Fast algorithm for image denoising with different boundary conditions

•We added the structural similarity index measurement (SSIM) values for all our experiments.•We tested more images with different noises and sizes, compared with other state-of- the-art algorithms that are mentioned by the reviewers.•More detailed explanations are given about the algorithms and diff...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2017-07, Vol.354 (11), p.4595-4614
Main Authors: Zhang, Xiaole, Shi, Yuying, Pang, Zhi-Feng, Zhu, Yonggui
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Fast Fourier transformations
Fourier transforms
Noise reduction
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Summary:•We added the structural similarity index measurement (SSIM) values for all our experiments.•We tested more images with different noises and sizes, compared with other state-of- the-art algorithms that are mentioned by the reviewers.•More detailed explanations are given about the algorithms and different boundary conditions. In recent works several authors have considered the L1 fidelity term, the L2 fidelity term and the combined L1 and L2 fidelity term for denoising models, and they used the fast Fourier transform (FFT) algorithm which can only use periodic boundary conditions (BCs). In this paper, we combine the augmented Lagrangian method (ALM) and the symmetric Red–Black Gauss–Seidel (SRBGS) method to propose three algorithms that are suitable for different BCs. Experimental results show that the proposed algorithms are effective and the model with the combined L1 and L2 fidelity term demonstrates more advantages in efficiency and accuracy than other models with the L1 fidelity term or the L2 fidelity term.
ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2017.04.011