基于全变分最小化和快速一阶方法的低剂量CT有序子集图像重建  

Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy

作　　者：毛宝林[1] 陈晓朝[1] 孝大宇[1] 范晟昱[1] 滕月阳[1] 康雁[1,2] 

机构地区：[1]东北大学中荷生物医学与信息工程学院,沈阳110819 [2]东北大学医学影像计算教育部重点实验室,沈阳110819

出　　处：《物理学报》2014年第13期415-421,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61372014;61201053;61302013);高等学校博士学科点专项科研基金(批准号:20110042110036);东北大学基础研究计划(批准号:N110619001)资助的课题~~

摘　　要：低剂量计算机断层成像(computed tomography,CT)具有减少X射线对患者的伤害的优势.本文主要针对从不完备投影数据重建出高质量低剂量CT图像的问题.通常,这个问题可以通过统计图像重建方法来实现,而统计重建算法需要非常多的迭代次数,导致了巨大的计算时间压力,以至于很难应用在实践中.为解决此问题,本文提出一种有序子集重建算法,该算法结合了全变分最小化和快速一阶方法以减少重建的迭代次数,采用Split Bregman交替方向法求解上述优化问题,利用投影到凸集合的方法加快迭代的收敛速率.实验结果表明,在同样的迭代次数下,本文提出的方法与基于有序子集的一阶方法相比较,相对重建误差的下降速度更快.Low-dose computed tomography（CT） has an advantage to reduce X-rays that are harmful to the body. This paper considers the issue of reconstructing high-quality low-dose CT images from incomplete projection data. Generally, this can be done by statistical image reconstruction methods. However, the huge number of iterations of the statistical reconstruction algorithms leads to long computing time, making them diffcult to be of practical value. To solve this problem, we propose a method to alleviate the issue by using total variation minimization and fast first-order method for the ordered subsets. We use Split Bregman alternating direction method to solve the optimization problem. Then, the projection onto convex sets method is used to speed up the convergence rate of the iterative method. Numerical experiments show that the relative reconstruction error of the proposed method can decrease faster than the first-order method of ordered subsets with the same iterative number.

关 键 词：全变分 投影到凸集合 交替方向法 有序子集 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]