Noumeir R, Mailloux G E, Lemieux R
Service de médecine nucléaire, Hôpital du Sacré-Coeur de Montréal 5400, Québec, Canada.
Int J Biomed Comput. 1995 Jun;39(3):299-310. doi: 10.1016/0020-7101(95)01111-q.
A Bayesian image reconstruction algorithm is proposed for emission tomography. It incorporates the Poisson nature of the noise in the projection data and uses a non-uniform entropy as an a priori probability distribution of the image in a maximum a posteriori (MAP) approach. The expectation maximization (EM) method was applied to find the MAP estimator. The Newton-Raphson numerical method whose convergence and positive solutions are proven, was used to solve the EM problem. The prior mean at iteration k was determined by smoothing the image obtained at iteration k-1. Comparisons between the ML and the MAP algorithm were carried out with a numerical phantom that contains a narrow valley region. The ML solution after 50 iterations was chosen as the initial solution for the MAP algorithm, since the global performance of the ML algorithm deteriorates with increasing number of iterations while its local performance in the valley region is always improving. The resulting algorithm is a compromise between ML who has the best local performance in the valley region and the MAP who has the best global performance.
提出了一种用于发射断层成像的贝叶斯图像重建算法。该算法考虑了投影数据中噪声的泊松特性，并在最大后验（MAP）方法中使用非均匀熵作为图像的先验概率分布。采用期望最大化（EM）方法来寻找MAP估计器。使用已证明收敛性和正解的牛顿 - 拉夫森数值方法来解决EM问题。通过对迭代k - 1时获得的图像进行平滑处理来确定迭代k时的先验均值。使用包含狭窄谷区的数字模型对最大似然（ML）算法和MAP算法进行了比较。由于ML算法的全局性能随着迭代次数的增加而恶化，而其在谷区的局部性能一直在提高，因此选择ML算法在50次迭代后的解作为MAP算法的初始解。所得算法是在谷区具有最佳局部性能的ML算法和具有最佳全局性能的MAP算法之间的一种折衷。
