A Descent Matrix-free Nonlinear Conjugate Gradient Algorithm for Impulse Noise Removal

Authors

  • Nasiru Salihu King Mongkhut's University of Technology Thonburi
  • Poom Kumam Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand.
  • Ibrahim Mohammed Sulaiman Universiti Utara Malaysia, UUM Sintok, Kedah, Malaysia
  • Suraj Salihu Gombe State University, Gombe, Nigeria

DOI:

https://doi.org/10.58715/ncao.2024.3.2

Keywords:

Unconstrained optimization, Conjugate gradient method, Conjugacy condition, Newton direction, Global convergence, Image reconstruction

Abstract

The convergence of the Polak, Ribie‘re-Polyak (PRP) conjugate gradient (CG) method requires some modifications for improved theoretical properties. In this article, we explore an optimal choice of the Perry conjugacy condition to propose a hybrid CG parameter for solving optimization and inverse problems, particularly in an image reconstruction model.
This parameter is selected to satisfy a combination of revised version of the PRP and Dai-Yuan (DY) CG methods. The numerical implementation includes inexact line search, showcasing the scheme's robustness (highest number of solved functions) compared to other known CG algorithms. The efficiency is shown in terms of Real error (RelErr), peak signal noise ratio (PNSR), and CPU time in seconds for impulse noise removal while for unconstrained minimization problems, the study evaluated the efficiency based on number of iterations, function evaluation, and CPU time in seconds. An interesting feature of the proposed method is its ability to converges to the minimizer regardless of the initial guess, relying on certain established assumptions.

Author Biography

Poom Kumam, Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand.

a. Center of Excellence in Theoretical and Computational Science (TaCS-CoE). Fixed Point Research
Laboratory,Fixed Point Theory and Applications Research Group, Faculty of Science, King
Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand.

c.  KMUTT-Fixed Point Research Laboratory, Room SCL 802, Science Laboratory Building,
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology
Thonburi (KMUTT), Bangkok 10140, Thailand.

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Published

2024-06-30

How to Cite

Salihu, N., Kumam, P., Mohammed Sulaiman, I., & Salihu, S. (2024). A Descent Matrix-free Nonlinear Conjugate Gradient Algorithm for Impulse Noise Removal. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 3(1), 25–46. https://doi.org/10.58715/ncao.2024.3.2

Issue

Vol. 3 No. 1 (2024): January - June, 2024

Section

Articles

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Copyright (c) 2024 Nasiru Salihu, Professor, Ibrahim Mohammed Sulaiman, Suraj Salihu

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