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Non-monotone Boosted DC and Caputo Fractional Tailored Finite Point Algorithm for Rician Denoising and Deblurring

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Abstract

Since MRI is often corrupted by Rician noise, in medical image processing, Rician denoising and deblurring is an important research. In this work, considering the validity of the non-convex log term in the Rician denoising and deblurring model estimated by the maximum a posteriori (MAP) and total variation, we apply nmBDCA to deal with the model. A non-monotonic line search applied in nmBDCA can achieve possible growth of objective function values controlled by parameters. After that, the obtained convex problem is solved separately by alternating direction method of multipliers (ADMM). For \(u-\)subproblem in ADMM scheme, Caputo fractional derivative and tailored finite point method are applied to denoising, which retain more texture details and suppress the staircase effect. We also demonstrate the convergence of the model and perform the stability analysis on the numerical scheme. Numerical results show that our method can well improve the quality of image restoration.

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Acknowledgements

The authors would like to thank the editor and reviewers for carefully reading earlier versions of this manuscript and providing valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, 610065, China

    Kexin Sun, Youcai Xu & Minfu Feng

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  1. Kexin Sun
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  2. Youcai Xu
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Contributions

Kexin Sun: Conceptualization, Methodology, Software, Data curation, Investigation, Formal Analysis, Writing—Original Draft Youcai Xu: Data Curation, Visualization, Investigation, Supervision Minfu Feng: Conceptualization, Funding Acquisition, Resources, Supervision, Writing—Review and Editing.

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Correspondence to Minfu Feng.

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Sun, K., Xu, Y. & Feng, M. Non-monotone Boosted DC and Caputo Fractional Tailored Finite Point Algorithm for Rician Denoising and Deblurring. J Math Imaging Vis 66, 167–184 (2024). https://doi.org/10.1007/s10851-023-01168-5

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