Image noise removal based on total variation
D.N.H. Thanh, S.D. Dvoenko

 

Tula State University

Full text of article: Russian language.

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Abstract:
Today, raster images are created by different modern devices, such as digital cameras, X-Ray scanners, and so on. Image noise deteriorates the image quality, thus adversely affecting the result of processing. Biomedical images are an example of digital images. The noise in such raster images is assumed to be a mixture of Gaussian noise and Poisson noise. In this paper, we propose a method to remove these noises based on the total variation of the image brightness function. The proposed model is a combination of two famous denoising models, namely, the ROF model and a modified ROF model.

Keywords:
total variation, ROF model, Gaussian noise, Poisson noise, image processing, biomedical image, Euler-Lagrange equation.

Citation:
Thanh DNH, Dvoenko SD. Image noise removal based on total variation. Computer Optics 2015; 39(4): 564-71. DOI: 10.18287/0134-2452-2015-39-4-564-571.

References:

  1. Chan TF, Shen J. Image processing and analysis: Variational, PDE, Wavelet, and stochastic methods. SIAM, 2005; 400 p.
  2. Burger M. Level set and PDE based reconstruction methods in imaging, Springer, 2008; 319 p.
  3. Chambolle A. An introduction to total variation for image analysis. Theoretical foundations and numerical methods for sparse recovery 2009; 9: 263-340.
  4. Xu J, Feng X, Hao Y. A coupled variational model for image denoising using a duality strategy and split Bregman. Multidimensional systems and signal processing 2014; 25: 83-94.
  5. Rankovic N, Tuba M. Improved adaptive median filter for denoising ultrasound images. Advances in computer science, WSEAS ECC’12 2012; 169-74.
  6. Lysaker M, Tai X. Iterative image restoration combining total variation minimization and a second-order functional. International journal of computer vision 2006; 66: 5-18.
  7. Li F, Shen C, Pi L. A new diffusion-based variational model for image denoising and segmentation. Journal mathematical imaging and vision 2006; 26(1-2): 115-25.
  8. Zhu Y. Noise reduction with low dose CT data based on a modified ROF model. Optics express 2012; 20(16): 17987-18004.
  9. Tran MP, Peteri R, Bergounioux M. Denoising 3D medical images using a second order variational model and wavelet shrinkage. Image analysis and recognition 2012; 7325: 138-45.
  10. Getreuer P. Rudin-Osher-Fatemi total variation denoising using split Bregman. IPOL 2012. Source: <http://www.ipol.im/pub/art/2012/g-tvd/>.
  11. Caselles V, Chambolle A, Novaga M. Handbook of mathematical methods in imaging, Springer, 2011. 1607 p.
  12. Rudin LI, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D. 1992; 60: 259-68.
  13. Chen K. Introduction to variational image processing models and application. International journal of computer mathematics 2013; 90(1): 1-8.
  14. Le T, Chartrand R, Asaki TJ. A variational approach to reconstructing images corrupted by Poisson noise. Journal of mathematical imaging and vision 2007; 27(3): 257-63.
  15. Luisier F, Blu T, Unser M. Image denoising in mixed Poisson-Gaussian noise. IEEE transaction on Image processing 2011; 20(3): 696-708.
  16. Jezierska A. An EM approach for Poisson-Gaussian noise modelling. EUSIPCO 19th 2011; 62(1): 13-30.
  17. Jezierska A. Poisson-Gaussian noise parameter estimation in fluorescence microscopy imaging. IEEE International Symposium on Biomedical Imaging 9th 2012; 1663-6.
  18. Wang C, Li T. An improved adaptive median filter for Image denoising. ICCEE 2012; 53(2.64): 393-8.
  19. Abe C, Shimamura T. Iterative Edge-Preserving adaptive Wiener filter for image denoising. ICCEE 2012; 4(4): 503-6.
  20. Zosso D, Bustin A. A Primal-Dual Projected Gradient Algorithm for Efficient Beltrami Regularization. Computer Vision and Image Understanding, 2014; Source: <http://www.math.ucla.edu/~zosso/> .
  21. Wang Z. Image quality assessment: From error visibility to structural similarity. IEEE transaction on Image processing 2004; 13(4): 600-12.
  22. Wang Z, Bovik AC. Modern image quality assessment. Morgan & Claypool Publisher 2006: 146 p.
  23. Scherzer O. Variational methods in Imaging. Springer 2009; 320.
  24. Zeidler E. Nonlinear functional analysis and its applications: Variational methods and optimization. Springer 1985; 662.
  25. Rubinov A, Yang X. Applied Optimization: Lagrange-type functions in constrained non-convex optimization. Springer 2003; 286.
  26. Gill PE, Murray W. Numerical methods for constrained optimization, Academic Press Inc 1974; 283.
  27. Immerker J. Fast noise variance estimation. Computer vision and image understanding 1996; 64(2): 300-2.
  28. Thomos N, Boulgouris NV, Strintzis MG. Optimized Transmission of JPEG2000 streams over Wireless channels. IEEE transactions on image processing 2006; 15(1): 54-67.
  29. Nick V. Getty images. Source: <http://well.blogs.nytimes.com/2009/09/16/what-sort-of-exercise-can-make-you-smarter/>.
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