Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

A denoising algorithm via wiener filtering in the shearlet domain

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

Abstract

An image denoising algorithm via wiener filtering in the shearlet domain is proposed in this paper, it makes full use of the advantages of them. Shearlets have the features of directionality, localization, anisotropy and multiscale, the image can be decomposed more accurately, and the noise information locates at the high frequency contents in the frequency spectrum, which can help the removal of noise. The wiener filtering is based on minimizing the mean square error criteria; and it has a good performance on removing the Gaussian white noise. So the combination between them can remove noise more effectively. The noisy image is decomposed by the shearlet transform at any scales and in any directions firstly, the high and low frequency coefficients are thus acquired. And then, in the shearlet domain, the high frequency parts are filtered by wiener filtering. Finally, the inverse shearlet transform is adopted to obtain the denoised image. At the end of paper, the experiments show that the proposed algorithm could get better results than others.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Aboshosha A, Hassan M, Ashour M, El Mashade M (2009) Image denoising based on spatial filters, an analytical study. Computer Engineering & Systems, 2009. ICCES 2009. International Conference on. 245–250

  2. Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE transactions on image processing 9(9):1532–1546

    Article  MATH  MathSciNet  Google Scholar 

  3. Do MN, Vetterli M (2005) The contourlet transform: An efficient directional multiresolution image representation. IEEE Transaction on Image Processing 14(12):2091–2106

    Article  MathSciNet  Google Scholar 

  4. Easley G, Labate D, Lim W-Q (2008) Sparse directional image representations using the discrete shearlet transform. Appl Comput Harmon Anal 25:25–46

    Article  MATH  MathSciNet  Google Scholar 

  5. Eslami R, Radha H (2006) Translation-invariant contourlet transform and its application to image denoising. Image Processing, IEEE Transactions on 15(11):3362–3374

    Article  Google Scholar 

  6. Guo K, Labate D (2007) Optimally Sparse Multidimensional Representation using Shearlets. SIAM J Math Anal 39(1):298–318

    Article  MATH  MathSciNet  Google Scholar 

  7. Hu H, Sun H, Deng C, Chen X, Liu Z, Zhan H-x (2010) Image de-noising algorithm based on shearlet transform. Journal of computer application 30(6):1562–1564

    Article  Google Scholar 

  8. Jiao Licheng, Hou Biao, Wang Shuang, Liu Fang (2008) Image Multiscale Geometric Analysis: Theory and Applications. Xian Electronic Science & Technology University Press. Xi’an

  9. Kazubek M (2003) Wavelet domain image denoising by thresholding and Wiener filtering. Signal Processing Letters, IEEE 10(11):324–326

    Article  Google Scholar 

  10. Kim D, Oh H-S, Naveau P (2011) Hybrid wavelet denoising procedure of discontinuous surfaces. IET Image Process 5(8):684–692

    Article  MathSciNet  Google Scholar 

  11. Kutyniok G, Labate D (2009) Resolution of the Wavefront Set using Continuous Shearlets. Trans Amer Math Soc 361:2719–2754

    Article  MATH  MathSciNet  Google Scholar 

  12. Lee YW (1960) Statistical Theory of Communication. John Wiley and Sons, Inc., New York

    MATH  Google Scholar 

  13. Liu S-p, Fang Y (2008) Image Denosing Based on Contourlet Transform and Wiener Filter. Comput Eng 34(5):210–212, in Chinese

    MathSciNet  Google Scholar 

  14. Liu YX, Peng YH, Qu HJ, Yin Y (2007) Energy-based adaptive orthogonal FRIT and its application in image denoising. Science in China Series F: Information Sciences 50(2):212–226

    Article  MATH  MathSciNet  Google Scholar 

  15. Liu G, Zeng X, Liu Y (2012) Image denoising by random walk with restart Kernel and non-subsampled contourlet transform. IET Signal Process 6(2):148–158

    Article  MathSciNet  Google Scholar 

  16. Miao Q-g, Shi C, Xu P-f, Yang M, Shi Y-b (2011) A Novel Algorithm of Image Fusion Using Shearlets. Opt Commun 284(6):1540–1547

    Article  Google Scholar 

  17. Na Deng, Chang-sen Jiang. Selection of Optimal Wavelet Basis for Signal Denoising. 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2012). 2012.

  18. Patel VM, Easley GR, Healy DM (2009) Shearlet-Based Deconvolution. IEEE Transaction on Image Processing 18(12):2673–2684

    Article  MathSciNet  Google Scholar 

  19. Ramin Eslami, Hayder Radha. Translation-Invariant Contourlet Transform and Its Application to Image Denoising. IEEE Transaction on image processing, 15(11), NOV. 2006

  20. Shao-Wei D, Yan-Kui S, Xiao-Lin T, Ze-Sheng T (2007) Image denoising based on complex contourlet transform. Wavelet Analysis and Pattern Recognition, 2007. ICWAPR’07 International Conference on 4:1742–1747

    Google Scholar 

  21. Shearlet webpage, http://www.shearlet.org.

  22. Shui P-L (2005) Image denoising algorithm via doubly local Wiener filtering with directional windows in wavelet domain. Signal Processing Letters, IEEE 12(10):681–684

    Article  Google Scholar 

  23. Shui P-L, Zhou Z-F, Li J-X (2007) Image denoising algorithm via best wavelet packet base using Wiener cost function. Image Processing, IET 1(3):311–318

    Article  Google Scholar 

  24. Tian P, Li Q, Ma P, Niu Y (2008) A New Method Based on Wavelet Transform for Image Denoising. Journal of Image and Graphics 13(3):395–399, in Chinese

    Google Scholar 

  25. Xiaohua Zhang, Qiang Zhang, LC Jiao. Image Denoising With Non-local Means In The Shearlet Domain.

  26. Xie J-c, Zhang D-l, Xu W-l (2002) Overview on Wavelet Image Denoising. Journal of Image and Graphics 7(3):209–217, in Chinese

    Google Scholar 

  27. Xuesen Q, Jian S (1981) Engineering cybernetics. Science Publishing House, Beijing

    Google Scholar 

  28. Zhou Z-F, Shui P-L (2007) Contourlet-based image denoising algorithm using directional windows. Electron Lett 43(2):92–93

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful comments and advices which contributed much to the improvement of this paper. The work was jointly supported by the National Natural Science Foundations of China under grant No. 61072109, 61272280, 41271447, the Fundamental Research Funds for the Central Universities under grant No. K5051203020 and K5051203001, the Creative Project of the Science and Technology State of xi’an under grant No. CXY1133(1) and CXY1119(6).

Author information

Authors and Affiliations

  1. School of Computer, Xidian University, Xi’an, 710071, Shaanxi, China

    Pengfei Xu, Qiguang Miao, Xing Tang & Junying Zhang

Authors
  1. Pengfei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiguang Miao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xing Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Junying Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiguang Miao.

Appendix

Appendix

The additional test images:

Fig. 11
figure 11

The additional test images and their corresponding noisy images with σ = 50

Full size image
Fig. 12
figure 12

The PSNR performance analysis of different methods

Full size image
Fig. 13
figure 13figure 13

The results and the local enlarged images acquired by different methods

Full size image
Fig. 14
figure 14figure 14

The results and the local enlarged images acquired by STWN and STTD

Full size image
Fig. 15
figure 15

The PSNR performance analysis of STWN and STTD

Full size image
Table 4 The comparison of performances between the proposed algorithm and the denoising methods in other domains
Full size table
Table 5 The comparison of performances between STWN and STTD
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, P., Miao, Q., Tang, X. et al. A denoising algorithm via wiener filtering in the shearlet domain. Multimed Tools Appl 71, 1529–1558 (2014). https://doi.org/10.1007/s11042-012-1290-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-012-1290-y

Keywords

Search

Navigation