Volume 10, Issue 1
Total Variation Based Parameter-Free Model for Impulse Noise Removal

Federica Sciacchitano, Yiqiu Dong & Martin S. Andersen

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 186-204.

Published online: 2017-10

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  • Abstract

We propose a new two-phase method for reconstruction of blurred images corrupted by impulse noise. In the first phase, we use a noise detector to identify the pixels that are contaminated by noise, and then, in the second phase, we reconstruct the noisy pixels by solving an equality constrained total variation minimization problem that preserves the exact values of the noise-free pixels. For images that are only corrupted by impulse noise (i.e., not blurred) we apply the semi-smooth Newton's method to a reduced problem, and if the images are also blurred, we solve the equality constrained reconstruction problem using a first-order primal-dual algorithm. The proposed model improves the computational efficiency (in the denoising case) and has the advantage of being regularization parameter-free. Our numerical results suggest that method is competitive in terms of its restoration capabilities with respect to the other two-phase methods. 

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@Article{NMTMA-10-186, author = {}, title = {Total Variation Based Parameter-Free Model for Impulse Noise Removal}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {1}, pages = {186--204}, abstract = {

We propose a new two-phase method for reconstruction of blurred images corrupted by impulse noise. In the first phase, we use a noise detector to identify the pixels that are contaminated by noise, and then, in the second phase, we reconstruct the noisy pixels by solving an equality constrained total variation minimization problem that preserves the exact values of the noise-free pixels. For images that are only corrupted by impulse noise (i.e., not blurred) we apply the semi-smooth Newton's method to a reduced problem, and if the images are also blurred, we solve the equality constrained reconstruction problem using a first-order primal-dual algorithm. The proposed model improves the computational efficiency (in the denoising case) and has the advantage of being regularization parameter-free. Our numerical results suggest that method is competitive in terms of its restoration capabilities with respect to the other two-phase methods. 

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1613}, url = {http://global-sci.org/intro/article_detail/nmtma/12342.html} }
TY - JOUR T1 - Total Variation Based Parameter-Free Model for Impulse Noise Removal JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 186 EP - 204 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.m1613 UR - https://global-sci.org/intro/article_detail/nmtma/12342.html KW - AB -

We propose a new two-phase method for reconstruction of blurred images corrupted by impulse noise. In the first phase, we use a noise detector to identify the pixels that are contaminated by noise, and then, in the second phase, we reconstruct the noisy pixels by solving an equality constrained total variation minimization problem that preserves the exact values of the noise-free pixels. For images that are only corrupted by impulse noise (i.e., not blurred) we apply the semi-smooth Newton's method to a reduced problem, and if the images are also blurred, we solve the equality constrained reconstruction problem using a first-order primal-dual algorithm. The proposed model improves the computational efficiency (in the denoising case) and has the advantage of being regularization parameter-free. Our numerical results suggest that method is competitive in terms of its restoration capabilities with respect to the other two-phase methods. 

Federica Sciacchitano, Yiqiu Dong & Martin S. Andersen. (2020). Total Variation Based Parameter-Free Model for Impulse Noise Removal. Numerical Mathematics: Theory, Methods and Applications. 10 (1). 186-204. doi:10.4208/nmtma.2017.m1613
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