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Image Multiplicative Denoising Using Adaptive Euler’s Elastica as the Regularization

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Abstract

Variational models involving Euler’s elastica energy have been widely used in many fields of digital image processing, such as image inpainting and additive Gaussian noise removal. In this paper, according to the signal dependence of multiplicative noise, the Euler’s elastica functional is modified to adapt for the multiplicative denoising problem. And a novel multiplicative noise removal model based on adaptive Euler’s elastica is proposed. Furthermore, we develope two fast numerical algorithms to solve this high-order nonlinear model: Aiming at the evolution case of Euler–Lagrange equation, a semi-implicit iterative scheme is designed and the additive operator splitting algorithm is used to speed up the calculation; Expanding the augmented Lagrangian algorithm that has been successfully applied in recent years, we obtain a restricted proximal augmented Lagrangian method. Numerical experiments show the effectiveness of the two algorithms and the significant advantages of our model over the standard total variation denoising model in alleviating the staircase effect and restoring the tiny geometrical structures, especially, the line-like feature.

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Funding

This work is supported by “the National Natural Science Foundation of China” (Grant Nos. 71773024, 12171123, 11871133, 11971131, U1637208, 61873071, 51476047), “the Natural Science Foundation of Hei longjiang Province of China” (Grant Nos. G2018006, LC2018001), “the Heilongjiang Postdoctoral Spmental Fund” (LBH-Q18064), “Guangdong Basic and Applied Basic Research Foundation” (2020B1515310010).

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Yu Zhang, Zhichang Guo & Boying Wu

  2. School of Economy and Management, Harbin Institute of Technology, Harbin, 150001, China

    Songsong Li

  3. Department of Computer Science, Mathematics, Physics and Statistics, The University of British Columbia - Okanagan, Kelowna, BC, V1V 1V7, Canada

    Shan Du

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  1. Yu Zhang
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Correspondence to Zhichang Guo.

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The second author is supported by “the National Natural Science Foundation of China” (Grant No. 71773024), “the Natural Science Foundation of Heilongjiang Province of China” (Grant No. G2018006), “the Heilongjiang Postdoctoral Scientific Research Developmental Fund” (LBHQ18064). The third author is supported by “the National Natural Science Foundation of China” (Grant Nos. 12171123, 11971131, 11871133), “the Natural Science Foundation of Heilongjiang Province of China” (Grant No. LC2018001), “Guangdong Basic and Applied Basic Research Foundation” (2020B1515310010). The last author is supported by “the National Natural Science Foundation of China” (Grant Nos. 11971131, U1637208, 61873071, 51476047), “Guangdong Basic and Applied Basic Research Foundation” (2020B1515310010)

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Zhang, Y., Li, S., Guo, Z. et al. Image Multiplicative Denoising Using Adaptive Euler’s Elastica as the Regularization. J Sci Comput 90, 69 (2022). https://doi.org/10.1007/s10915-021-01721-7

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  • DOI: https://doi.org/10.1007/s10915-021-01721-7

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