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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 10 — Oct. 1, 2013
  • pp: 1956–1966

High-order total variation-based multiplicative noise removal with spatially adapted parameter selection

Jun Liu, Ting-Zhu Huang, Zongben Xu, and Xiao-Guang Lv  »View Author Affiliations

JOSA A, Vol. 30, Issue 10, pp. 1956-1966 (2013)

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Multiplicative noise is one common type of noise in imaging science. For coherent image-acquisition systems, such as synthetic aperture radar, the observed images are often contaminated by multiplicative noise. Total variation (TV) regularization has been widely researched for multiplicative noise removal in the literature due to its edge-preserving feature. However, the TV-based solutions sometimes have an undesirable staircase artifact. In this paper, we propose a model to take advantage of the good nature of the TV norm and high-order TV norm to balance the edge and smoothness region. Besides, we adopt a spatially regularization parameter updating scheme. Numerical results illustrate the efficiency of our method in terms of the signal-to-noise ratio and structure similarity index.

© 2013 Optical Society of America

OCIS Codes
(030.4280) Coherence and statistical optics : Noise in imaging systems
(030.6140) Coherence and statistical optics : Speckle
(100.2000) Image processing : Digital image processing
(100.3020) Image processing : Image reconstruction-restoration
(280.6730) Remote sensing and sensors : Synthetic aperture radar

ToC Category:
Image Processing

Original Manuscript: May 6, 2013
Revised Manuscript: July 20, 2013
Manuscript Accepted: July 25, 2013
Published: September 10, 2013

Jun Liu, Ting-Zhu Huang, Zongben Xu, and Xiao-Guang Lv, "High-order total variation-based multiplicative noise removal with spatially adapted parameter selection," J. Opt. Soc. Am. A 30, 1956-1966 (2013)

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  1. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. Rev. D 60, 259–268 (1992).
  2. D. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995). [CrossRef]
  3. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20, 89–97 (2004). [CrossRef]
  4. A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model Simul. 4, 490–530 (2005). [CrossRef]
  5. A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express 18, 8338–8352 (2010). [CrossRef]
  6. C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images (SciTech Publishing, Inc., 2004).
  7. P. J. Green, “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination,” Biometrika 82, 711–732 (1995). [CrossRef]
  8. S. Yun and H. Woo, “A new multiplicative denoising variational model based on m-th root transformation,” IEEE Trans. Image Process. 21, 2523–2533 (2012). [CrossRef]
  9. J. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).
  10. J. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976). [CrossRef]
  11. S. Q. Huang, D. Z. Liu, G. Q. Gao, and X. J. Guo, “A novel method for speckle noise reduction and ship target detection in SAR images,” Pattern Recogn. 42, 1533–1542 (2009). [CrossRef]
  12. 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, 2003), pp. 103–119.
  13. G. Aubert and J. F. Aujol, “A variational approach to remove multiplicative noise,” SIAM J. Appl. Math. 68, 925–946 (2008). [CrossRef]
  14. J. Shi and S. Osher, “A nonlinear inverse scale space method for a convex multiplicative noise model,” SIAM J. Imag. Sci. 1, 294–321 (2008). [CrossRef]
  15. Y. Huang, M. Ng, and Y. Wen, “A new total variation method for multiplicative noise removal,” SIAM J. Imag. Sci. 2, 20–40 (2009). [CrossRef]
  16. J. Bioucas-Dias and M. Figueiredo, “Multiplicative noise removal using variable splitting and constrained optimization,” IEEE Trans. Image Process. 19, 1720–1730 (2010). [CrossRef]
  17. G. Steidl and T. Teuber, “Removing multiplicative noise by Douglas–Rachford splitting methods,” J. Math. Imag. Vis. 36, 168–184 (2010). [CrossRef]
  18. M. Bertero, P. Boccacci, G. Desiderà, and G. Vicidomini, “Image deblurring with Poisson data: from cells to galaxies,” Inverse Problems 25, 123006 (2009). [CrossRef]
  19. M. Bertalmio, V. Caselles, B. Rougé, and A. Solé, “TV based image restoration with local constraints,” J. Sci. Comput. 19, 95–122 (2003). [CrossRef]
  20. A. Almansa, C. Ballester, V. Caselles, and G. Haro, “A TV based restoration model with local constraints,” J. Sci. Comput. 34, 209–236 (2008). [CrossRef]
  21. Y. Q. Dong, M. Hintermüller, and M. M. Rincon-Camacho, “Automated regularization parameter selection in multi-scale variation models for image restoration,” J. Math. Imaging Vision 40, 82–104 (2011). [CrossRef]
  22. G. Gilboa, N. Sochen, and Y. Y. Zeevi, “Variational denoising of partly textured images by spatially varying constraints,” IEEE Trans. Image Process. 15, 2281–2289 (2006). [CrossRef]
  23. F. Li, M. Ng, and C. Shen, “Multiplicative noise removal with spatial-varying regularization parameters,” SIAM J. Imag. Sci. 3, 1–20 (2010). [CrossRef]
  24. D. Q. Chen and L. Z. Cheng, “Spatially adapted total variation model to remove multiplicative noise,” IEEE Trans. Image Process. 21, 1650–1662 (2012). [CrossRef]
  25. T. Chan, A. Marquina, and P. Mulet, “High-order total variation-based image restoration,” SIAM J. Sci. Comput. 22, 503–516 (2000). [CrossRef]
  26. 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 Trans. Image Process. 121579–1590 (2003). [CrossRef]
  27. S. Lefkimmiatis, A. Bourquard, and M. Unser, “Hessian-based norm regularization for image restoration with biomedical applications,” IEEE Trans. Image Process. 21, 983–995 (2012). [CrossRef]
  28. H. Z. Chen, J. P. Song, and X. C. Tai, “A dual algorithm for minimization of the LLT model,” Adv. Comput. Math. 31, 115–130 (2009). [CrossRef]
  29. F. Li, C. M. Shen, J. S. Fan, and C. L. Shen, “Image restoration combining a total variational filter and a fourth-order filter,” J. Visual Commun. Image Rep. 18, 322–330 (2007). [CrossRef]
  30. M. Lysaker and X. C. Tai, “Iterative image restoration combining total variation minimization and a second-order functional,” Int. J. Comput. Vis. 66, 5–18 (2006). [CrossRef]
  31. K. Papafitsoros and C. B. Schönlieb, “A combined first and second order variational approach for image reconstruction,” J. Math. Imaging Vis. (2013). doi 10.1007/s10851-013-0445-4. [CrossRef]
  32. K. Bredies, K. Kunisch, and T. Pock, “Total generalized variation,” SIAM J. Imag. Sci. 3, 492–526 (2010). [CrossRef]
  33. C. L. Wu and X. C. Tai, “Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models,” SIAM J. Imag. Sci. 3, 300–339 (2010). [CrossRef]
  34. E. Esser, “Applications of Lagrangian-based alternating direction methods and connections to split Bregman,” (UCLA, 2009).
  35. T. Goldstein, B. O’Donoghue, and S. Setzer, “Fast alternating direction optimization methods,” , (UCLA, 2012).
  36. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004). [CrossRef]

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