河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
中国期刊方阵入选期刊
中国高校优秀科技期刊
华北优秀期刊
河北省优秀科技期刊

协同采编系统

友情链接

基于最远块投影的自适应分块迭代CQ算法

王培元^1,2

李刚³

周海云^1,4

1. 军械工程学院基础部, 河北石家庄 050003;
2. 海军航空兵学院第二飞行训练基地, 山西长治 046011;
3. 河北广播电视大学开放教育学院, 河北石家庄 050071;
4. 河北师范大学数学与信息科学学院, 河北石家庄 050024
DOI： 10.11826/j.issn.1000-5854.2014.06.006

Adaptive Block Iterative CQ Algorithm of Furthest Projection

WANG Peiyuan^1,2, LI Gang³, ZHOU Haiyun^1,4

PDF
下载
HTML

摘要/Abstract

摘要：

针对分块迭代CQ算法,因子集的无序性和步长的不稳定性而导致的收敛速度较慢的问题,提出了一种基于最远块投影的自适应分块迭代CQ算法.该方法通过逐次对子集最远块进行投影,可以获取较快的收敛速度;利用类-Armijo搜索的方法可以获取合适的步长参数.在证明了算法收敛性的同时,结合短扫描CT投影重建问题对2种算法的实验结果进行了对比分析.结果表明所提出算法能够取得较快的收敛速度和较高的重建精度.

Abstract：

With the randomness of the subsets and volatile step-sizes,the block iterative CQ algorithm has slow convergence speed.A furthest block projection adaptive CQ algorithm is proposed.The faster convergence speed can be obtained by projecting onto the furthest subset successively and better step-sizes can be obtained from the Armijo-like search methods.The limited view CT image reconstruction problem is simulated with the two algorithms.The results show that the proposed algorithm has faster convergence speed and better reconstructed precision.

关键词

关键词： 分块迭代 ; 最远块投影 ; 自适应 ; CQ算法

Key words： block iteration ; furthest block projection ; adaption ; CQ algorithm

参考文献 12

[1] CENSOR Y,ELFVING T.A Multiprojection Algorithms Using Bregman Projection in a Product Space [J].Numer Math,1994,8:221-239.
[2] BAUSCHKE H H,BORWEIN J M.On Projection Algorithms for Solving Convex Feasibility Problems [J].SIAM Rev,1996,3(38):367-426.
[3] BYRNE C L.A Unified Treatment of Some Iterative Algorithms in Signal Processing and Image Reconstruction [J].Inverse Probl,2004,20:103-120.
[4] BYRNE C L.Iterative Projection onto Convex Sets Using Multiple Bregman Distances [J].Inverse Probl,1999,15:1295-1313.
[5] BYRNE C L.Bregman-Legendre Multidistance Projection Algorithms for Convex Feasibility and Optimization [C]//Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications,Amsterdam:Elsevier Science Publishers,2001:87-99.
[6] BYRNE C L.Iterative Oblique Projection onto Convex Sets and the Split Feasibility Problem [J].Inverse Probl,2002,18:441-453.
[7] JEFFREY A F.Iterative Methods for Image Reconstruction [M].Tutorial：ISBI,2006.
[8] 张燕,杨洋.相容线性系统的行投影块迭代算法 [J].南京师范大学学报：工程技术版,2006,6(1)：47-51.
[9] QU B,XIU N.A Note on the CQ Algorithm for the Split Feasibility Problem [J].Inverse Probl,2005,21:1655-1665.
[10] GENSOR Y,BORTFELD T,MARTTN B,et al.A Unified Approach for Inversion Problems in Intensity-moulated Radiation Therapy [J].Phys Med Biol,2006,51:2353-2365.
[11] MALCOLM H H,RICHARD S L.Accelerated Image Reconstruction Using Ordered Subsets of Projection Data [J].IEEE Trans on Medical Imaging,1994,13(4):601-609.
[12] 印胤,刘力.扇束图像重建中OSEM算法及子集划分的研究 [J].CT理论与应用研究,2003,12(3):1-8.