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Year 2017, Volume: 46 Issue: 6, 1043 - 1052, 01.12.2017

Abstract

References

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  • A. Chambolle, An algorithm for total variation minimization and applications, Jour. Math. Imag. Vision, 20 (2004), pp. 89-97.
  • S.G. Chang, Bin Yu and M. Vetterli, Adaptive wavelet thresholding for image denoising and compression, IEEE Transactions on Image Processing, Vol. 9, Issue 9 (2002), pp. 1532-1546.
  • D. Cremers et Al, Convex relaxation techniques for segmentation, stereo and multiview reconstruction, dans Markov Random Fields for Vision and Image Processing, MIT Press, 2011.
  • N. Daili, Some Augmented Lagrangian Algorithms applied to convex nondifferentiable optimization problems, Journal of Information & Optimization Sciences (JIOS), Vol. 33, No: 4&5 (2012), pp. 487-526.
  • N. Daili and Kh. Saadi, Epsilon-Proximal Point Algorithms for Nondifferentiable Convex Optimization Problems and Applications, AMO - Advanced Modeling and Optimization, Vol. 14, No: 1 (2012), pp. 175-195.
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  • Pankaj Hedaoo and Swati S. Godbole, wavelet thresholding approach for image denoising, International Journal of Network Security & its Applications (ijnsa), vol. 3, no: 4, 2011.
  • J. Jeena ; P. Salice and J. Neetha, denoising using soft thresholding, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 2, Issue 3, 2013.
  • M. Kazubek, Signal, Wavelet domain image de-noising by thresholding and Wiener filtering, Processing Letters IEEE, Vol. 10, Issue 265, Vol. 3 (2003).
  • Suresh Kumar, Papendra Kumar and Manoj Gupta, Performance Comparison of Median and Wiener Filter in Image De-noising, Ashok Kumar Nagawat, International Journal of Computer Applications, Vol. 12, No. 4 (2010), p. 27.
  • J. Lellmann et Al, Fast and exact primal-dual iterations for variational problems in computer vision, dans Proc. of ECCV: Part II, Heraklion Crete, Greece, 2010, pp. 494-505.
  • J.J. Moreau, Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. France (BSMF), Vol. 93(1965), pp. 273-299.
  • L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp. 259-268.
  • E.Y. Sidky et Al, Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm, Physics in Medicine and Biology, Vol. 57, Number 10(2012), pp. 3065-3091.

The robustness of proximal penalty algorithms in restoration of noisy image

Year 2017, Volume: 46 Issue: 6, 1043 - 1052, 01.12.2017

Abstract

The nondifferentiable convex optimization has an importance crucial in the image restoration for this and in this article we present the performance of the Prox method adapted to the restoration of noisy images. Following of our article ([12]), we illustrate in this work thesuperior efficacy of this algorithm “Prox” ([12]) then we are comparing the obtained numerical results with the algorithms of Wiener filtering ([7], [16]), total variation ([5]) and wavelet soft-thresholding denoising ([1], [12], [13]), in terms of image quality and convergence.

Our first experiments showed that by applying of Prox algorithm for restoration of noised image by the white Gaussian noise we obtain a top results of denosed image with high quality (net, not rehearsed and unsmoothed; textures are preserved) in addition to the convergence of the algorithm is ensured whatever the values of SNR.

References

  • S. Anthoine et Al, Some proximal methods for Poisson intensity CBCT and PET, Inverse Problems and Imaging, Vol. 6, Number 4 (2012).
  • A. Auslender et Al, Penalty-Proximal in convex programming, J.O.T.A., Vol. 55 (1987), pp. 1-21.
  • G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, volume 147 of Applied Mathematical Sciences, Springer-Verlag, 2002.
  • F. Bach et Al, Optimization with sparsity-inducing, Foundations and Trends in Machine Learning, Vol. 4, Number 1 (2012), pp. 1-106.
  • M. Bergounioux, Quelques méthodes mathématiques pour le traitement d’image, Notes de cours, 2009.
  • A. Chambolle, An algorithm for total variation minimization and applications, Jour. Math. Imag. Vision, 20 (2004), pp. 89-97.
  • S.G. Chang, Bin Yu and M. Vetterli, Adaptive wavelet thresholding for image denoising and compression, IEEE Transactions on Image Processing, Vol. 9, Issue 9 (2002), pp. 1532-1546.
  • D. Cremers et Al, Convex relaxation techniques for segmentation, stereo and multiview reconstruction, dans Markov Random Fields for Vision and Image Processing, MIT Press, 2011.
  • N. Daili, Some Augmented Lagrangian Algorithms applied to convex nondifferentiable optimization problems, Journal of Information & Optimization Sciences (JIOS), Vol. 33, No: 4&5 (2012), pp. 487-526.
  • N. Daili and Kh. Saadi, Epsilon-Proximal Point Algorithms for Nondifferentiable Convex Optimization Problems and Applications, AMO - Advanced Modeling and Optimization, Vol. 14, No: 1 (2012), pp. 175-195.
  • D. L. Donoho, “Denoising by soft-thresholding”, IEEE Trans. Inf. Theory, Vol. 41, no: 3 (1995), pp. 613-627.
  • S. Gheraibia and N. Daili, Restoration of the noised images by the proximal penalty algorithm, Pacific Journal of Applied Mathematics, Volume 7, Number 3 (2015), pp. 149-161.
  • Pankaj Hedaoo and Swati S. Godbole, wavelet thresholding approach for image denoising, International Journal of Network Security & its Applications (ijnsa), vol. 3, no: 4, 2011.
  • J. Jeena ; P. Salice and J. Neetha, denoising using soft thresholding, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 2, Issue 3, 2013.
  • M. Kazubek, Signal, Wavelet domain image de-noising by thresholding and Wiener filtering, Processing Letters IEEE, Vol. 10, Issue 265, Vol. 3 (2003).
  • Suresh Kumar, Papendra Kumar and Manoj Gupta, Performance Comparison of Median and Wiener Filter in Image De-noising, Ashok Kumar Nagawat, International Journal of Computer Applications, Vol. 12, No. 4 (2010), p. 27.
  • J. Lellmann et Al, Fast and exact primal-dual iterations for variational problems in computer vision, dans Proc. of ECCV: Part II, Heraklion Crete, Greece, 2010, pp. 494-505.
  • J.J. Moreau, Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. France (BSMF), Vol. 93(1965), pp. 273-299.
  • L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp. 259-268.
  • E.Y. Sidky et Al, Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm, Physics in Medicine and Biology, Vol. 57, Number 10(2012), pp. 3065-3091.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sabrina Gheraibia This is me

Amar Guesmia This is me

Noureddine Daili This is me

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 6

Cite

APA Gheraibia, S., Guesmia, A., & Daili, N. (2017). The robustness of proximal penalty algorithms in restoration of noisy image. Hacettepe Journal of Mathematics and Statistics, 46(6), 1043-1052.
AMA Gheraibia S, Guesmia A, Daili N. The robustness of proximal penalty algorithms in restoration of noisy image. Hacettepe Journal of Mathematics and Statistics. December 2017;46(6):1043-1052.
Chicago Gheraibia, Sabrina, Amar Guesmia, and Noureddine Daili. “The Robustness of Proximal Penalty Algorithms in Restoration of Noisy Image”. Hacettepe Journal of Mathematics and Statistics 46, no. 6 (December 2017): 1043-52.
EndNote Gheraibia S, Guesmia A, Daili N (December 1, 2017) The robustness of proximal penalty algorithms in restoration of noisy image. Hacettepe Journal of Mathematics and Statistics 46 6 1043–1052.
IEEE S. Gheraibia, A. Guesmia, and N. Daili, “The robustness of proximal penalty algorithms in restoration of noisy image”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 6, pp. 1043–1052, 2017.
ISNAD Gheraibia, Sabrina et al. “The Robustness of Proximal Penalty Algorithms in Restoration of Noisy Image”. Hacettepe Journal of Mathematics and Statistics 46/6 (December 2017), 1043-1052.
JAMA Gheraibia S, Guesmia A, Daili N. The robustness of proximal penalty algorithms in restoration of noisy image. Hacettepe Journal of Mathematics and Statistics. 2017;46:1043–1052.
MLA Gheraibia, Sabrina et al. “The Robustness of Proximal Penalty Algorithms in Restoration of Noisy Image”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 6, 2017, pp. 1043-52.
Vancouver Gheraibia S, Guesmia A, Daili N. The robustness of proximal penalty algorithms in restoration of noisy image. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1043-52.