正电子发射断层重建是一类不适定问题,因此正则化方法常用来抑制噪声提高重建的质量.依据Mumford-Shah泛函模型提出了该类重建问题的统一变分模型.基于这一模型,提出了一种新的基于扩散方程的PET重建算法,同时给出了线性和非线性两种方法.实验结果表明,两种方法均有良好的重建性能,并且非线性方法通过合理的设置参数,能体现出较为优越的抗噪声性能和边缘保持特性.

In PET image reconstruction, regularization methods are usually considered to suppress noise effects in reconstructed images. In this paper, the Mumford-Shah functional model was firstly investigated and the new variational framework for PET reconstruction was then proposed. The resultant linear diffusion equation based reconstruction method was derived accordingly. Based on this linear method, the new nonlinear diffusion method was also presented to provide more advantages for the image edge preservation. Simulation results suggest that both linear and nonlinear diffusion equations based methods have nice performance in final reconstructions. Also, results have verified that the nonlinear diffusion equation based reconstruction method is superior to the linear one in both noise smooth and edge preservation.