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A Spectral Gradient Projection Method for Sparse Signal Reconstruction in Compressive Sensing

Author

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  • Auwal Bala Abubakar
  • Kanikar Muangchoo
  • Auwal Muhammad
  • Abdulkarim Hassan Ibrahim

Abstract

In this paper, a new spectral gradient direction is proposed to solve the l1 -regularized convex minimization problem. The spectral parameter of the proposed method is computed as a convex combination of two existing spectral parameters of some conjugate gradient method. Moreover, the spectral gradient method is applied to the resulting problem at each iteration without requiring the Jacobian matrix. Furthermore, the proposed method is shown to have converge globally under some assumptions. Numerically, the proposed method is efficient and robust in terms of its quality in reconstructing sparse signal and low computational cost compared to the existing methods.

Suggested Citation

  • Auwal Bala Abubakar & Kanikar Muangchoo & Auwal Muhammad & Abdulkarim Hassan Ibrahim, 2020. "A Spectral Gradient Projection Method for Sparse Signal Reconstruction in Compressive Sensing," Modern Applied Science, Canadian Center of Science and Education, vol. 14(5), pages 1-86, May.
    • Handle: RePEc:ibn:masjnl:v:14:y:2020:i:5:p:86
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    Cited by:

    1. Abubakar, Auwal Bala & Kumam, Poom & Ibrahim, Abdulkarim Hassan & Chaipunya, Parin & Rano, Sadiya Ali, 2022. "New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 670-683.

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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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