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Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach

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  • Halilu, Abubakar Sani
  • Majumder, Arunava
  • Waziri, Mohammed Yusuf
  • Ahmed, Kabiru

Abstract

In recent years there is a vast application of conjugate gradient methods to restore the disturbed signals in compressive sensing. This research aims at developing a scheme, which is more effective for restoring disturbed signals than the popular PCG method (Liu & Li, 2015). To realize the desired goal, a new conjugate gradient approach combined with the projection scheme of Solodov and Svaiter [Kluwer Academic Publishers, pp. 355-369(1998)] for solving monotone nonlinear equations with convex constraints is presented. The main idea employed in this algorithm is to approximate the Jacobian matrix via acceleration parameter in order to propose an effective conjugate gradient parameter. In addition, the step length is calculated using inexact line search technique. The proposed approach is proved to converge globally under some mild conditions . The numerical experiment, depicts the efficacy our method. Apart from generating search directions that are vital for global convergence, a significant contribution of the new method lies in its applications to solve the ℓ1-norm regularization problem in signal recovery. Experiments with the scheme and the effective PCG solver, existing in the previous literature, shows that the new method provides much better results.

Suggested Citation

  • Halilu, Abubakar Sani & Majumder, Arunava & Waziri, Mohammed Yusuf & Ahmed, Kabiru, 2021. "Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 520-539.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:520-539
    DOI: 10.1016/j.matcom.2021.03.020
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    References listed on IDEAS

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    1. Milena J. Petrović & Predrag S. Stanimirović, 2014. "Accelerated Double Direction Method for Solving Unconstrained Optimization Problems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, April.
    2. Milena J. Petrović & Predrag S. Stanimirović & Nataša Kontrec & Julija Mladenović, 2018. "Hybrid Modification of Accelerated Double Direction Method," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, November.
    3. Waziri, Mohammed Yusuf & Ahmed, Kabiru & Sabi’u, Jamilu, 2019. "A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 645-660.
    4. Chuanwei Wang & Yiju Wang & Chuanliang Xu, 2007. "A projection method for a system of nonlinear monotone equations with convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 33-46, August.
    5. Mohammed Yusuf Waziri & Jamilu Sabi’u, 2015. "A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-8, September.
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    1. Najib Ullah & Abdullah Shah & Jamilu Sabi’u & Xiangmin Jiao & Aliyu Muhammed Awwal & Nuttapol Pakkaranang & Said Karim Shah & Bancha Panyanak, 2023. "A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing," Mathematics, MDPI, vol. 11(5), pages 1-26, March.

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