IEEE Trans Med Imaging. 2024 Jun;43(6):2347-2357. doi: 10.1109/TMI.2024.3365302. Epub 2024 Jun 5.
An alternating direction method of multipliers (ADMM) framework is developed for nonsmooth biconvex optimization for inverse problems in imaging. In particular, the simultaneous estimation of activity and attenuation (SAA) problem in time-of-flight positron emission tomography (TOF-PET) has such a structure when maximum likelihood estimation (MLE) is employed. The ADMM framework is applied to MLE for SAA in TOF-PET, resulting in the ADMM-SAA algorithm. This algorithm is extended by imposing total variation (TV) constraints on both the activity and attenuation map, resulting in the ADMM-TVSAA algorithm. The performance of this algorithm is illustrated using the penalized maximum likelihood activity and attenuation estimation (P-MLAA) algorithm as a reference.
针对医学成像反问题中的非光滑双凸优化问题，开发了一种交替方向乘子法（ADMM）框架。特别是，当使用最大似然估计（MLE）时，飞行时间正电子发射断层扫描（TOF-PET）中的同时估计活动和衰减（SAA）问题具有这种结构。将 ADMM 框架应用于 TOF-PET 中的 SAA 的 MLE，得到 ADMM-SAA 算法。通过对活动和衰减图施加总变差（TV）约束，将该算法扩展为 ADMM-TVSAA 算法。使用惩罚最大似然活动和衰减估计（P-MLAA）算法作为参考，说明了该算法的性能。
