A fast OS-type Bayesian reconstruction with an edge-preserving median prior

We have previously proposed a new median prior (MP) with edge-preserving and local monotonic properties using preconditioned conjugate gradient reconstruction algorithm (PCG-MP). In our experience, PCG-MP is difficult to implement, and complex to adjust the hyper-parameters. To solve these problems, we applied a separable paraboloidal surrogate (SPS) [3] to MP and combined with a fast convergent OS-type algorithm, called COSEM. Based on preliminary studies, the new algorithm, MAPCOSEM-MP, showed similar performances in preserving edges as PCG-MP but the algorithm and the hyper-parameters of MAPCOSEM-MP is easier to tune up. To evaluate further the performance of MAPCOSEM-MP, we conducted the bias-variance studies using two phantoms with different conditions and then compared with MAPCOSEM-MM (smoothing membrane prior). The preliminary results show that MP performs better for larger ROIs, while compatible to those of MM in smaller ROIs.