基于MRF二次Membrane-Plate混合自适应先验的PET图像的收敛Bayesian重建算法

Convergent Bayesian reconstruction algorithm for positron emission tomography based on MRF quadratic Membrane-Plate hybrid adaptive prior

对于如何抑制正电子发射成像(positron emission tomography,PET)中的噪声效果的问题,Bayesian重建或者最大化后验估计(maximum a posteriori,MAP)的方法在重建图像质量和收敛性方面具有相对于其他方法的优越性。基于Bayesian理论,本文提出了一种新的能够保持其先验能量函数凸性的马尔可夫随机场(Markov Random Fields,MRF)混合多阶二次先验(quadratic hybrid multi-order,QHM),该QHM先验综合了二次-阶(quadratic membrane,QM)先验和二次二阶(quadratic plate,QP)先验,且能够根据不同阶数的二次先验和待重建表面的性质自适应的发挥QM先验和QP先验的作用。文中还给出了使用该新的混合先验的收敛重建算法。模拟实验结果的视觉和量化比较证明了对于PET重建,该先验在抑制背景噪声和保持边缘方面具有很好的表现。

As to problem of suppressing noise effects in reconstructed images of positron emission tomography （PET）, many methods have been proposed in the past twenty years. Among all the methods, Bayesian reconstruction, or maximum a posteriori （MAP） method, has its superiority over others in the regard of image quality. In the frame of Bayesian theory, a new MRF （Markov random fields） hybrid prior with convex energy function, which combines quadratic membrane （QM） prior and quadratic plate （QP） prior, is proposed in this paper. The new prior makes an adaptive use of QM prior and QP prior based on the properties of the smoothness priors of different orders. Convergent reconstruction algorithm using the proposed hybrid prior is also given. Visional and quantitative comparisons of the simulated experiments prove the new hybrid prior＇ good performance in lowering noise effect and preserving edges for PET reconstruction.