Abstract
In Positron emission tomography (PET), image reconstruction using maximum likelihood expectation maximization (MLEM) suffers a problem which small noise could make reconstruction image exhibit high variance due to ill-condition. This motivates the development of some practical solutions to produce acceptable image. In this work, we consider the maximum a posteriori (MAP) estimation which combines the likelihood function with image prior under the paradigm of Bayesian statistics. The One-Step-Late (OSL) algorithm is used for the corresponding image reconstruction. The selection of proper image prior is the emphasis of this work. Different prior has different affect on reconstruction image. For example, quadratic prior has a well-known over-smoothing problem, which leads to the blurring of edges. Non-quadratic prior has better performance in maintaining edge information, but it is difficult in optimization. In this research, we proposed an approximate (AP) prior which can preserve edge regions by introducing the same penalty to those regions with same contrast. We also compare AR prior with other image priors such as: Quadratic, L1-Norm, Huber, Geman and McClure, Relative difference and Thin Plate. We use several point and line sources, and Hoffman phantom to evaluate the performance of various image priors. The proposed AR prior exhibits the best performance in terms of resolution and contrast recovery.