Recently we developed a Bayesian-FBP (Filtered Backprojection) algorithm for CT image reconstruction. This algorithm is also referred to as the FBP-MAP (FBP Maximum a Posteriori) algorithm. This non-iterative Bayesian algorithm has been applied to real-time MRI, in which the k-space is under-sampled. This current paper investigates the possibility to extend this Bayesian-FBP algorithm by introducing more controlling parameters. Thus, our original Bayesian-FBP algorithm became a special case of the extended Bayesian-FBP algorithm. A cardiac patient data set is used in this paper to evaluate the extended Bayesian-FBP algorithm, and the result from a well-establish iterative algorithm with L 1 -norms is used as the gold standard. If the parameters are selected properly, the extended Bayesian-FBP algorithm can outperform the original Bayesian-FBP algorithm.