基于凸非凸有限元全变差正则的扩散光学层析成像  

Diffusion Optical Tomography Based on Convex-Nonconvex Finite Element Total Variation Regularization

作　　者：李金兰 谢朝阳 刘国奇[2] 邹健[1] Li Jinlan;Xie Zhaoyang;Liu Guoqi;Zou Jian(School of Information and Mathematics,Yangtze University,Jingzhou 434020,Hubei,China;College of Computer and Information Engineering,Henan Normal University,Xinxiang 453007,Henan,China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434020 [2]河南师范大学计算机与信息工程学院,河南新乡453007

出　　处：《激光与光电子学进展》2023年第12期254-261,共8页Laser & Optoelectronics Progress

基　　金：国家自然科学基金(61901160)。

摘　　要：为避免扩散光学层析成像中L1正则项带来的有偏估计问题,提出一种基于凸非凸有限元的全变差(CNC-FETV)正则重构模型。首先,应用有限元方法将求解域剖分为有限个三角形,用一个连续分段多项式函数逼近每个三角形上的吸收系数值,再对导出的差分矩阵进行逐个单元组装,得到有限元的全变差(FETV)正则表示。然后,利用基于凸非凸稀疏正则的构造方法得到凸非凸有限元全变差正则项,并在理论上证明该非凸正则项在一定条件下可保持目标函数的整体凸性。最后,利用交替方向乘子法求解所提模型。数值实验表明,所提CNC-FETV模型在扩散光学层析成像重构的视觉效果和评价指标值上都要优于已有的Tikhonov和FETV正则模型。A reconstruction model based on convex-nonconvex finite element total variation(CNC-FETV)regularization is proposed to avoid the biased estimation of L1 regularization in diffuse optical tomography.First,the finite element method was used to divide the computational domain into a finite number of triangles,after which a continuous piecewise polynomial function was used to approximate the absorption coefficient value in each triangle.Then,the derived difference matrix was assembled element by element to obtain a representation of the FETV regularization.Subsequently,the CNCFETV regularization was obtained by the construction method based on convex-nonconvex sparse regularization.Results theoretically proved that the nonconvex regularization term could maintain the overall convexity of the objective function under certain conditions.Finally,the alternating direction multiplier method was used to solve the proposed model.Numerical experiments show that compared with the Tikhonov and FETV regularization models,the proposed CNCFETV regularization model has superior performances in both numerical criteria and visual effects for diffusion optical tomography reconstructions.

关 键 词：扩散光学层析成像术 凸非凸稀疏正则 有限元法 交替方向乘子法 

分 类 号：TP751[自动化与计算机技术—检测技术与自动化装置]