中文摘要：

在正电子发射断层成像（PFT）中，最大后验重建引入图像先验分布信息，将重建结果约束在正则空间中，但是不恰当的约束将导致重建图像过度平滑；经典正逆各项异性扩散模型仅考虑图像的梯度信息，不能完整表征图像的特征。针对该问题，提出了一种基于正逆扩散的优质PET重建算法，将灰度方差与正逆扩散模型结合，并采用改进模型进行正逆各项异性扩散，进行中值先验分布的贝叶斯重建。仿真结果表明，新算法克服了传统算法图像退化的缺点，优化了重建质量，能获得较高的信噪比和较好的图像视觉效果。

英文摘要：

In positron emission tomography （PET） imaging, the maximum a posterior （MAP） algorithm restrict the recon- struction results in a regular space by introducing prior information, but improper constraint cause excessive smoothing. The classic forward-and-backward （FAB） anisotropic diffusion model consider only the image gradient information, can not charac- terize the image feature completely. To solve this problem, a high quality PET reconstruction algorithm based on forward-and- backward diffusion is proposed. Firstly, combining the gray variance and the forward-and-backward diffusion model; Secondly, using the improved model doing forward-an＆backward diffusion; Finally, reconstruct the image with the median prior diffusion Bayesian algorithm. The simulation results show that, the new algorithm overcome the drawback of the traditional algorithms on degrading the reconstructed images, optimize reconstructed quality. The proposed algorithm can obtain a higher signal-to-noise ratio （SNR） and a superior visual effect.