非线性体效应的逆问题  

Inverse Problem in Non-linear Partial Volume Effect

作　　者：黄建衡[1] 刘鑫[1] 雷耀虎[1] 李冀[1] 郭金川[1] HUANG Jianheng;LIU Xin;LEI Yaohu;LI Ji;GUO Jinchuan(Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province,College of Physics and Optoelectronic Engineering,Shenzhen University,Shenzhen,Guangdong 518060,China)

机构地区：[1]深圳大学物理与光电工程学院,光电子器件与系统(教育部、广东省)重点实验室,广东深圳518060

出　　处：《光子学报》2021年第2期13-20,共8页Acta Photonica Sinica

基　　金：国家自然科学基金(Nos.61571305,61101175,62075141,61405120,61605119);深圳市基础研究项目基金(No.JCYJ20170302142617703);深圳大学教师科研启动项目基金(Nos.2018041,2017017)。

摘　　要：非线性体效应在计算机断层扫描重构的理论与应用中,仍然是一个悬而未决的问题。本文利用优化重构算法来解决非线性体效应,建立了离散非线性X射线投影变换模型,将X射线投影变换的逆问题变为一个非凸的优化问题,通过裁剪原用于求解凸优化问题的一阶原对偶算法,提出非线性迭代重构算法来解决非凸问题。通过构建成像系统模型对算法的收敛性和重构精度进行了模拟验证,模拟中重建的图像首先通过检验在极窄的显示窗口中显示小于1%的对比度,然后使用相对于真实图像的差异的l2范数进行定量分析。模拟结果表明,在计算精度范围内,非线性重构算法可以收敛到真实图像,而且对于图像衬度小于1%的细节,重构图像也可以显示出来。该研究结果可为设计有效补偿非线性体效应伪影的计算机断层扫描成像应用算法提供参考。Non-linear partial volume effect is still an unsolved problem in the theory and application of computed tomography reconstruction.In this work,an optimization-based reconstruction algorithm for effectively solving this effect was studied and developed.The discrete non-linear X-ray projection transformation model was established,when the inverse problem of X-ray projection transformation was transformed into a non-convex optimization.A non-linear iterative reconstruction algorithm was formulated to solve the non-convex optimization problem by tailoring the first-order primal-dual algorithm developed originally for solving convex optimization problems.Using computer-simulation studies,the convergence and reconstruction accuracy of the algorithm was demonstrated in this investigation.Images reconstructed were examined first through visual inspection with extremely narrow display window for revealing a contrast level of less than 1%,and then assessed with quantitative metrics such as the normalized l2-norm of the difference relative to its truth images.The simulation results show that the nonlinear reconstruction algorithm can converge to the real image within the range of calculation accuracy,and the reconstructed image can also be displayed for the details with image contrast less than 1%.This would provide a reference for the design of computed tomography imaging application algorithm which can effectively compensate the non-linear partial volume effect artifacts.

关 键 词：X射线 计算机断层扫描 非线性 非凸 优化 迭代算法 

分 类 号：O434.1[机械工程—光学工程]