Abstract
This paper presents a new anisotropic diffusion model which is based on a new diffusion coefficient for image denoising. In the proposed model, a new diffusion coefficient and a method of automatically set gradient threshold parameter are introduced into an anisotropic diffusion model, which weakens the staircasing effect and preserves fine edges in a processed image. Comparative experiments show that the new model achieves the more satisfied denoising results than the other existing models.
References
Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12:629–639
Qiao NS, Zou BJ (2013) Nonlocal orientation diffusion partial differential equation model for optics image denoising. Optik 124:1889–1891
Sun Z, Chen S, Qiao L (2014) A general non-local denoising model using multi-kernel-induced measures. Pattern Recogn 47:1751–1763
Maleki A, Narayan M, Baraniuk RG (2013) Anisotropic nonlocal means denoising. Appl Comput Harmon Anal 35:452–482
Chen S, Liu M, Zhang W, Liu J (2013) Edge preserving image denoising with a closed form solution. Pattern Recogn 46:976–988
Wang X, Yang H, Fu Z (2013) Edge structure preserving image denoising using OAGSM/NC statistical model. Digit Signal Process 23:200–212
Jin J, Yang B, Liang K, Wang X (2014) General image denoising framework based on compressive sensing theory. Comput Graph 38:382–391
Oh S, Woo H, Yun S, Kang M (2013) Non-convex hybrid total variation for image denoising. J Vis Commun Image R 24:332–344
Bao L, Robini M, Liu W, Zhu Y (2013) Structure adaptive sparse denoising for diffusion tensor MRI. Med Image Anal 17:442–457
Liu X, Huang L (2014) A new nonlocal total variation regularization algorithm for image denoising. Math Comput Simul 97:224–233
Yang M, Liang J et al (2013) Non-local means theory based Perona–Malik model for image denosing. Neurocomputing 120:262–267
Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York
Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13:600–612
Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phys D 60(1–4):259–268
Arian M, Manjari N, Richard B (2013) Anisotropic nonlocal means denoising. Appl Comput Harmon Anal 35:452–482
Wang Y, Ren W, Wang H (2013) Anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising. Comput Math Appl 66:1729–1742
Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532–1546
Somnath M, Mandal JK (2013) Wavelet based denoising of medical images using sub-band adaptive thresholding through genetic algorithm. Proc Technol 10:680–689
Elad M (2002) On the origin of the bilateral filter and ways to improve it. IEEE Trans Image Process 11:1141–1151
Yang HY, Wang XY, Qu TX, Fu ZK (2011) Image denoising using bilateral filter and Gaussian scale mixtures in shiftable complex directional pyramid domain. Comput Elect Eng 37(5):656–668
Buades A, Coll B, Morel J (2005) A non-local algorithm for image denoising. In: Proceedings of IEEE international conference on computer vision
Hu J, Luo YP (2013) Non-local means algorithm with adaptive patch size and bandwidth. Optik 124:5639–5645
Yang M, Liang J, Zhang J, Gao H, Meng F, Li X, Song S (2013) Non-local means theory based Perona–Malik model for image denosing. Neurocomputing 120:262–267
Jidesh P (2014) A convex regularization model for image restoration. Comput Elect Eng 40:66–78
Hashemi S, Beheshti S, Cobbold R, Paul N (2015) Adaptive updating of regularization parameters. Signal Process 113:228–233
Liu X (2015) Efficient algorithms for hybrid regularizers based image denoising and deblurring. Comput Math Appl 69:675–687
Chen D, Chen Y, Xue D (2015) Fractional-order total variation image denoising based on proximity algorithm. Appl Math Comput 257:537–545
Bigun J, Grandlund GH, (1987) Optimal orientation detection of linear symmetry, Proceedings 1st IEEE ICCV, London, June
Goldstein T, Osher S (2009) The split Bregman method for \(L_1\)-regularized problems. SIAM J Imag Sci 2(2):323–343
Liu K, Tan J, Su B (2014) An adaptive image denoising model based on Tikhonov and TV regularizations. Adv Multimed. doi:10.1155/2014/934834
Lysaker M, Lundervold A, Tai XC (2003) Noise removal using fourth-order partial differential equation with application to medical magnetic resonance images in space and time. IEEE Trans Image Process 12(12):1579–1590
Li ZC, Liu J, Tang J, Lu H (2015) Robust structured subspace learning for data representation. IEEE Trans Patt Anal Mach Intell 37(10):2085–2098
Acknowledgements
The authors are grateful to the anonymous reviewers and the associate editor for their valuable comments, which have greatly helped us to improve this work. This work has been supported by the Transformation Project of High-Tech Result of CQEC KJZH14207.
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Xu, Y., Yuan, J. Anisotropic diffusion equation with a new diffusion coefficient for image denoising. Pattern Anal Applic 20, 579–586 (2017). https://doi.org/10.1007/s10044-016-0590-7
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DOI: https://doi.org/10.1007/s10044-016-0590-7