图像重建中的一种加速投影算法

An accelerated projection algorithm in image reconstruction

投影算法是解决凸集图像重建问题最普遍的工具,该算法主要有循环投影算法和平行投影算法,前者的核心思想是计算初始估计量到集合上的周期性投影,后者则是在每次迭代中都需要计算到所有集合上的投影。平行投影算法虽然通过并行操作提高了收敛速度,但是每次迭代步长依然局限于(0,2),这在一定程度上影响了它的收敛。为了寻求收敛速度更快,重建效果更好的加速投影算法,对平行投影算法进行改进,通过引入外推因子,提出一种加速投影算法,并在相应条件下证明新算法的收敛性。新算法使得每次的迭代步长均大于2,从而保证每次迭代的结果更加靠近解集。实验结果也表明,新提出的加速投影算法比平行投影算法收敛速度更快并且效率更高。

The projection algorithms mainly including projection onto convex sets algorithm and parallel projection method are the most pervasive tools for solving convex set image reconstruction problem. In the former of these two algorithm,an initial estimate is sequentially projected onto the individual sets according to a periodic schedule. While in the latter,the calculations of the projections onto all sets at each iteration are required.Although parallel projection method improves the convergence speed through the parallel operation,but iteration step-size is still limited in the interval(0,2) at each iteration,which affects its convergence. In order to seek the accelerated projection algorithm with better convergence and better reconstruction,an accelerated projection algorithm is proposed by introducing an extrapolation factor on the basis of parallel projection method(PPM),and the convergence is proved under certain conditions. This new algorithm makes the step-size larger than 2,and it ensures that each iteration is closer to the solution set. The experimental results show that the accelerated projection algorithm converges more quickly and more efficient than PPM.