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Total variation image reconstruction algorithm based on non-convex function

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Abstract

The total variation method has been widely used because it can preserve important sharp edges and target boundaries in the image, but one of its shortcomings is that the \(L_{1}\) norm would cause excessive punishment. To overcome excessive penalization, suppress step effects, and maintain a clean contour, this article introduces the \(L_{q}\) non-convex function to design a new regularization term and proposes a new non-convex variational model. For non-convex variational optimization problems, the algorithm employs the alternating direction method of multipliers to obtain optimal approximate solutions, and rigorous convergence proofs are provided based on rich mathematical theory. By comparing with advanced fractional-order and other total variation recovery algorithms, it can be observed that this algorithm achieves better visual effects and quantitative analysis results on images with complex texture structures.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Interested researchers can contact the author [contact email] to obtain the corresponding data and code.

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Funding

Funding for this study was received from the National Natural Science Foundation of China (12361037) and the High Quality Postgraduate Courses of Yunnan Province (109920210027).

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Authors and Affiliations

  1. Department of Mathematics, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China

    Shaojiu Bi, Minmin Li, Guangcheng Cai & Xi Zhang

Authors
  1. Shaojiu Bi
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  2. Minmin Li
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  3. Guangcheng Cai
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  4. Xi Zhang
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Contributions

BS, CG and LM contributed to conceptualization, software, data curation and supervision; BS was responsible for methodology, formal analysis, investigation, resources, writing-original draft, writing-review and editing and project administration; BS and CG were involved in validation; BS and ZX took part in visualization; and CG acquired in funding. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Guangcheng Cai.

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Bi, S., Li, M., Cai, G. et al. Total variation image reconstruction algorithm based on non-convex function. SIViP (2024). https://doi.org/10.1007/s11760-024-03089-1

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  • DOI: https://doi.org/10.1007/s11760-024-03089-1

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