined at each iteration step automatically without requiring the user to select it. The adaptive chi-square criterion was used to control and stop the iteration process. The MLAP-MENT algorithm has been tested using the 3D heart phantom. The important aim of the work was to evaluate the potential of the algorithm in the defect detection. The defect was modeled as a small region of decreased count density. In numerical experiments we investigated the convergence properties of the algorithm. A comparison to the maximum-likelihood-based (OS EM) algorithm was performed.