基于Chambolle-Pock框架的核TV多通道图像重建算法  

Nuclear TV Multi-channel Image Reconstruction Algorithm Based on Chambolle-pock Framework

作　　者：马靓怡 乔志伟[1] MA Jingyi;QIAO Zhiwei(School of Computer and Information Technology,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学计算机与信息技术学院,太原030006

出　　处：《CT理论与应用研究（中英文）》2022年第6期731-747,共17页Computerized Tomography Theory and Applications

基　　金：国家自然科学基金面上项目(模型与数据耦合驱动的快速四维EPRI肿瘤氧成像(62071281));中央引导地方科技发展资金项目(新型TV和学习先验联合约束的快速四维EPRI成像方法(YDZJSX2021A003));山西省重点研发计划(电子顺磁共振成像(EPRI)中美联合实验室平台建设(201803D421012));山西省留学人员科技活动择优资助项目(基于压缩感知的四维EPRI成像方法研究(2018-172));山西省回国留学人员科研资助项目(基于新型四维TV正则机理的快速EPRI肿瘤氧成像方法研究(2020-008))。

摘　　要：总变差最小化算法是一种基于压缩感知理论的图像重建算法,能够从稀疏投影或含噪投影数据中高精度地重建图像,已经被广泛应用于计算机断层成像、磁共振成像、电子顺磁共振成像。能谱CT、T1或T2加权的MRI及EPRI均属于多通道成像。逐通道TV算法可以实现较高精度的图像重建,然而忽略了各通道图像之间的相似性。核TV算法是一种考虑了通道间图像相似性的TV类算法,可以实现高精度图像重建。面向多通道图像重建,以CT重建为研究范例,本文提出一种Chambolle-Pock算法框架下的核TV多通道图像重建算法。通过仿真模体和真实CT图像模体的重建实验,验证算法的正确性,分析算法的收敛性,探索算法参数对收敛速率的影响,评估算法的稀疏重建能力及含噪投影重建能力。结果表明,相对于逐通道TV算法,所提算法可以取得更高的重建精度。核TV算法是一种高精度的多通道图像重建算法,可以应用于各种成像模态的多通道重建场合。Total variation (TV) minimum algorithm is an image reconstruction algorithm based on compressed sensing theory,which can realize the reconstruction of images with high accuracy from sparse projection or noisy projection data and has been widely used in computed tomography(CT),magnetic resonance imaging(MRI)and electronic paramagnetic resonance imaging(EPRI).Energy spectrum CT,T1 or T2 weighted MRI and EPRI both belong to multi-channel imaging.The channel-by-channel TV algorithm can achieve high-precision image reconstruction,but it ignores the similarity among the images of each channel while Nuclear TV algorithm is a TV algorithm that considers the image similarity among channels,and can realize high-precision image reconstruction.For multi-channel image reconstruction,taking CT reconstruction as an example,this paper proposes a nuclear TV multi-channel image reconstruction algorithm based on the framework of Chambolle-pock algorithm.Through the reconstruction experiments of simulated phantom and real CT image phantom,the accuracy of the algorithm is verified,the convergence of the algorithm is analyzed,the influence of algorithm parameters on the convergence rate is explored,and the sparse reconstruction ability and noisy projection reconstruction ability of the algorithm are evaluated.The experimental results show that the proposed algorithm can achieve higher reconstruction accuracy than the channel-by-channel TV algorithm.Nuclear TV algorithm is a high-precision multi-channel image reconstruction algorithm,which can be applied to multi-channel reconstruction of various imaging modes.

关 键 词：图像重建 多通道 总变差最小 图像相似性 压缩感知 

分 类 号：O242[理学—计算数学] TP391.41[理学—数学]