A Global Variational Filter for Restoring Noised Images with Gamma Multiplicative Noise

Authors

  • N. Diffellah Department of Electronics, University of Biskra, Algeria | Department of Electronics, Bachir El Ibrahimi University, Algeria
  • Z. E. Baarir LESIA Laboratory, Mohamed Khider University, Algeria
  • F. Derraz Telecommunications Laboratory, Abou Bekr Belkaid University, Algeria
  • A. Taleb-Ahmed Polytechnic University of Hauts-de-France, France

Abstract

In this paper, we focus on a globally variational method to restore noisy images corrupted by multiplicative gamma noise. Our problem is assumed as a regularization problem in total variation (TV) framework with data fitting term which is deduced by maximizing the a-posteriori probability density (MAP estimation). We need to evaluate the proximal operator of a data fitting term then we numerically adapt the Douglas-Rachford (DR) splitting method to solve the problem. Our experiments use real images with different levels of noise. To validate the effectiveness of the proposed method, we compare the proposed method with other variational models. Our method shows effective suppression of noise, excellent edge preservation, and the measures of image quality such as PSNR (peak signal-to-noise ratio), VSNR (visual signal-to-noise ratio) and SSIM (structural similarity index) explain the proposed model΄s good performance.

Keywords:

multiplicative gamma noise, restoration, regularization, data fitting, total variation, MAP estimation, proximal operator, PSNR, SSIM, VSNR

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References

D. L. Donoho, I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage”, Journal of the American Statistical Association, Vol. 90, No. 432, pp. 1200-1224, 1995 DOI: https://doi.org/10.1080/01621459.1995.10476626

P. Bao, M. Zhang, “Noise reduction for magnetic resonance images via adaptive multiscale products thresholding”, IEEE Transactions on Medical Imaging, Vol. 22, No. 9, pp. 1089-1099, 2003 DOI: https://doi.org/10.1109/TMI.2003.816958

L. Zhang, R. Zhang, X. Wu, D. Zhang, “Pca-based spatially adaptive denoising of cfa images for single-sensor digital cameras”, IEEE Transactions on Image Processing, Vol. 18, No. 4, pp. 797-812, 2009 DOI: https://doi.org/10.1109/TIP.2008.2011384

S. Geman, D. Geman, “Stochastic relaxation, gibbs distributions, and the bayesian restoration of images”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, No. 6, pp. 721-741, 1984 DOI: https://doi.org/10.1109/TPAMI.1984.4767596

L. Zhang, W. Donga, D. Zhang, G. Shib, “Two-stage image denoising by principal component analysis with local pixel grouping”, Pattern Recognition, Vol. 43, No. 4, pp. 1531-1549, 2010 DOI: https://doi.org/10.1016/j.patcog.2009.09.023

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithms”, Physica D: Nonlinear Phenomena, Vol. 60, No. 1-4, pp. 259-268, 1992 DOI: https://doi.org/10.1016/0167-2789(92)90242-F

G. Aubert, P. Kornprobst, Mathematical Problems in Image Pro-cessing Partial Differential Equations and the Calculus of Variations, Springer, 2006 DOI: https://doi.org/10.1007/978-0-387-44588-5

A. Chambolle, “An algorithm for total variation minimization and applications”, Journal of Mathematical Imaging and Vision, Vol. 20, No. 1-2, pp. 89-97, 2004 DOI: https://doi.org/10.1023/B:JMIV.0000011321.19549.88

P. L. Combettes, “Solving monotone inclusions via compositions of non expansive averaged operators”, Optimization: A Journal of Mathematical Programming and Operations, Vol. 53, No. 5-6, pp. 475-504, 2004 DOI: https://doi.org/10.1080/02331930412331327157

C. Chaux, P. L. Combettes, J. C. Pesquet, V. R. Wajs, “A variational formulation for frame-based inverse problems”, Inverse Problems, Vol. 23, No. 1, pp. 1495-1518, 2007 DOI: https://doi.org/10.1088/0266-5611/23/4/008

P. L. Combettes, J. C. Pesquet, “A douglas-rachford splitting ap-proach to nonsmooth convex variational”, IEEE Journal of Selected Topics in Signal Processing, Vol. 1, No. 4, pp. 564-574, 2007. DOI: https://doi.org/10.1109/JSTSP.2007.910264

P. L. Combettes, J. C. Pesquet, “A proximal decomposition method for solving convex variational inverse problems”, Inverse Problems, Vol. 24, No. 6, pp. 065014, 2008 DOI: https://doi.org/10.1088/0266-5611/24/6/065014

J. Huang, S. Zhang, H. Li, D. Metaxas, “Composite splitting algorithms for convex optimization”, Computer Vision and Image Understanding, Vol. 115, No. 12, pp. 1610-1622, 2011 DOI: https://doi.org/10.1016/j.cviu.2011.06.011

Q. Fan, D. Jiang, Y. Jiao, “A multi-parameter regularization model for image restoration”, Signal Processing, Vol. 114, pp. 131-142, 2015 DOI: https://doi.org/10.1016/j.sigpro.2015.02.021

Y. Yu, S. Acton, “Speckle reducing anisotropic diffusion”, IEEE Transactions on Image Processing, Vol. 11, pp. 1260-1270, 2002 DOI: https://doi.org/10.1109/TIP.2002.804276

S. A. Fernandez, C. A. Lopez, “On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering”, IEEE Transactions on Image Processing, Vol. 15, No. 11, pp. 2694-2701, 2006 DOI: https://doi.org/10.1109/TIP.2006.877360

K. Krissian, C. Westin, R. Kikinis, K. Vosburgh, “Oriented speckle reducing anisotropic diffusion”, IEEE Transactions on Image Processing, Vol. 16, No. 5, pp. 1412-1424, 2007 DOI: https://doi.org/10.1109/TIP.2007.891803

G. Liu, X. Zeng, F. Tian, Z. Li, K. Chaibou, “Speckle reduction by adaptive window anisotropic diffusion”, Signal Processing, Vol. 89, No. 11, pp. 2233-2243, 2009 DOI: https://doi.org/10.1016/j.sigpro.2009.04.042

A. Buades, B. Coll, J. M. Morel, “A review of image denoising algorithms, with a new one”, SIAM Journal on Multiscale Modeling and Simulation, Vol. 4, No. 2, pp. 490-530, 2005 DOI: https://doi.org/10.1137/040616024

C. A. Deledalle, L. Denis, F. Tupin, “Iterative weighted maximum likelihood denoising with probabilistic patchbased weights”, IEEE Transactions on Image Processing, Vol. 18, No. 12, pp. 2661-2672, 2009 DOI: https://doi.org/10.1109/TIP.2009.2029593

L. Rudin, P. L. Lions, S. Osher, “Multiplicative denoising and deblurring: Theory and algorithms”, in: Geometric Level Set Methods in Imaging, Vision, and Graphics, Springer, 2003

G. Aubert J. F. Aujol, “A variational approach to removing multiplicative noise”, SIAM Journal on Applied Mathematics, Vol. 68, No. 4, pp. 925-946, 2008 DOI: https://doi.org/10.1137/060671814

J. Shi, S. Osher, “A nonlinear inverse scale space method for a convex multiplicative noise model”, SIAM Journal on Imaging Sciences, Vol. 1, No. 4, pp. 294-321, 2008 DOI: https://doi.org/10.1137/070689954

Y. M. Huang, M. K. Ng, Y. W. Wen, “A new total variation method for multiplicative noise removal”, SIAM Journal on Imaging Sciences, Vol. 2, No. 1, pp. 20-40, 2009. DOI: https://doi.org/10.1137/080712593

R. Bernardes, C. Maduro, P. Serranho, A. Arajo, S. Barbeiro, J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter”, Optics Express, Vol. 18, No. 23, pp. 24 048-24 059, 2010 DOI: https://doi.org/10.1364/OE.18.024048

Y. Dong, T. Zeng, “A convex variational model for restoring blurred images with multtiplicative noise”, SIAM Journal on Imaging Sciences, Vol. 6, No. 3, pp. 1598-1625, 2013 DOI: https://doi.org/10.1137/120870621

X. L. Zhao, F. Wang, M. K. Ng, “A new convex optimization model for multiplicative noise and blur removal”, SIAM Journal on Imaging Sciences, Vol. 7, No. 1, pp. 456-475, 2014 DOI: https://doi.org/10.1137/13092472X

Y. Han, C. Xu, G. Baciu, X. Feng, “Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer”, International Journal of Computer Mathematics, Vol. 91, No. 10, pp. 2243–2259, 2014

Y. Hao, J. Xu, “An effective dual method for multiplicative noise removal”, Journal of Visual Communication and Image Representation, Vol. 25, No. 2, pp. 306-312, 2014 DOI: https://doi.org/10.1016/j.jvcir.2013.11.004

Y. Han, C. Xu, G. Baciu, X. Feng, “Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer”, International Journal of Computer Mathematics, Vol. 91, No. 10, pp. 2243-2259, 2014 DOI: https://doi.org/10.1080/00207160.2013.871002

J. Lu, L. Shen, C. Xu, Y. Xu, “Multiplicative noise removal in imaging: An exp-model and its fixed-point proximity algorithm”, Applied and Computational Harmonic Analysis, Vol. 41, No. 2, pp. 518-539, 2016 DOI: https://doi.org/10.1016/j.acha.2015.10.003

A. Ullah, W. Chen, M. A. Khan, H. G. Sun, “A new variational approach for multiplicative noise and blur removal”, PLoS One, Vol. 12, No. 1, pp. e0161787, 2017 DOI: https://doi.org/10.1371/journal.pone.0161787

P. L. Combettes, V. R. Wajs, “Signal recovery by proximal forward backward splitting”, SIAM Journal on Multiscale Modeling & Simulation, Vol. 4, No. 4, pp. 1168-1200, 2005 DOI: https://doi.org/10.1137/050626090

H. H. Bauschke, R. S. Burachik, P. L. Combettes, V. Elser, D. Rusel Luke, H. Wolkowicz, Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer, 2011 DOI: https://doi.org/10.1007/978-1-4419-9569-8

D. M. Chandler, S. S. Hemami, “Vsnr: A wavelet-based visual signal-to-noise ratio for natural images”, IEEE Transactions on Image Processing, Vol. 16, No. 9, pp. 2284-2298, 2007 DOI: https://doi.org/10.1109/TIP.2007.901820

Z. Wang, A. Bovik, H. Sheikh, E. Simoncelli, “Image quality assessment: From error visibility to structural similarity”, IEEE Transactions on Image Processing, Vol. 13, No. 4, pp. 600-612, 2004 DOI: https://doi.org/10.1109/TIP.2003.819861

M. V. Sarode, P. R. Deshmukhnn, “Image sequence denoising with motion estimation in color image sequences”, Engineering, Technology & Applied Science Research, Vol. 1, No. 6, pp. 139-143, 2011 DOI: https://doi.org/10.48084/etasr.54

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How to Cite

[1]
N. Diffellah, Z. E. Baarir, F. Derraz, and A. Taleb-Ahmed, “A Global Variational Filter for Restoring Noised Images with Gamma Multiplicative Noise”, Eng. Technol. Appl. Sci. Res., vol. 9, no. 3, pp. 4188–4195, Jun. 2019.

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