An improved linear convergence of FISTA for the LASSO problem with application to CT image reconstruction

作     者：Li, Qian Zhang, Wei 

作者机构：Shanghai Univ Engn Sci Sch Math Phys & Stat Shanghai 201620 Peoples R China Natl Univ Singapore Ctr Excellence Modelling & Simulat Next Generat P Singapore 119077 Singapore 

出 版 物：《JOURNAL OF COMBINATORIAL OPTIMIZATION》 (组合优化杂志)

年 卷 期：2021年第42卷第4期

页      面：831-847页

核心收录：

学科分类：12[管理学] 120202[管理学-企业管理（含：财务管理、市场营销、人力资源管理）] 0202[经济学-应用经济学] 02[经济学] 1202[管理学-工商管理] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China 

主　　题：LASSO problem Fast iterative shrinkage thresholding algorithm Linear convergence CT image reconstruction 

摘      要：The LASSO problem has been explored extensively for CT image reconstruction, the most useful algorithm to solve the LASSO problem is the FISTA. In this paper, we prove that FISTA has a better linear convergence rate than ISTA. Besides, we observe that the convergence rate of FISTA is closely related to the acceleration parameters used in the algorithm. Based on this finding, an acceleration parameter setting strategy is proposed. Moreover, we adopt the function restart scheme on FISTA to reconstruct CT images. A series of numerical experiments is carried out to show the superiority of FISTA over ISTA on signal processing and CT image reconstruction. The numerical experiments consistently demonstrate our theoretical results.