基于重启策略的快速迭代收缩阈值算法的荧光分子断层成像重建  

Reconstruction for Fluorescence Molecular Tomography Using Fast Iterative Shrinkage Thresholding Algorithm Based on Restart Strategy

作　　者：高家琛 钟升 谢琼[2] 袁娅婷 易黄建[1] Gao Jiachen;Zhong Sheng;Xie Qiong;Yuan Yating;Yi Huangjian(School of Information Science&Technology,Northwest University,Xi’an 710127,Shaanxi,China;The First Hospital of Hunan University of Chinese Medicine,Changsha 410007,Hunan,China)

机构地区：[1]西北大学信息科学与技术学院,陕西西安710127 [2]湖南中医药大学第一附属医院,湖南长沙410007

出　　处：《光学学报》2024年第16期244-249,共6页Acta Optica Sinica

基　　金：陕西省教育厅创新团队项目(21JP123);陕西省大学生创新创业项目(S202310697548)。

摘　　要：提出一种改进的快速迭代收缩阈值算法(FISTA)来求解荧光分子断层成像(FMT)目标函数,并采用重启策略搜索步长,在迭代中提供合适的Lipschitz常数,从而加快FISTA的收敛速度。数值仿真实验和真实小鼠实验结果表明,与经典的FISTA对比,基于重启策略的快速迭代收缩阈值算法(R-FISTA)能够在保证FMT重建精度的同时加快重建速度。Objective Fluorescence molecular tomography(FMT)is a non-invasive technique that enables quantitative analysis of pathological processes at the cellular and molecular levels in vivo.The reconstruction of FMT is an ill-posed inverse problem,making it challenging to achieve fast and accurate reconstruction.Regularization methods,such as Tikhonov regularization and sparsity regularization,are typically used to address this issue.Given that tumors are small and sparse compared to the entire imaging domain,sparsity regularization is usually beneficial.The fast iterative shrinkage thresholding algorithm(FISTA)is proposed for the L 1-norm regularization problem and has shown good performance.Classical FISTA employs a linearly increasing search strategy to determine the Lipschitz constant.However,if the proximal gradient condition is satisfied during the initial stages of algorithm iteration,the Lipschitz constant remains unchanged,hindering the convergence of the algorithm.To address this issue,we propose a step-size search method based on a restart strategy,which can provide appropriate Lipschitz constants during the iterations to accelerate the convergence speed of FISTA.Methods In this study,an adaptive Lipschitz constant is provided at each iteration.The Lipschitz constant is increased by a growth factor containing gradient information.When the Lipschitz constant remains unchanged between two iterations,it may be too large,resulting in a small step size and slow convergence.Therefore,a truncation restart strategy is employed.The initial Lipschitz constant is selected as the current Lipschitz constant.We call this method restart fast iterative shrinkage thresholding algorithm(R-FISTA).Results and Discussions To test the performance of R-FISTA,numerical simulation experiments and in vivo experiments are conducted with both classical FISTA and R-FISTA.In the simulation experiments with different numbers of excitation points,R-FISTA takes less time compared to FISTA(Table 2 and Fig.2).In addition,different levels(5%,10%

关 键 词：生物光学 荧光分子断层成像 快速迭代收缩阈值算法 图像重建 重启策略 

分 类 号：Q632[生物学—生物物理学]