Involve: A Journal of Mathematics

  • Involve
  • Volume 10, Number 2 (2017), 327-344.

Total variation based denoising methods for speckle noise images

Arundhati Bagchi Misra, Ethan Lockhart, and Hyeona Lim

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper, we introduce a new algorithm based on total variation for denoising speckle noise images. Total variation was introduced by Rudin, Osher, and Fatemi in 1992 for regularizing images. Chambolle proposed a faster algorithm based on the duality of convex functions for minimizing the total variation, but his algorithm was built for Gaussian noise removal. Unlike Gaussian noise, which is additive, speckle noise is multiplicative. We modify the original Chambolle algorithm for speckle noise images using the first noise equation for speckle denoising, proposed by Krissian, Kikinis, Westin and Vosburgh in 2005. We apply the Chambolle algorithm to the Krissian et al. speckle denoising model to develop a faster algorithm for speckle noise images.

Article information

Involve, Volume 10, Number 2 (2017), 327-344.

Received: 19 December 2015
Revised: 26 February 2016
Accepted: 19 March 2016
First available in Project Euclid: 13 December 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 68U10: Image processing 94A08: Image processing (compression, reconstruction, etc.) [See also 68U10]
Secondary: 65M06: Finite difference methods 65N06: Finite difference methods 65K10: Optimization and variational techniques [See also 49Mxx, 93B40] 49K20: Problems involving partial differential equations

anisotropic diffusion speckle noise denoising total variation (TV) model Chambolle algorithm fast speckle denoising


Bagchi Misra, Arundhati; Lockhart, Ethan; Lim, Hyeona. Total variation based denoising methods for speckle noise images. Involve 10 (2017), no. 2, 327--344. doi:10.2140/involve.2017.10.327.

Export citation


  • L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion, II”, SIAM J. Numer. Anal. 29:3 (1992), 845–866.
  • J. L. Carter, Dual methods for total variation-based image restoration, Ph.D thesis, University of California, Los Angeles, 2001,
  • F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion”, SIAM J. Numer. Anal. 29:1 (1992), 182–193.
  • A. Chambolle, “An algorithm for total variation minimization and applications”, J. Math. Imaging Vision 20:1–2 (2004), 89–97.
  • A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging”, J. Math. Imaging Vision 40:1 (2011), 120–145.
  • A. Chambolle, V. Caselles, D. Cremers, M. Novaga, and T. Pock, “An introduction to total variation for image analysis”, pp. 263–340 in Theoretical foundations and numerical methods for sparse recovery, Radon Ser. Comput. Appl. Math. 9, Walter de Gruyter, Berlin, 2010.
  • T. Chan and L. Vese, “Variational image restoration and segmentation models and approximations”, CAM report 97-47, University of California, Los Angeles, 1997,
  • T. F. Chan, G. H. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration”, SIAM J. Sci. Comput. 20:6 (1999), 1964–1977.
  • R. Chan, H. Yang, and T. Zeng, “A two-stage image segmentation method for blurry images with Poisson or multiplicative gamma noise”, SIAM J. Imaging Sci. 7:1 (2014), 98–127.
  • Y. Dong and T. Zeng, “A convex variational model for restoring blurred images with multiplicative noise”, SIAM J. Imaging Sci. 6:3 (2013), 1598–1625.
  • Y.-M. Huang, L. Moisan, M. K. Ng, and T. Zeng, “Multiplicative noise removal via a learned dictionary”, IEEE Trans. Image Process. 21:11 (2012), 4534–4543.
  • Y. Huang, M. Ng, and T. Zeng, “The convex relaxation method on deconvolution model with multiplicative noise”, Commun. Comput. Phys. 13:4 (2013), 1066–1092.
  • Y.-M. Huang, D.-Y. Lu, and T. Zeng, “Two-step approach for the restoration of images corrupted by multiplicative noise”, SIAM J. Sci. Comput. 35:6 (2013), A2856–A2873.
  • Z. Jin and X. Yang, “A variational model to remove the multiplicative noise in ultrasound images”, J. Math. Imaging Vision 39:1 (2011), 62–74.
  • K. Joo and S. Kim, “PDE-based image restoration, I: Anti-staircasing and anti-diffusion”, research report, University of Kentucky, 2003.
  • K. Joo and S. Kim, “PDE-based image restoration, II: Numberical schemes and color image denoising”, research report, University of Kentucky, 2003.
  • S. Kim, “Loss and recovery of fine structures in pde-based image denoising”, September 6–9 2004, Talk at the fifth conference on Mathematics and Image Analysis, Paris.
  • S. Kim and H. Lim, “A non-convex diffusion model for simultaneous image denoising and edge enhancement”, pp. 175–192 in Proceedings of the Sixth Mississippi State–UBA Conference on Differential Equations and Computational Simulations, edited by J. Graef et al., Electron. J. Differ. Equ. Conf. 15, Southwest Texas State Univ., San Marcos, TX, 2007.
  • P. Kornprobst, R. Deriche, and G. Aubert, “Nonlinear operators in image restoration”, pp. 325–331 in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (San Juan, 1997), 1997.
  • K. Krissian, R. Kikinis, C.-F. Westin, and K. Vosburgh, “Speckle-constrained filtering of ultrasound images”, pp. 547–552 in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Washington D.C., 2005), vol. 2, 2005.
  • A. Marquina and S. Osher, “Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal”, SIAM J. Sci. Comput. 22:2 (2000), 387–405.
  • P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion”, IEEE Trans. Pattern Anal. Mach. Intell. 12:7 (1990), 629–639.
  • L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms”, Phys. D 60:1–4 (1992), 259–268.
  • L. Vese and T. Chan, “Reduced non-convex functional approximations for image restoration & segmentation”, CAM report 97-56, University of California, Los Angeles, 1997,
  • Y. Wen, R. H. Chan, and T. Zeng, “Primal-dual algorithms for total variation based image restoration under Poisson noise”, Sci. China Math. 59:1 (2016), 141–160.