A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

Auwal Bala Abubakar; Kanikar Muangchoo; Abdulkarim Hassan Ibrahim; Abubakar Bakoji Muhammad; Lateef Olakunle Jolaoso; Kazeem Olalekan Aremu

doi:10.1109/ACCESS.2021.3053141

A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

Auwal Bala Abubakar, Kanikar Muangchoo^*, Abdulkarim Hassan Ibrahim, Abubakar Bakoji Muhammad, Lateef Olakunle Jolaoso, Kazeem Olalekan Aremu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.

Original language	English
Article number	9328771
Pages (from-to)	18262-18277
Number of pages	16
Journal	IEEE Access
Volume	9
DOIs	https://doi.org/10.1109/ACCESS.2021.3053141
State	Published - 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2013 IEEE.

Keywords

Derivative-free algorithm
Monotone operator equations
image restoration
projection technique

ASJC Scopus subject areas

General Computer Science
General Materials Science
General Engineering

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10.1109/ACCESS.2021.3053141

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title = "A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration",

abstract = "In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.",

keywords = "Derivative-free algorithm, Monotone operator equations, image restoration, projection technique",

author = "Abubakar, \{Auwal Bala\} and Kanikar Muangchoo and Ibrahim, \{Abdulkarim Hassan\} and Muhammad, \{Abubakar Bakoji\} and Jolaoso, \{Lateef Olakunle\} and Aremu, \{Kazeem Olalekan\}",

note = "Publisher Copyright: {\textcopyright} 2013 IEEE.",

year = "2021",

doi = "10.1109/ACCESS.2021.3053141",

language = "English",

volume = "9",

pages = "18262--18277",

journal = "IEEE Access",

issn = "2169-3536",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

AU - Abubakar, Auwal Bala

AU - Muangchoo, Kanikar

AU - Ibrahim, Abdulkarim Hassan

AU - Muhammad, Abubakar Bakoji

AU - Jolaoso, Lateef Olakunle

AU - Aremu, Kazeem Olalekan

PY - 2021

Y1 - 2021

N2 - In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.

AB - In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.

KW - Derivative-free algorithm

KW - Monotone operator equations

KW - image restoration

KW - projection technique

UR - https://www.scopus.com/pages/publications/85099732146

U2 - 10.1109/ACCESS.2021.3053141

DO - 10.1109/ACCESS.2021.3053141

M3 - Article

AN - SCOPUS:85099732146

SN - 2169-3536

VL - 9

SP - 18262

EP - 18277

JO - IEEE Access

JF - IEEE Access

M1 - 9328771

ER -

A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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