基于CT图像重建的多重集合分裂可行性问题应用分析

Apply the Multiple-Sets Split Feasibility Problem to CT Image Reconstruction

为了较好地应用CQ算法解决稀疏角度CT图像重建的问题,提出了一种新的实时的分块逐次混合算法.首先将稀疏角度CT图像重建的问题转化成分裂可行性问题.其次,通过分析非空闭凸集C和Q的不同的定义,在N维实空间中分别针对不同的CQ算法给出了7种不同的实现方案.通过试验,分别对不同算法及其方案的重建精度和收敛速度进行了对比分析,并对多重集合分裂可行性问题算法中约束权因子的选取及其对输出的影响进行了研究,从而给出了CQ算法在稀疏角度CT图像重建问题中应用的最佳凸集定义方案.以此为基础,给出了所提出算法的最佳实现方案.试验结果表明,该算法收敛速度快,重建精度高,为多重集合分裂可行性问题及其改进算法在该重建问题上的应用提供了参考.

To apply the CQ algorithm on the sparse angular CT image reconstruction better, a new real-time block successive mixed algorithm was proposed. Firstly, the problem of image reconstruction was transformed into the split feasibility problem. Secondly, through analyzing the different defineitions of nonempty closed convex sets C and Q, 7 different implementation cases in N dimension real space were proposed. Through simulations the convergence rate and reconstruction precision to different cases were analyzed, and how to select the constraint weights in algorithm and the output was studied. Then it obtains the best cases of CQ algorithm applyied on sparse angular CT image reconstruction were obtained. Therefore, the best case of proposed algorithm is obtained. The results show that the proposed algorithm has faster con-vergence rate and better reconstruction precision. New ideas for applying the split feasibility problem and its extending norms to the CT incomplete projection data image reconstruction were proposed.