We consider regularization methods of Kaczmarz type in connection with the expectation-maximization (EM) algorithm for solving ill-posed equations. For noisy data, our methods are stabilized extensions of the well established ordered-subsets expectation-maximization iteration (OS-EM). We show monotonicity properties of the methods and present a numerical experiment which indicates that the extended OS-EM methods we propose are much faster than the standard EM algorithm.
Ovidius University of Constanta（奥维迪乌斯康斯坦察大学）；“Gheorghe Mihoc - Caius Iacob” Institute of Statistical Mathematics and Applied Mathematics of the Romanian Academy（罗马尼亚科学院格奥尔基·米霍克-卡尤斯·雅各布统计数学与应用数学研究所）
Refined upper bounds for the convergence of the randomized extended Kaczmarz and Gauss-Seidel algorithms
School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University（厦门大学数学科学学院、福建省数学建模与高性能科学计算重点实验室）
A Relaxed Randomized Averaging Block Extended Bregman-Kaczmarz Method for Combined Optimization Problems
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（同济大学上海智能无人系统研究院）；School of Mathematical Sciences, Tongji University（同济大学数学科学学院）；The Institute for Advanced Study, Shenzhen University（深圳大学高等研究院）；Key Laboratory of Intelligent Computing and Applications (Ministry of Education), School of Mathematical Sciences, Tongji University（同济大学数学科学学院智能计算与应用教育部重点实验室）
Deterministic and randomized Kaczmarz methods for $AXB=C$ with applications to color image restoration
School of Mathematics and Statistics, Beijing Jiaotong University（北京交通大学数学与统计学院）；Department of Mathematics and Computer Science, TU Eindhoven（埃因霍温理工大学数学与计算机科学系）
Worth Their Weight: Randomized and Regularized Block Kaczmarz Algorithms without Preprocessing
Department of Mathematics, UC Berkeley（数学系，加州大学伯克利分校）；Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory（应用数学与计算研究部，劳伦斯伯克利国家实验室）
Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors
Spiceworks；Goucher College（古彻学院）；Yale University（耶鲁大学）；Colorado School of Mines（科罗拉多矿业学院）；Claremont Graduate University（克莱蒙特研究生大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Montana State University（蒙大拿州立大学）
Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging
Institute of Applied Mathematics, University of Bonn, Germany（波恩大学应用数学研究所）；Euler Institute, Università della svizzera italiana, Switzerland（瑞士意大利欧拉研究所；格拉茨大学数学与计算科学系）；Department of Mathematics and Scientific Computing, University of Graz, Austria（波恩心脏中心，第二内科部，波恩大学医院）；Heart Center Bonn, Department of Internal Medicine II, University Hospital Bonn, Germany（特伦托大学数学系）；Department of Mathematics, University of Trento, Italy
