不同凸集条件下CQ算法的应用分析

The Application of CQ Algorithm under Different Convex Sets

针对CQ算法,通过定义不同条件的下非空闭凸集C和Q,并结合讨论稀疏角度的CT重建问题,在R^N空间中给出了5种不同的实现方案,每种实现方案相对于CT重建模型,具备不同的物理含义.给定相同的迭代步数,通过仿真试验,分别对不同方案的重建精度进行了分析,从而确定了在相同收敛条件下CQ算法在应用时的最佳方案,为分裂可行性问题及其扩展形式在工程领域的应用提供了新的思路.

CQ algorithm is an important method to solve the split feasibility problem. The paper defines nonempty convex sets C and Q on different condition, then have the same split feasibility problem. To combine with the problem of sparse angular CT reconstruction, we propose five different implementations. Each implementation has its physics mean to CT reconstruction model. We set the same iterations, the through simulations we analyse the convergence rate and reconstruction precision to different cases. Therefore, we have the best case of CQ algorithm＇s application on the same convergence condition. It proposes new ideas for the engineering application of the split feasibility problem and its extend norms.