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Image denoising using local adaptive layered Wiener filter in the gradient domain

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Abstract

This paper presents a new image denoising algorithm. Our method is inspired by locally adaptive window-based denoising using maximum likelihood (LAWML). In the research, we find, as with wavelet coefficients, the gradient image coefficients can also be modeled as zero-mean Gaussian random variables with high local correlation. So, we implement the local adaptive Wiener filter in the gradient domain. But unlike LAWML, the layered denoising is adopted in our method. At the same time, the relation between wavelet-based and diffusion-based denoising method is disclosed further. The tests demonstrate the proposed method gets the desired results both subjectively and objectively compared to the related gradient domain algorithms and wavelet-based image denoising methods. At the same time, the tests also show the proposed method outperforms some other diffusion filters and wavelet-based methods and Non-Local means (NL-means) filter in most cases.

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References

  1. Blu T, Luisier F (2007) The SURE-LET approach to image denoising. IEEE Trans Image Process 16(11):2778–2786

    Article  MathSciNet  Google Scholar 

  2. Buades A, Coll B, Morel JM (2005) A non local algorithm for image denoising. IEEE Int Conf Comput Vis Pattern Recog 20–25:60–65

    Google Scholar 

  3. Catte F, Lions P, Morel J, Coll T (1992) Image selective smoothing and edge detection by nonlinear diffusion. SIAM J Numer Anal 29(1):182–193

    Article  MATH  MathSciNet  Google Scholar 

  4. Chao S, Tsai D (2010) An improved anisotropic diffusion model for detail and edge-preserving smoothing. Pattern Recogn Lett 31(13):2012–2023

    Article  Google Scholar 

  5. Dabov K, Foi A, Katkovnik V, Egiazarian KO (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–3745

    Article  MathSciNet  Google Scholar 

  6. Easley GR, Labate D, Colonna F (2009) Shearlet based total variation for denoising. IEEE Trans Image Process 18(2):260–268

    Article  MathSciNet  Google Scholar 

  7. Ghael SP, Sayeed AM, Baraniuk RG (1997) Improved wavelet denoising via empirical Wiener filtering. Proceedings of SPIE, San Diego, pp 389–399

    Google Scholar 

  8. Hajiaboli MR, Ahmad MO, Wang C (2012) An edge-adapting Laplacian kernel for nonlinear diffusion filters. IEEE Trans Image Process 21(4):1561–1572

    Article  MathSciNet  Google Scholar 

  9. Li HC, Fan PZ, Khan MK (2012) Context-adaptive anisotropic diffusion for image denoising. IET Electron Lett 48(14):827–829

    Article  Google Scholar 

  10. Lu J, Shi K, Min D, Lin L, Do Minh N (2012) Cross-Based Local Multipoint Filtering. IEEE Conference on Computer Vision and Pattern Recognition, Providence, RI, 16–21 June 2012, pp 430–437

  11. Luisier F, Blu T, Unser M (2007) A new SURE approach to image denoising: interscale orthonormal wavelet thresholding. IEEE Trans Image Process 6(12):593–606

    Article  MathSciNet  Google Scholar 

  12. Mihcak MK, Kozintsev I (1999) Ramchandran K. Spatially adaptive statistical modeling of wavelet image coefficients and its application to denoising. In Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing Phoenix, AZ, 15–19 Mar 1999, pp 3253–3256

  13. Perona P, Malik J (1990) Scale-Space edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639

    Article  Google Scholar 

  14. Portilla J, Strela V, Wainwright MJ, Simoncelli EP (2003) Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans Image Process 12(11):1338–1351

    Article  MATH  MathSciNet  Google Scholar 

  15. Steidl G, Weickert J, Brox T, Mrazek P, Welk M (2005) On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs. SIAM J Numer Anal 42(2):686–713

    Article  MathSciNet  Google Scholar 

  16. Sun J, Xu ZB (2010) Scale selection for anisotropic diffusion filter by Markov random field model. Pattern Recogn 43(8):2630–2645

    Article  MATH  Google Scholar 

  17. Welk M, Steidl G, Weickert J (2008) Locally analytic schemes: a link between diffusion filtering and wavelet shrinkage. Appl Comput Harmon A 24(2):195–224

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang L, Dong W, Zhang D, Shi G (2010) Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recogn 43(8):1531–1549

    Article  MATH  Google Scholar 

  19. Zhang X, Feng X (2014) Hybrid gradient-domain image denoising. Int J Electron Commun (AEU) 68(3):179–185

    Article  Google Scholar 

  20. Zhang X, Feng X (2014) Multiple-step local Wiener filter with proper stopping in wavelet domain. J Vis Commun Image R 25(2):254–262

    Article  Google Scholar 

  21. Zhang X, Feng X, Wang W, Zhang S, Dong Q (2013) Gradient-based Wiener filter for image denoising. Comput Electr Eng 39:933–943

    Google Scholar 

  22. Zhong J, Sun H (2008) Wavelet-based multiscale anisotropic diffusion with adaptive statistical analysis for image restoration. IEEE Trans Circ Syst I Regul Pap 55(9):2716–2725

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is partially supported by the National Nature Science Foundation of China (Grant Nos. 61102018 and 61271294) and Natural Science Foundation of Shaanxi Province (No. 2014JM8312) and Natural Science Foundation of Xianyang Normal University (No. 11XSYK304).

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Authors and Affiliations

  1. Institute of Graphics and Image Processing, Xianyang Normal University, Xianyang, 712000, China

    Xiaobo Zhang

  2. Department of Mathematics, Xidian University, Xi’an, 710071, China

    Xiangchu Feng

Authors
  1. Xiaobo Zhang
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  2. Xiangchu Feng
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Correspondence to Xiaobo Zhang.

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Zhang, X., Feng, X. Image denoising using local adaptive layered Wiener filter in the gradient domain. Multimed Tools Appl 74, 10495–10514 (2015). https://doi.org/10.1007/s11042-014-2182-0

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  • DOI: https://doi.org/10.1007/s11042-014-2182-0

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