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Image denoising based on mixed total variation regularization with decision-making scheme

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Abstract

The denosing method based on total variation has achieved a remarkable denoising performance. However, it usually generates some staircase effects. To overcome the defect of total variation, a novel image denoising method based on total variation is proposed for improving image quality. The present research contains two contributions. Firstly, the mixed total variation model is proposed to suppress staircase effects. Secondly, the optimal threshold and the regularization parameter are all achieved by the decision-making scheme rather than experience. The difference is that the regularization parameter is achieved by the generalized cross-validation approach and the optimal threshold is achieved by the estimated standard deviation of noise. Experiments on some synthetic noisy images and the noisy images on TID2008 database demonstrate that our method is superior to state-of-the-art denoising method in terms of visual quality and objective evaluation.

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References

  1. Antoni B, Coll B, Morel JM (2005) A review of image denoising algorithms, with a new one. SIAM Journal on Multiscale Modeling and Simulation 4(2):490–530

    Article  MathSciNet  Google Scholar 

  2. Brox T, Kleinschmidt O, Cremers D (2008) Efficient nonlocal means for denoising of textural patterns. IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 17(7):1083–1092

    Article  MathSciNet  Google Scholar 

  3. Chen D, Sheng H, Chen Y, Xue D (2013) Fractional-order variational optical flow model for motion estimation. Philos Trans 371(1990):20120148

    Article  Google Scholar 

  4. Chen Y, Tao J, Wang J et al (2019) The novel sensor network structure for classification processing based on the machine learning method of the ACGAN. Sensors 19(14):3145

    Article  Google Scholar 

  5. David LD, Iain MJ (1995) Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc 90(432):1200–1224

    Article  MathSciNet  Google Scholar 

  6. Donoho DL, Johnstone IM (1994) Ideal spatial adaptation via wavelet shrinkage. Biometrika 81:425–455

    Article  MathSciNet  Google Scholar 

  7. Gabriela G, Batard T, Marcelo B et al (2016) A decomposition framework for image Denoising algorithms. IEEE Transactions Image Processing 25(1):388–399

    Article  MathSciNet  Google Scholar 

  8. Garnett R, Huegerich T, Chui C, He W (2005) A universal noise removal algorithm with an impulse detector. IEEE Trans Image Process 14(11):1747–1754

    Article  Google Scholar 

  9. Golub GH, Heath M, Wahba G (1979) Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter. Technometrics 21(2):215–223

    Article  MathSciNet  Google Scholar 

  10. Iglesias JA, Mercier G, Scherzer O (2018) A note on convergence of solutions of total variation regularized linear inverse problems. Inverse Problems 34(5)

  11. Jeong HK, Farhan A, Kwang NC (2017) Image denoising feedback framework using split Bregman approach. Expert Syst Appl 87:252–266

    Article  Google Scholar 

  12. Li H, Suen CY (2016) A novel Non-local means image denoising method based on grey theory. Pattern Recogn 49:237–248

    Article  Google Scholar 

  13. Luisier F, Blu T, Unser M (2007) A new SURE approach to image Denoising: Interscale orthonormal wavelet Thresholding. IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 16(3):593–606

    Article  MathSciNet  Google Scholar 

  14. Nguyen MP, Chun SY (2017) Bounded Self-Weights Estimation Method for Non-Local Means Image Denoising Using Minimax Estimators. IEEE Trans Image Process 26(4):1637–1649

    Article  MathSciNet  Google Scholar 

  15. Ren C, He X, Nguyen TQ (2016) Single Image Super-Resolution via Adaptive High-Dimensional Non-Local Total Variation and Adaptive Geometric Feature. IEEE Trans Image Process 26(1):90–106

    MathSciNet  MATH  Google Scholar 

  16. Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D Nonlinear Phenomena 60(1–4):259–268

    Article  MathSciNet  Google Scholar 

  17. Shahdoosti HR, Hazavei SM (2017) Combined ripplet and total variation image denoising methods using twin support vector machines. Multimed Tools Appl (12):1–19

  18. TID2008(Tampere image database): http://www.ponomarenko.info/tid2008.htm

  19. Tran-Dinh Q (2017) Adaptive smoothing algorithms for nonsmooth composite convex minimization. Comput Optim Appl 66(3):425–451

    Article  MathSciNet  Google Scholar 

  20. Wu L, Chen Y, Jin J et al (2017) Four-directional fractional-order total variation regularization for image denoising. Journal of Electronic Imaging 26(5): 053003):1–13

    Article  Google Scholar 

  21. Xie L, Shen J, Han J et al (2017) Dynamic multi-view hashing for online image retrieval. Twenty-Sixth International Joint Conference on Artificial Intelligence

  22. Yao S, Chang Y, Qin X et al (2018) Principal component dictionary-based patch grouping for image denoising. J Vis Commun Image Represent 50:111–122

    Article  Google Scholar 

  23. You YL, Kaveh M (2000) Fourth-order partial differential equations for noise removal. IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 9(10):1723–1730

    Article  MathSciNet  Google Scholar 

  24. Zhang J, Wei Z (2011) A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising. Appl Math Model 35(5):2516–2528

    Article  MathSciNet  Google Scholar 

  25. Zhou LY, Tang JX (2017) Fraction-order total variation blind image restoration based on L1-norm. Appl Math Model 51:469–476

    Article  MathSciNet  Google Scholar 

  26. Zhu L, Shen J, Xie L et al (2017) Unsupervised visual hashing with semantic assistant for content-based image retrieval. IEEE Trans Knowl Data Eng 29(2):472–486

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the editor and anonymous reviewers for their helpful comments and valuable suggestions.

Funding

This work is supported by National Natural Science Foundation of China (61901059) and Hubei Provincial Natural Science Foundation of China (2019CFB233).

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Authors and Affiliations

  1. Electronics and Information School, Yangtze University, Jingzhou, Hubei, China

    Luoyu Zhou

  2. University of Huddersfield, Huddersfield, UK

    Tao Zhang

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  1. Luoyu Zhou
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  2. Tao Zhang
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Correspondence to Luoyu Zhou.

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Zhou, L., Zhang, T. Image denoising based on mixed total variation regularization with decision-making scheme. Multimed Tools Appl 79, 7543–7557 (2020). https://doi.org/10.1007/s11042-019-08531-y

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  • DOI: https://doi.org/10.1007/s11042-019-08531-y

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