A relaxed inertial and viscosity method for split feasibility problem and applications to image recovery

Haitao Che (), Yaru Zhuang (), Yiju Wang () and Haibin Chen ()
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Haitao Che: Weifang University
Yaru Zhuang: Qufu Normal University
Yiju Wang: Qufu Normal University
Haibin Chen: Qufu Normal University

Journal of Global Optimization, 2023, vol. 87, issue 2, No 14, 619-639

Abstract: Abstract In this paper, by combining Polyak’s inertial extrapolation technique for minimization problem with the viscosity approximation for fixed point problem, we develop a new type of numerical solution method for split feasibility problem. Under suitable assumptions, we establish the global convergence of the designed method. The given experimental results applied on the sparse reconstruction problem show that the proposed algorithm is not only robust to different levels of sparsity and amplitude of signals and the noise pixels but also insensitive to the diverse values of scalar weight. Further, the proposed algorithm achieves better restoration performance compared with some other algorithms for image recovery.

Keywords: Split feasibility problem; Sparse reconstruction; Inertial extrapolation; Convergence; Image recovery; 65H10; 90C33; 47H09 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01246-9

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