We recently developed a family of image reconstruction algorithms that look like the emission maximum-likelihood expectation-maximization (ML-EM) algorithm. In this study, we extend these algorithms to Bayesian algorithms. The family of emission-EM-lookalike algorithms utilizes a multiplicative update scheme. The extension of these algorithms to Bayesian algorithms is achieved by introducing a new simple factor, which contains the Bayesian information. One of the extended algorithms can be applied to emission tomography and another to transmission tomography. Computer simulations are performed and compared with the corresponding un-extended algorithms. The total-variation norm is employed as the Bayesian constraint in the computer simulations. The newly developed algorithms demonstrate a stable performance. A simple Bayesian algorithm can be derived for any noise variance function. The proposed algorithms have properties such as multiplicative updating, non-negativity, faster convergence rates for bright objects, and ease of implementation. Our algorithms are inspired by Green’s one-step-late algorithm. If written in additive-update form, Green’s algorithm has a step size determined by the future image value, which is an undesirable feature that our algorithms do not have.

中文翻译：

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将排放期望最大化相似算法扩展到贝叶斯算法


我们最近开发了一系列图像重建算法，类似于发射最大似然期望最大化 (ML-EM) 算法。在本研究中，我们将这些算法扩展到贝叶斯算法。发射电磁相似算法系列采用乘法更新方案。这些算法对贝叶斯算法的扩展是通过引入一个新的简单因子来实现的，该因子包含贝叶斯信息。一种扩展算法可应用于发射断层扫描，另一种可应用于透射断层扫描。进行计算机模拟并与相应的未扩展算法进行比较。计算机模拟中采用总变差范数作为贝叶斯约束。新开发的算法表现出稳定的性能。可以为任何噪声方差函数导出简单的贝叶斯算法。所提出的算法具有乘法更新、非负性、明亮物体收敛速度更快以及易于实现等特性。我们的算法受到格林的一步迟算法的启发。如果以加性更新形式编写，格林算法的步长由未来图像值决定，这是我们的算法不具备的不良特征。