Abstract: A fuzzy diffusion Positron Emission Tomography (PET) reconstruction algorithm based on anatomical non-local means prior was proposed to solve the problem in traditional Maximum A Posteriori (MAP) algorithm, that the details at low gradient value of reconstruction image cannot be maintained effectively and the appeared ladder artifacts. Firstly, the median prior distribution MAP reconstruction algorithm was improved, namely an anisotropic diffusion filter combined with fuzzy function was introduced before each median filtering. Secondly, the fuzzy membership function was used as diffusion coefficient in the anisotropic diffusion process, and the details of the image were considered by anatomical non-local prior information. The simulation results show that, compared with the traditional algorithms, the new algorithm improves the Signal-to-Noise Ratio (SNR) and anti-noise capability, and has good visual effects and clear edges. Thus the algorithm achieves a good balance between noise reduction and edge maintenance.

Key words: Maximum A Posterior (MAP), image reconstruction, fuzzy membership, median prior, anisotropic diffusion

摘要： 针对传统最大后验(MAP)算法出现阶梯伪影以及不能有效保持重建图像低梯度值处细节信息的问题,提出了一种基于解剖非局部先验的模糊扩散正电子发射计算机断层扫描(PET)重建算法。首先,对中值先验分布的MAP重建进行改进,在每次中值滤波前引入结合模糊函数的各向异性扩散滤波器;然后,采用模糊隶属度函数作为各向异性扩散过程的扩散系数,并结合解剖非局部先验来考虑图像的细节信息。仿真结果表明,与传统算法相比,该算法提高了信噪比(SNR),具有良好的抗噪性;同时视觉效果较好,图像边缘清晰,在抑制噪声和边缘保持方面取得了良好的折中。

关键词: 最大后验, 图像重建, 模糊隶属度, 中值先验, 各向异性扩散