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Linked References

1. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D, vol. 60, no. 1–4, pp. 259–268, 1992. View at Google Scholar · View at Scopus
2. A. Chambolle and P.-L. Lions, “Image recovery via total variation minimization and related problems,” Numerische Mathematik, vol. 76, no. 2, pp. 167–188, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
3. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, London, UK, 1998. View at MathSciNet
4. T. F. Chan and J. Shen, Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods, SIAM, Philadelphia, Pa, USA, 2005. View at MathSciNet
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. View at Publisher · View at Google Scholar · View at MathSciNet
6. T. F. Chan, S. Esedoglu, and F. E. Park, “Image decomposition combining staircase reduction and texture extraction,” Journal of Visual Communication and Image Representation, vol. 18, no. 6, pp. 464–486, 2007. View at Publisher · View at Google Scholar · View at Scopus
7. S. Hu, Z. Liao, and W. Chen, “Image denoising based on dilated singularity prior,” Mathematical Problems in Engineering, vol. 2012, Article ID 767613, 15 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
8. S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Mathematical Problems in Engineering, vol. 2010, Article ID 750352, 14 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
9. S. Becker, J. Bobin, and E. J. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences, vol. 4, no. 1, pp. 1–39, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
10. A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Transactions on Image Processing, vol. 18, no. 11, pp. 2419–2434, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
11. Y. L. Wang, J. F. Yang, W. T. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM Journal on Imaging Sciences, vol. 1, no. 3, pp. 248–272, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
12. L. Xiao, L. L. Huang, and Z. H. Wei, “A weberized total variation regularization-based image multiplicative noise removal algorithm,” Eurasip Journal on Advances in Signal Processing, vol. 2010, Article ID 490384, 2010. View at Publisher · View at Google Scholar · View at Scopus
13. S. Durand, J. Fadili, and M. Nikolova, “Multiplicative noise removal using L1 fidelity on frame coefficients,” Journal of Mathematical Imaging and Vision, vol. 36, no. 3, pp. 201–226, 2010. View at Publisher · View at Google Scholar · View at Scopus
14. P. J. Green, “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination,” Biometrika, vol. 82, no. 4, pp. 711–732, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
15. C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, SciTech Publishing, 2004.
16. J. Goodman, “Some fundamental properties of speckle,” Journal of the Optical Society of America, vol. 66, pp. 1145–1150, 1976. View at Publisher · View at Google Scholar
17. L. Rudin, P.-L. 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., pp. 103–119, Springer, New York, NY, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
18. G. Aubert and J.-F. Aujol, “A variational approach to removing multiplicative noise,” SIAM Journal on Applied Mathematics, vol. 68, no. 4, pp. 925–946, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
19. Y.-M. Huang, M. K. Ng, and 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. View at Publisher · View at Google Scholar · View at MathSciNet
20. J. M. Bioucas-Dias and M. A. T. Figueiredo, “Multiplicative noise removal using variable splitting and constrained optimization,” IEEE Transactions on Image Processing, vol. 19, no. 7, pp. 1720–1730, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
21. G. Steidl and T. Teuber, “Removing multiplicative noise by Douglas-Rachford splitting methods,” Journal of Mathematical Imaging and Vision, vol. 36, no. 2, pp. 168–184, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
22. T. Chan, A. Marquina, and P. Mulet, “High-order total variation-based image restoration,” SIAM Journal on Scientific Computing, vol. 22, no. 2, pp. 503–516, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
23. M. Lysaker, A. Lundervold, and X. C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Transactions on Image Processing, vol. 12, no. 12, pp. 1579–1590, 2003. View at Publisher · View at Google Scholar · View at Scopus
24. G. Steidl, “A note on the dual treatment of higher-order regularization functionals,” Computing, vol. 76, no. 1-2, pp. 135–148, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
25. B. Chen, J.-L. Cai, W.-S. Chen, and Y. Li, “A multiplicative noise removal approach based on partial differential equation model,” Mathematical Problems in Engineering, vol. 2012, Article ID 242043, 14 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
26. J. Zhang, Z. H. Wei, and L. Xiao, “Adaptive fractional-order multi-scale method for image denoising,” Journal of Mathematical Imaging and Vision, vol. 43, no. 1, pp. 39–49, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
27. S. Lefkimmiatis, A. Bourquard, and M. Unser, “Hessian-based norm regularization for image restoration with biomedical applications,” IEEE Transactions on Image Processing, vol. 21, no. 3, pp. 983–995, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
28. H.-Z. Chen, J.-P. Song, and X.-C. Tai, “A dual algorithm for minimization of the LLT model,” Advances in Computational Mathematics, vol. 31, no. 1–3, pp. 115–130, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
29. Y. Hu and M. Jacob, “Higher degree total variation (HDTV) regularization for image recovery,” IEEE Transactions on Image Processing, vol. 21, no. 5, pp. 2559–2571, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
30. F. Li, C. M. Shen, J. S. Fan, and C. L. Shen, “Image restoration combining a total variational filter and a fourth-order filter,” Journal of Visual Communication and Image Representation, vol. 18, no. 4, pp. 322–330, 2007. View at Publisher · View at Google Scholar · View at Scopus
31. M. Lysaker and X. C. Tai, “Iterative image restoration combining total variation minimization and a second-order functional,” International Journal of Computer Vision, vol. 66, no. 1, pp. 5–18, 2006. View at Publisher · View at Google Scholar · View at Scopus
32. K. Papafitsoros and C. B. Schönlieb, “A combined first and second order variational approach for image reconstruction,” http://arxiv.org/abs/1202.6341.
33. D. P. Bertsekas, A. Nedic, and E. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, Belmont, Mass, USA, 2003. View at MathSciNet
34. C. L. Byne, “Alternating minimization as sequential unconstrained minimization: a survey,” Journal of Optimization Theory and Applications, vol. 156, no. 3, pp. 554–566, 2012. View at Google Scholar
35. H. H. Bauschke, P. L. Combettes, and D. Noll, “Joint minimization with alternating Bregman proximity operators,” Pacific Journal of Optimization, vol. 2, no. 3, pp. 401–424, 2006. View at Google Scholar · View at MathSciNet
36. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600–612, 2004. View at Publisher · View at Google Scholar · View at Scopus