基于广义惩罚加权最小二乘的低剂量CT重建方法  

GENERALIZED PENALIZED WEIGHTED LEAST-SQUARES APPROACH FOR LOW-DOSE X-RAY CT RECONSTRUCTION

作　　者：牛善洲[1] 刘宏 朱赟[2] 喻高航 马建华[4] Niu Shanzhou;Liu Hong;Zhu Yun;Yu Gaohang;Ma Jianhua(School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341000,China;School of Physics and Electronic Information,Gannan Normal University,Ganzhou 341000,China;School of Science,Hangzhou Dianzi University,Hangzhou 310000,China;School of Biomedical Engineering,Southern Medical University,Guangzhou 510515,China)

机构地区：[1]赣南师范大学数学与计算机科学学院,赣州341000 [2]赣南师范大学物理与电子信息学院,赣州341000 [3]杭州电子科技大学理学院,杭州310000 [4]南方医科大学生物医学工程学院,广州510515

出　　处：《数值计算与计算机应用》2021年第3期289-302,共14页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11701097,12071104,U1708261);江西省科技创新杰出青年人才资助计划项目(20192BCB23019);江西省“双千计划”科技创新高端人才(青年)项目;赣州市科技创新人才计划;江西省重点研发计划一般项目(20202BBE53024);江西省科技支撑计划重点项目(20161BBF60089);江西省教育厅科学技术研究项目(GJJ170822);浙江省自然科学基金(LD19A010002)资助.

摘　　要：针对低剂量CT成像问题,本文提出了一个基于广义惩罚加权最小二乘的低剂量CT重建方法,并在一定条件下建立了算法的全局收敛性定理.首先对投影数据进行统计建模构建广义加权最小二乘保真项,并且将二次先验信息引入投影数据的恢复过程中,从而达到抑制噪声的目的,最后使用经典的滤波反投影算法对恢复后的投影数据进行解析重建.实验结果表明,与惩罚加权最小二乘方法相比,新方法可以有效地抑制低剂量CT图像中的噪声和伪影,同时可以很好地保持图像的结构信息和空间分辨率.In this paper,we propose a generalized penalized weighted least-squares(PWLS)approach for low-dose CT imaging.Incorporating with a quadratic functional regularization,a generalized penalized weighted least-squares(GPWLS)approach was proposed to projection(sinogram)noise reduction,and then inverts the Radon transform for image reconstruction by filtered backprojction(FBP)algorithm.Both qualitative and quantitative studies were conducted using digital phantoms to evaluate the proposed GPWLS method.Experimental results show that the GPWLS method can achieve images with several noticeable advantages over the existing methods in terms of noise reduction and contrast-to-noise ratio.

关 键 词：低剂量CT 投影数据恢复 惩罚加权最小二乘 广义惩罚加权最小二乘 

分 类 号：R814.2[医药卫生—影像医学与核医学] TP391.41[医药卫生—放射医学]