- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 834035, 13 pages
A Fast High-Order Total Variation Minimization Method for Multiplicative Noise Removal
1School of Science, Huaihai Institute of Technology, Lianyungang, Jiangsu 222005, China
2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
Received 17 October 2012; Revised 10 March 2013; Accepted 13 March 2013
Academic Editor: Fatih Yaman
Copyright © 2013 Xiao-Guang Lv et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- 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.
- 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.
- M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, London, UK, 1998.
- T. F. Chan and J. Shen, Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods, SIAM, Philadelphia, Pa, USA, 2005.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- P. J. Green, “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination,” Biometrika, vol. 82, no. 4, pp. 711–732, 1995.
- C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, SciTech Publishing, 2004.
- J. Goodman, “Some fundamental properties of speckle,” Journal of the Optical Society of America, vol. 66, pp. 1145–1150, 1976.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- G. Steidl, “A note on the dual treatment of higher-order regularization functionals,” Computing, vol. 76, no. 1-2, pp. 135–148, 2006.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- K. Papafitsoros and C. B. Schönlieb, “A combined first and second order variational approach for image reconstruction,” http://arxiv.org/abs/1202.6341.
- D. P. Bertsekas, A. Nedic, and E. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, Belmont, Mass, USA, 2003.
- 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.
- 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.
- 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.