超拉普拉斯重叠组稀疏先验的稀疏角度CT重建  

Overlapping group sparsity on hyper-Laplacian prior of sparse angle CT reconstruction

作　　者：齐子文 孔慧华[1,2] 李佳欣 潘晋孝[1,2] Qi Ziwen;Kong Huihua;Li Jiaxin;Pan Jinxiao(School of Mathematics,North University of China,Taiyuan,Shanxi 030051,China;Shanxi Key Laboratory of Signal Capturing&Processing,North University of China,Taiyuan,Shanxi 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051 [2]信息探测与处理山西省重点实验室,山西太原030051

出　　处：《光电工程》2023年第10期62-72,共11页Opto-Electronic Engineering

基　　金：国家自然科学基金资助项目(62201520,62103384,62122070);山西省基础研究计划项目(202103021224190)。

摘　　要：对于稀疏角度下的投影数据,计算机断层扫描在图像重建中容易出现伪影和噪声较多的问题,难以满足工业及医学诊断要求。本文提出一种基于重叠组稀疏和超拉普拉斯先验的稀疏角度CT迭代图像重建算法。其中重叠组稀疏反映图像梯度稀疏性,从图像梯度的角度考虑相邻元素之间互相重叠交叉的关系。而超拉普拉斯先验能够精确地近似图像梯度的重尾分布,能够使得重建图像整体的质量提升。本文提出的算法模型采用交替方向乘子法,主分量最小化法和梯度下降法求解目标函数。实验结果表明,在稀疏角度CT重建的条件下,本文提出的算法在保留结构细节、抑制图像重建过程中产生的噪声和阶梯伪影方面有着一定的改善。For the sparse angle projection data,the problem of artifact and noise is easy to appear in the image reconstruction of computed tomography,which is difficult to meet the requirements of industrial and medical diagnosis.In this paper,a sparse angle CT iterative reconstruction algorithm based on overlapping group sparsity and hyper-Laplacian prior is proposed.The overlapping group sparsity reflects the sparsity of image gradient,and the overlapping cross relation between the adjacent elements is considered from the perspective of the image gradient.The hyper-Laplacian prior can accurately approximate the heavy-tailed distribution of the image gradient and improve the overall quality of the reconstructed image.The algorithm model proposed in this paper uses alternating direction multiplier method,principal component minimization method and gradient descent method to solve the objective function.The experimental results show that under the condition of the sparse angle CT reconstruction,the proposed algorithm has certain improvement in preserving structural details and suppressing noise and staircase artifacts generated in the process of image reconstruction.

关 键 词：CT重建 稀疏角度 图像梯度 重叠组稀疏 超拉普拉斯先验 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]