Soares E J, Byrne C L, Glick S J
Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA, USA.
IEEE Trans Med Imaging. 2000 Apr;19(4):261-70. doi: 10.1109/42.848178.
Researchers have shown increasing interest in block-iterative image reconstruction algorithms due to the computational and modeling advantages they provide. Although their convergence properties have been well documented, little is known about how they behave in the presence of noise. In this work, we fully characterize the ensemble statistical properties of the rescaled block-iterative expectation-maximization (RBI-EM) reconstruction algorithm and the rescaled block-iterative simultaneous multiplicative algebraic reconstruction technique (RBI-SMART). Also included in the analysis are the special cases of RBI-EM, maximum-likelihood EM (ML-EM) and ordered-subset EM (OS-EM), and the special case of RBI-SMART, SMART. A theoretical formulation strategy similar to that previously outlined for ML-EM is followed for the RBI methods. The theoretical formulations in this paper rely on one approximation, namely, that the noise in the reconstructed image is small compared to the mean image. In a second paper, the approximation will be justified through Monte Carlo simulations covering a range of noise levels, iteration points, and subset orderings. The ensemble statistical parameters could then be used to evaluate objective measures of image quality.
由于其具有的计算和建模优势，研究人员对块迭代图像重建算法表现出越来越浓厚的兴趣。尽管它们的收敛特性已有详尽记录，但对于它们在存在噪声的情况下的表现却知之甚少。在这项工作中，我们全面刻画了重缩放块迭代期望最大化（RBI - EM）重建算法和重缩放块迭代同步乘法代数重建技术（RBI - SMART）的总体统计特性。分析中还包括RBI - EM的特殊情况，即最大似然期望最大化（ML - EM）和有序子集期望最大化（OS - EM），以及RBI - SMART的特殊情况SMART。对于RBI方法，遵循了一种与先前为ML - EM概述的类似的理论公式化策略。本文中的理论公式依赖于一种近似，即重建图像中的噪声与平均图像相比很小。在第二篇论文中，将通过涵盖一系列噪声水平、迭代点和子集排序的蒙特卡罗模拟来证明这种近似的合理性。然后，总体统计参数可用于评估图像质量的客观度量。
