基于正交投影和广义投影（POCS）算法的研究进展

基金项目:

work was supported in part by an NKBRSF grant (G1998030606) and an NSFC grant (60272018)

详细信息

Review on POCS Algorithms for Image Reconstruction

1. School of Mathematics, Peking University, Beijing 100871, China;
2. Department of Information Science, National Science Foundation of China Beijing 100085, China

Funds:

work was supported in part by an NKBRSF grant (G1998030606) and an NSFC grant (60272018)

摘要: 目的在于提请有关读者关注近年来关于图象重建的凸集投影算法的进展,这一重要的方法及应用。方法主要讨论了基于正交投影和广义投影的算法。对基于正交投影的算法,并讨论了一般形式的加权松弛格式,这包含了分块格式和同时格式。并以三个定理报道有关的算法收敛性结果。结果分别包含了相容和不相容条件和弱强收敛下的结果。对基于广义投影的算法,有关的基本概念和例子,基本算法的收敛性结果。结论报道最近关于引入松弛系数的工作和在CT图象重建中的应用。
- POCS /
- Iterative Algorithm /
- Convergence /
- Image reconstruction.
Abstract: Purpose : A brief review on recent advances in POCS algorithms for image reconstruction with a preference towards practical applications and relevant convergence results in various formulations and topologies for the consistent and inconsistent cases. Mathematical details are minimized for a wide readership. Method : POCS based iterative algorithms. Result : Various recent results and applications are presented. Conclusion : The powerful algorithmic formulation of the POCS scheme will find various important applications in image reconstruction
- POCS /
- Iterative Algorithm /
- Convergence /
- Image reconstruction