基于ADMM的TV最小化稀疏重建算法研究

发布时间：2018-04-13 15:37

本文选题：ADMM算法 + TV最小化　；参考：《中北大学》2017年硕士论文

【摘要】：在CT扫描中,射线对病人有一定危害,低剂量成像是CT技术的一个重要研究内容。低剂量可以通过稀疏视角下的投影采集来实现,然而用解析法对稀疏投影的重建会引入严重的伪影。基于压缩感知的重建算法可以实现精确稀疏重建,其中总变差最小是其经典代表。自适应梯度下降-投影到凸集是一种可以用来求解TV最小这一最优化问题的有效算法,然而因为其算法参数较多,选择最优参数需要经验选取。ADMM算法可以用来有效求解1范数问题,所以本文研究基于ADMM的TV算法,主要做了如下工作:(1)设计并实现了基于ADMM的TV算法,通过与FBP算法的比较,论证了TV算法的稀疏重建能力。(2)设计了一种基于有序子集技术的ADMM算法—OS-ADMM.该算法可以提高ADMM算法的收敛速度。其中,重点研究了子集划分规则和子集内投影顺序的编排方法。(3)设计了一种TV优化问题中的平衡因子的自适应选取方法。研究表明,该方法选取出的平衡因子可以获得高精度的重建图像。ADMM算法可以有效求解TV最小化问题,其算法参数不需要人为选取,并保证算法可以收敛。该文提出的平衡因子的自适应选取方法和OS-ADMM算法的综合运用,将实现基于ADMM算法的高速高精度重建。
[Abstract]:In CT scanning, radiation is harmful to patients, low dose imaging is an important research content of CT technology.The low dose can be achieved by the projection acquisition in sparse view, but the reconstruction of sparse projection by analytical method will introduce serious artifacts.Compression sensing based reconstruction algorithm can achieve accurate sparse reconstruction, in which the minimum total variation is the classical representation.Adaptive gradient descent projection onto convex sets is an effective algorithm for solving the minimum TV optimization problem, however, because of its large number of parameters,It is necessary to select the optimal parameters by experiential selection. ADMM algorithm can be used to solve the 1-norm problem effectively. Therefore, the TV algorithm based on ADMM is studied in this paper. The main work is as follows: 1) Design and implement TV algorithm based on ADMM, and compare it with FBP algorithm.This paper demonstrates the sparse reconstruction ability of TV algorithm. We design a ADMM algorithm based on ordered subset technique-OS-ADMM.This algorithm can improve the convergence speed of ADMM algorithm.Among them, we focus on the subsets partition rules and the layout method of projection order in subsets. We design an adaptive selection method of equilibrium factors in TV optimization problems.The results show that the balance factor selected by this method can obtain high precision reconstruction image. ADMM algorithm can effectively solve the TV minimization problem. The algorithm parameters do not need to be artificially selected and the algorithm can converge.The proposed adaptive selection method of balance factor and the comprehensive application of OS-ADMM algorithm will realize high speed and high precision reconstruction based on ADMM algorithm.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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