A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing

Abdulkarim Hassan Ibrahim; Poom Kumam; Auwal Bala Abubakar; Wachirapong Jirakitpuwapat; Jamilu Abubakar

doi:10.1016/j.heliyon.2020.e03466

A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing

Heliyon. 2020 Mar 2;6(3):e03466. doi: 10.1016/j.heliyon.2020.e03466. eCollection 2020 Mar.

Authors

Abdulkarim Hassan Ibrahim¹, Poom Kumam^{1

2}, Auwal Bala Abubakar^{1

3}, Wachirapong Jirakitpuwapat¹, Jamilu Abubakar^{1

4}

Affiliations

¹ KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
² Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
³ Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano, Kano, Nigeria.
⁴ Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.

Abstract

Combining the projection method of Solodov and Svaiter with the Liu-Storey and Fletcher Reeves conjugate gradient algorithm of Djordjević for unconstrained minimization problems, a hybrid conjugate gradient algorithm is proposed and extended to solve convex constrained nonlinear monotone equations. Under some suitable conditions, the global convergence result of the proposed method is established. Furthermore, the proposed method is applied to solve the $ℓ_{1}$ -norm regularized problems to restore sparse signal and image in compressive sensing. Numerical comparisons of the proposed algorithm versus some other conjugate gradient algorithms on a set of benchmark test problems, sparse signal reconstruction and image restoration in compressive sensing show that the proposed scheme is computationally more efficient and robust than the compared schemes.

Keywords: Applied mathematics; Compressive sensing; Computer science; Conjugate gradient method; Convex constraints; Projection method.