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Image denoising based on the fractional-order total variation and the minimax-concave

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Abstract

The total variation model has attracted considerable attention for its good balance of noise reduction and edge maintenance, but it produces blocky effects. In this paper, a novel model for noise reduction and staircase effects elimination was proposed for images polluted by the additive white Gaussian noise, which is based on fractional-order differentiation. The new non-convex regularization term can express as the minimax-concave penalty of the fractional-order total variation (FOTV) term. The FOTV term can suppress staircase effects while preserving small-scale edges and textures information well. The non-convex regularizer can estimate the edge more accurately than the convex regularizer. We set the non-convexity parameter and the regularization parameter in the appropriate range to maintain the convexity of the proposed objective function. To effectively solve the new model, we use the alternating direction method of multipliers to minimize the objective function. Experimental results illustrate that the new model performs better than other models and yields clearer denoised images.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, China

    Xiaohui Chen & Ping Zhao

Authors
  1. Xiaohui Chen
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  2. Ping Zhao
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Contributions

Conceptualization: XC; Methodology: XC; Formal analysis and investigation: XC; Writing - original draft preparation: XC; Writing - review and editing: XC, PZ; Supervision: PZ. All authors discussed the results and contributed to the final manuscript

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Correspondence to Xiaohui Chen.

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Chen, X., Zhao, P. Image denoising based on the fractional-order total variation and the minimax-concave. SIViP 18, 1601–1608 (2024). https://doi.org/10.1007/s11760-023-02876-6

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  • DOI: https://doi.org/10.1007/s11760-023-02876-6

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