扰动因素影响下对修正的OS-EM算法的收敛分析
PDF下载 (381)于文杰,王金平 *.扰动因素影响下对修正的OS-EM算法的收敛分析[J].宁波大学学报(理工版),2017,30(2):117-120.DOI:
YU Wen-jie,WANG Jin-ping *.Convergence analysis of the modified OS-EM algorithm for noisy data[J].Journal of Ningbo University(Natural Science & Engineering Edition),2017,30(2):117-120.DOI:
| Title: | Convergence analysis of the modified OS-EM algorithm for noisy data |
| 作者: | 于文杰, 王金平 * |
| Author(s): | YU Wen-jie, WANG Jin-ping * |
| 关键词: | 不适定性方程; OS-EM 迭代; 收敛性; Kullback-Leiber距离 |
| Keywords: | ill-posed equations; OS-EM iteration; convergence; Kullback-Leiber distance |
| 分类号: | O177.6; O175.5 |
| 文献标识码: | A |
| 摘要: | 在扰动因素影响下, 通过引入松弛参数对Ordered-Subsets Expectation-Maximization (OS- EM)算法进行修正. 基于修正迭代的 收敛性, 我们通过修改相应停止规则中的参数得到了一些主要的单调性结果, 进而证明了迭代的 收敛性. |
| Abstract: | In the noisy data case, we modify the Ordered-Subset Expectation-Maximization (OS-EM) algorithm by introducing a relaxation parameter. Based on the convergence of modified iteration in norm, we obtained some main monotonic results by modifying the parameters of the corresponding stopping rule, and proved the convergence for this modified iteration in norm. |
| 参考文献 /References: | [1] DEMPSTER A P, LAIRD N M, RUBIN D B. Maximum likelihood from incomplete data via the EM algorithm[J]. Journal of the Royal Statistical Society, 1997, 39(1):1-38. [2] HUDSON H M, LARKIN R S. Accelerated image reconstruction using ordered subsets of projection data[J]. IEEE Transactions on Medical Imaging, 1994, 13(4):601-609. [3] HALTMEIER M, LEITAO A, RESMERITA E. On the regularization methods of EM-Kaczmarz type[J]. Inverse Problems, 2009, 25(7):1-17. [4] RESMERITA E, ANDERSSEN R S. Joint additive Kullback-Leibler residual minimization and regulariza- tion for linear inverse problems[J]. Mathematical Methods Applicable Scientia, 2007, 30(13):1527-1544. [5] RESMERITA E, ENGL H W, IUSEM A N. The expec- tation-maximization algorithm for ill-posed integral equations: A convergence analysis[J]. Inverse Problems, 2007, 24(5):2575-2588. |
| 备注/Memo: | 收稿日期: 2016－06－22. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（61271398）. 第一作者: 于文杰（1989－）, 女, 浙江宁波人, 在读硕士研究生, 主要研究方向: 积分变换与图像处理. E-mail: yuwenjie912@163.com *通信作者: 王金平（1962－）, 男, 湖北武汉人, 教授, 主要研究方向: 积分变换与图像处理. E-mail: wangjinping@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
