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

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  • Qian Li

    (Shanghai University Of Engineering Science)

  • Wei Zhang

    (National University of Singapore)

Abstract

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.

Suggested Citation

  • Qian Li & Wei Zhang, 2021. "An improved linear convergence of FISTA for the LASSO problem with application to CT image reconstruction," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 831-847, November.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:4:d:10.1007_s10878-019-00453-7
    DOI: 10.1007/s10878-019-00453-7
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    References listed on IDEAS

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    1. Jian Chang & Lingjuan Zhang, 2019. "Case Mix Index weighted multi-objective optimization of inpatient bed allocation in general hospital," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 1-19, January.
    2. Ling Gai & Jiandong Ji, 2019. "An integrated method to solve the healthcare facility layout problem under area constraints," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 95-113, January.
    3. Liwei Zhong & Yanqin Bai, 2019. "Three-sided stable matching problem with two of them as cooperative partners," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 286-292, January.
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