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Proximal algorithm for minimization problems in l0-regularization for nonlinear inverse problems

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Abstract

In this paper, we study a proximal method for the minimization problem arising from l0-regularization for nonlinear inverse problems. First of all, we prove the existence of solutions and give an optimality condition for solutions to the minimization problem. Then, we propose and prove the convergence of the proximal method for this minimization problem, which is controlled by step size conditions. Finally, we illustrate performance of the proximal method by applying it to a numerical example.

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Acknowledgements

The authors would like to thank all three implicit referees for their valuable comments. We have learned a lots from their comments and revised the paper to obtain the final version, which much be better than the original one.

Funding

This research was supported by Science and Technology Development Fund - Ministry of Training and Education under project B2021-DNA-15.

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Authors and Affiliations

  1. Department of Mathematics, The University of Danang - University of Science and Education, 459 Ton Duc Thang, Danang, Vietnam

    Pham Quy Muoi & Duong Xuan Hiep

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  1. Pham Quy Muoi
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  2. Duong Xuan Hiep
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Correspondence to Pham Quy Muoi.

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Muoi, P.Q., Hiep, D.X. Proximal algorithm for minimization problems in l0-regularization for nonlinear inverse problems. Numer Algor 91, 367–388 (2022). https://doi.org/10.1007/s11075-022-01266-2

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