A new efficient variational model for multiplicative noise removal

References

• G. Aubert and J.F. Aujol, A variational approach to remove multiplicative noise, SIAM J. Appl. Math. 68 (2008), pp. 925–946. doi: 10.1137/060671814
   Web of Science ®Google Scholar
• J.M. Bioucas-Dias and M.A.T. Figueiredo, Multiplicative noise removal using variable splitting and constrained optimization, IEEE Trans. Image Process. 19 (2010), pp. 1720–1730. doi: 10.1109/TIP.2010.2045029
   PubMed Web of Science ®Google Scholar
• S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Found. Trends Mach. Learning 3 (2010), pp. 1–122. doi: 10.1561/2200000016
   Google Scholar
• K. Bredies, K. Kunisch, and T. Pock, Total generalized variation, SIAM J. Imaging Sci. 3(3) (2010), pp. 92–526. doi: 10.1137/090769521
   Web of Science ®Google Scholar
• A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis. 40(1) (2011), pp. 120–145. doi: 10.1007/s10851-010-0251-1
   Web of Science ®Google Scholar
• J. Darbon, M. Sigelle, and F. Tupin, A note on nice-levelable MRFs for SAR image denoising with contrast preservation, Tech. Rep., 2006.
   Google Scholar
• Y. Dong and T.Y. Zeng, A convex variational model for restoring blurred images with multiplicative noise, SIAM J. Imaging Sci. 6(3) (2013), pp. 1598–1625. doi: 10.1137/120870621
   Web of Science ®Google Scholar
• P. Escande, P. Weiss, and W. Zhang, A variational model for multiplicative structured noise removal, J. Math. Imaging Vis. 57 (2016), pp. 1–13.
   PubMed Web of Science ®Google Scholar
• M. Figueiredo and J. Bioucas-Dias, Restoration of Poissonian images using alternating direction optimization, IEEE Trans. Image Process. 19 (2010), pp. 3133–3145. doi: 10.1109/TIP.2010.2053941
   PubMed Web of Science ®Google Scholar
• Y.M. Gao, F. Liu, and X.P. Yang, Total generalized variation restoration with non-quadratic fidelity, Multidimens. Syst. Signal Process. 29 (2018), pp. 1459–1484. doi: 10.1007/s11045-017-0512-x
   Web of Science ®Google Scholar
• P. Getreuer, M. Tong, and L. Vese, A variational model for the restoration of MR images corrupted by blur and Rician noise, Advances in Visual Computing, Las Vegas, NV, 2011, pp. 686–698.
   Google Scholar
• T. Goldstein and S. Osher, The split Bregman algorithm for L1 regularized problems, SIAM J. Imaging Sci. 2 (2009), pp. 323–343. doi: 10.1137/080725891
   Web of Science ®Google Scholar
• G. Grimmett and D. Welsh, Probability: An Introduction, Oxford Science Publications, 1986.
   Google Scholar
• J. Huang and X.P. Yang, Fast reduction of speckle noise in real ultrasound images, Signal Process. 93(4) (2013), pp. 684–694. doi: 10.1016/j.sigpro.2012.09.005
   Web of Science ®Google Scholar
• Y.M. Huang, M.K. Ng, and Y.W. Wen, A new total variation method for multiplicative noise removal, SIAM J. Imaging Sci. 2 (2009), pp. 20–40. doi: 10.1137/080712593
   Web of Science ®Google Scholar
• Y.M. Huang, D.Y. Lu, and T.Y. Zeng, Two-step approach for the restoration of images corrupted by multiplicative noise, SIAM J. Sci. Comput. 35(6) (2013), pp. 2856–2873. doi: 10.1137/120898693
   Web of Science ®Google Scholar
• Y.M. Huang, H.Y. Yan, and T.Y. Zeng, Multiplicative noise removal based on unbiased box-Cox transformation, Commun. Comput. Phys. 22(3) (2017), pp. 803–828. doi: 10.4208/cicp.OA-2016-0074
   Web of Science ®Google Scholar
• L. Jiang, J. Huang, X.G. Lv, and J. Liu, Alternating direction method for the high-order total variation-based Poisson noise removal problem, Numer. Algorithms 69 (2015), pp. 495–516. doi: 10.1007/s11075-014-9908-y
   Web of Science ®Google Scholar
• Z.M. Jin and X.P. Yang, A variational model to remove the multiplicative noise in ultrasound images, J. Math. Imaging Vis. 39 (2011), pp. 62–74. doi: 10.1007/s10851-010-0225-3
   Web of Science ®Google Scholar
• P. Kornprobst, R. Deriche, and G. Aubert, Image sequence analysis via partial differential equations, J. Math. Imaging Vis. 11(1) (1999), pp. 5–26. doi: 10.1023/A:1008318126505
   Web of Science ®Google Scholar
• X. Liu and L. Huang, Poissonian image reconstruction using alternating direction algorithm, J. Electron. Imaging 22 (2013), p. 033007.
   Web of Science ®Google Scholar
• J. Lu, L. Shen, C. Xu, and Y. Xu, Multiplicative noise removal in imaging: An exp-model and its fixed-point proximity algorithm, J. Math. Imaging Vis. 41(2) (2016), pp. 518–539.
   Google Scholar
• T. Pock, D. Cremers, H. Bischof, and A. Chambolle, An algorithm for minimizing the Mumford-Shah functional, Proceedings of the 12th IEEE Int'l Conf. Computer Vision, 2009, pp. 1133–1140.
   Google Scholar
• L. Rudin, P. Lions, and S. Osher, Multiplicative denoising and deblurring: Theory and algorithms, in Geometric Level Sets in Imaging, Vision, and Graphics, S. Osher and N. Paragios, eds., Springer, New York, NY, 2003, pp. 103–119.
   Google Scholar
• L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. Rev. D 60 (1992), pp. 259–268.
   Google Scholar
• J. Shi and S. Osher, A nonlinear inverse scale space method for a convex multiplicative noise model, SIAM J. Imaging Sci. 1 (2008), pp. 294–321. doi: 10.1137/070689954
   Web of Science ®Google Scholar
• G. Steidl and T. Teuber, Removing multiplicative noise by Douglas-Rachford splitting methods, J. Math. Imaging Vis. 36 (2010), pp. 168–184. doi: 10.1007/s10851-009-0179-5
   Web of Science ®Google Scholar
• A. Tikhonov and V. Arsenin, Solution of Ill-Posed Problems, V. H. Winston, Washington, DC, 1977.
   Google Scholar
• C. Wu and X. Tai, Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF vectorial TV and high order models, SIAM J. Imaging Sci. 3(3) (2012), pp. 300–339. doi: 10.1137/090767558
   Web of Science ®Google Scholar