An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery

Nipa Jun-on; Raweerote Suparatulatorn; Mohamed Gamal; Watcharaporn Cholamjiak; Nipa Jun-on; Raweerote Suparatulatorn; Mohamed Gamal; Watcharaporn Cholamjiak

doi:10.3934/math.2022102

AIMS Mathematics

2022, Volume 7, Issue 2: 1775-1790. doi: 10.3934/math.2022102

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Research article

An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery

1.
Faculty of Sciences, Lampang Rajabhat University, Lampang 52100, Thailand
2.
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
3.
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
4.
School of Science, University of Phayao, Phayao 56000, Thailand

Received: 11 June 2021 Accepted: 04 October 2021 Published: 02 November 2021
MSC : 47H04, 47H10

This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.
- weak convergence,
- parallel algorithm,
- $ G $-nonexpansive,
- inertial extrapolation,
- numerical discussion
Citation: Nipa Jun-on, Raweerote Suparatulatorn, Mohamed Gamal, Watcharaporn Cholamjiak. An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery[J]. AIMS Mathematics, 2022, 7(2): 1775-1790. doi: 10.3934/math.2022102

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Abstract

This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.

References

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