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.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
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.
GHERAİBİA, S., GUESMİA, A., DAİLİ, N. (2022). The robustness of proximal penalty algorithms in restoration of noisy image. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 6, 1043–1052. https://ajindex.com/articles/529949
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 (2