Skip to main content
Springer Nature Link
Log in

Gaussian mixture model learning based image denoising method with adaptive regularization parameters

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Gaussian mixture model learning based image denoising as a kind of structured sparse representation method has received much attention in recent years. In this paper, for further enhancing the denoised performance, we attempt to incorporate the gradient fidelity term with the Gaussian mixture model learning based image denoising method to preserve more fine structures of images. Moreover, we construct an adaptive regularization parameter selection scheme by combing the image gradient with the local entropy of the image. Experiment results show that our proposed method performs an improvement both in visual effects and peak signal to noise values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Beck A. (2015) On the convergence of alternating minimization for convex programming with applications to iteratively reweighted least squares and decomposition scheme. SIAM J Optim 25(1):185–209

    Article  MathSciNet  MATH  Google Scholar 

  2. Chantas G, Galatsanos N, Likas A (2005) Maximum a posteriori image restoration based on a new directional continuous edge image Prior. In: Image Processing, 2005. ICIP 2005. IEEE International Conference on. IEEE, 1, I-941-4

  3. Dabov K, Foi A, Katkovnik V et al (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095

    Article  MathSciNet  Google Scholar 

  4. Dong W, Shi G, Li X (2013) Nonlocal image restoration with bilateral variance estimation: a low-rank approach. IEEE Trans Image Process 22(2):700–711

    Article  MathSciNet  Google Scholar 

  5. Dong W, Zhang L, Shi G et al (2013) Nonlocally centralized sparse representation for image restoration. IEEE Trans Image Process 22(4):1620–1630

    Article  MathSciNet  Google Scholar 

  6. Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–3745

    Article  MathSciNet  Google Scholar 

  7. Gilboa G, Sochen N, Zeevi Y Y (2006) Variational denoising of partly textured images by spatially varying constraint. IEEE Trans Image Process 15(8):2281–2289

    Article  Google Scholar 

  8. Hu H, Froment J (2012) Nonlocal total variation for image denoising. In: 2012 Symposium on Photonics and Optoelectronics (SOPO), 1–4

  9. Jain P, Netrapalli P, Sanghavi S. (2013) Low-rank matrix completion using alternating minimization. In: Proceedings of the forty-fifth annual ACM symposium on Theory of computing, ACM, 665–674

  10. Kaganovsky Y, Degirmenci S, Han S et al (2015) Alternating minimization algorithm with iteratively reweighted quadratic penalties for compressive transmission tomography. SPIE Medical Imaging. International Society for Optics and Photonics, 94130J-94130J-10

  11. Layer T, Blaickner M et al (2015) PET image segmentation using a Gaussian mixture model and Markov random fields. EJNMMI Physics 2(1):1

    Article  Google Scholar 

  12. Liu K, Tan J, Ai L (2016) Hybrid regularizers-based adaptive anisotropic diffusion for image denoising. SpringerPlus 5(1):1

    Article  Google Scholar 

  13. Lixin Z, Deshen X (2008) Staircase effect alleviation by coupling gradient fidelity term. Image Vis Comput 26(8):1163–1170

    Article  Google Scholar 

  14. Nguyen T M, Wu Q M J (2012) Gaussian mixture model based spatial neighborhood relationships for pixel labeling problem. IEEE Trans Syst Man Cybern B Cybern 42(1):193–202

    Article  Google Scholar 

  15. Peleg T, Eldar Y C, Elad M (2012) Exploiting statistical dependencies in sparse representations for signal recovery. IEEE Trans Signal Process 60(5):2286–2303

    Article  MathSciNet  Google Scholar 

  16. Qin Y, Ma H, Chen J et al (2015) Gaussian mixture probability hypothesis density filter for multipath multitarget tracking in over-the-horizon radar. EURASIP Journal on Advances in Signal Processing 2015(1):1–18

    Article  Google Scholar 

  17. Ren J, Liu J, Guo Z (2013) Context-aware sparse decomposition for image denoising and super-resolution. IEEE Trans Image Process 22(4):1456–1469

    Article  MathSciNet  Google Scholar 

  18. Tang L, Fang Z (2016) Edge and contrast preserving in total variation image denoising. EURASIP Journal on Advances in Signal Processing 2016(1):1

    Article  MathSciNet  Google Scholar 

  19. Van Den Oord A, Schrauwen B (2014) The student-t mixture as a natural image patch prior with application to image compression. J Mach Learn Res 15(1):2061–2086

  20. Wang Y, Yang J, Yin W et al (2008) A new alternating minimization algorithm for total variation image reconstruction. SIAM J Imag Sci 1(3):248–272

    Article  MathSciNet  MATH  Google Scholar 

  21. Wen Y W, Chan R H (2012) Parameter selection for total-variation-based image restoration using discrepancy principle. IEEE Trans Image Process 21(4):1770–1781

    Article  MathSciNet  Google Scholar 

  22. Xie C C, Hu X L (2010) On a spatially varied gradient fidelity term in PDE based image denoising. 2010 3rd International Congress on Image and Signal Processing (CISP). IEEE, 2, 835–838

  23. Yan R, Shao L, Liu Y (2013) Nonlocal hierarchical dictionary learning using wavelets for image denoising. IEEE Trans Image Process 22(12):4689–4698

    Article  MathSciNet  Google Scholar 

  24. Yuan Q, Zhang L, Shen H et al (2010) Adaptive multiple-frame image super-resolution based on U-curve. IEEE Trans Image Process 19(12):3157–3170

    Article  MathSciNet  Google Scholar 

  25. Yu G, Sapiro G, Mallat S (2012) Solving inverse problems with piecewise linear estimators: From Gaussian mixture models to structured sparsity. IEEE Trans Image Process 21(5):2481–2499

    Article  MathSciNet  Google Scholar 

  26. Yuhui Z, Byeungwoo J, Danhua X, Wu QMJ, Hui Z (2015) Image segmentation by generalized hierarchical fuzzy c-means algorithm. J Intell Fuzzy Syst 28(2):961–973

    Google Scholar 

  27. Zeng Y H, Peng Z, Yang Y F (2016) A hybrid splitting method for smoothing Tikhonov regularization problem. Journal of Inequalities and Applications 2016(1):1–13

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhang J, Zhao D, Gao W (2014) Group-based sparse representation for image restoration. IEEE Trans Image Process 23(8):3336–3351

    Article  MathSciNet  Google Scholar 

  29. Zheng Y, Jeon B, Zhang J, Chen Y (2015) Adaptively determining regularization parameters in non-local total variation regularization for image denoising. Electron Lett:144–145

  30. Zheng Y, Zhang J, Wang S, Wang J, Chen Y (2012) An Improved Fast Nonlocal Means Filter Using Patch-oriented 2DPCA. International Journal of Hybrid Information Technology 5(3):33–40

    Google Scholar 

  31. Zuo Z, Zhang T, Lan X et al (2013) An adaptive non-local total variation blind deconvolution employing split Bregman iteration. Circuits, Systems, and Signal Processing 32(5):2407–2421

    Article  MathSciNet  Google Scholar 

  32. Zoran D, Weiss Y (2011) From learning models of natural image patches to whole image restoration. In: 2011 IEEE International Conference on Computer Vision (ICCV). IEEE, 479–486

Download references

Acknowledgments

This work was supported in part by the NSFC(Grants 61402234 and 61402235) and the PAPD.

Author information

Authors and Affiliations

  1. College of Math and Statistic, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Jianwei Zhang & Jing Liu

  2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Tong Li

  3. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Yuhui Zheng

  4. College of Information Engineering, Yangzhou University, Yangzhou, 215127, China

    Jin Wang

Authors
  1. Jianwei Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jing Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Tong Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Yuhui Zheng
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Jin Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jianwei Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Liu, J., Li, T. et al. Gaussian mixture model learning based image denoising method with adaptive regularization parameters. Multimed Tools Appl 76, 11471–11483 (2017). https://doi.org/10.1007/s11042-016-4214-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-016-4214-4

Keywords