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

Qian Li () and Wei Zhang ()
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Qian Li: Shanghai University Of Engineering Science
Wei Zhang: National University of Singapore

Journal of Combinatorial Optimization, 2021, vol. 42, issue 4, No 9, 847 pages

Abstract: 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.

Keywords: LASSO problem; Fast iterative shrinkage thresholding algorithm; Linear convergence; CT image reconstruction (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10878-019-00453-7

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