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A modified Dai–Kou-type method with applications to signal reconstruction and blurred image restoration

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Abstract

The classical Dai–Kou scheme (SIAM J Optim 23(1):296–320, 2013), which is popularly referred to as CGOPT, represents one of the most numerically efficient methods for unconstrained optimization. This article exploits nice properties of the scheme together with the projection method to present an adaptive Dai–Kou type method for solving constrained system of nonlinear monotone equations. The new scheme utilizes the backtracking line search strategy by Zhang and Zhou (J Comput Appl Math 196:478–484, 2006) to determine the step-size in the algorithm. In addition, the scheme requires less memory to implement as it avoids computing Jacobian matrix. This attribute makes it an ideal choice for large-scale problems. Other attributes of the scheme include its ability to generate search directions that satisfy the vital condition for global convergence and its applications to signal and image reconstruction problems in compressive sensing. The global convergence of the new scheme is proved using basic assumptions and numerical experiments conducted suggests that the new approach has a clear edge over four iterative schemes in the literature.

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Acknowledgements

The authors are grateful for the helpful and constructive comments by the anonymous reviewers and editors.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Mohammed Yusuf Waziri & Kabiru Ahmed

  2. Department of mathematics, Sule Lamido University, Kafin Hausa, Nigeria

    Abubakar Sani Halilu

  3. Numerical Optimization Research Group, Bayero University, Kano, Nigeria

    Mohammed Yusuf Waziri, Kabiru Ahmed & Abubakar Sani Halilu

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  1. Mohammed Yusuf Waziri
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Correspondence to Mohammed Yusuf Waziri.

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Waziri, M.Y., Ahmed, K. & Halilu, A.S. A modified Dai–Kou-type method with applications to signal reconstruction and blurred image restoration. Comp. Appl. Math. 41, 232 (2022). https://doi.org/10.1007/s40314-022-01917-z

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