一种基于模糊集理论的贝叶斯PET重建算法

A Bayesian Algorithm Based on Fuzzy Theory for PET Reconstruction

最大似然估计算法是PET重建的经典算法,是统计意义上的最优解,但是MLEM(Maximum Likelihood Expectation Maximization)算法具有不稳定性,即随迭代次数的增加,图像噪声反而会增加.针对这一缺点,研究了最大后验(Maximum A Posteriori,MAP)重建方法,分析了MAP方法中不恰当的约束造成的过分平滑等不良后果,提出了基于模糊理论的Bayesian重建方法,以提高重建结果的噪声性能并能够保持图像边界等有用的信息.主要方法是在重建过程中先用模糊加权均值滤波器滤波,再用中值滤波器进行滤波.仿真结果表明:该算法不仅能够抑制噪声,而且能够保持重建图像的边缘.

Maximum likelihood estimation,which is classical in PET reconstruction,is of statistically optimal solution.However,with the increasing of the iterations,the noise＇s influence on the reconstruction of the image increases.MAP（maximum a posteriori） reconstruction algorithm was studied.The negative effect of MAP such as over-smoothing caused by inappropriate constraints was analyzed.A new Bayesian reconstruction algorithm based on fuzzy theory was proposed to enhance the noise performance and to preserve the edge information.The fuzzy weight average filter and median filter were used in the algorithm.Simulations showed that the proposed method not only performed well for noise suppression,but also preferably kept the edges of the reconstruction image.