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Relaxed viscosity-type iterative methods with application to compressed sensing

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Abstract

An acceleration strategy via relaxation technique is incorporated in a viscosity-type method to approximate solutions of monotone inclusion problems that are fixed points of a nonexpansive operator. The iterates of the algorithm is proved to converge strongly in the setting of real Hilbert spaces. Furthermore, applications of the theorems to compressed sensing problems and a numerical implementation of the proposed methods in \(L_2([0,1])\) are presented.

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Acknowledgements

The authors would like to thank the anonymous referees for their esteemed comments and suggestions. This research was funded by National Science, Research and Innovation Fund (NSRF) and King Mongkut’s University of Technology North Bangkok with Contract no. KMUTNB-FF-65-60. The third and fourth authors acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.

Funding

This research was funded by National Science, Research and Innovation Fund (NSRF) and King Mongkut’s University of Technology North Bangkok with Contract no. KMUTNB-FF-65-60.

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Authors and Affiliations

  1. Faculty of Science, Energy and Environment, King Mongkut’s University of Technology North Bangkok, 19 Moo 11, Nonglalok, Bankhai, Rayong, 21120, Thailand

    Jitsupa Deepho

  2. Mathematics Institute, African University of Science and Technology, Abuja, Nigeria

    Abubakar Adamu

  3. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Abdulkarim Hassan Ibrahim

  4. Numerical Optimization Research Group, Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Nigeria

    Auwal Bala Abubakar

  5. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa, 0204, South Africa

    Abdulkarim Hassan Ibrahim & Auwal Bala Abubakar

  6. Operational Research Center in Healthcare, Near East University, Nicosia, Turkish Republic of Northern Cyprus

    Abubakar Adamu

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  1. Jitsupa Deepho
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Correspondence to Abubakar Adamu.

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Deepho, J., Adamu, A., Ibrahim, A.H. et al. Relaxed viscosity-type iterative methods with application to compressed sensing. J Anal 31, 1987–2003 (2023). https://doi.org/10.1007/s41478-022-00547-2

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