Alpha稳态噪声下基于Meridian范数的全变分图像去噪算法

杨真真; 杨震; 李雷; 金正猛

doi:10.11999/JEIT160657

Alpha稳态噪声下基于Meridian范数的全变分图像去噪算法

doi: 10.11999/JEIT160657

2.
(南京邮电大学视觉认知计算与应用研究中心南京 210023) ②(南京邮电大学宽带无线通信与传感网技术教育部重点实验室南京 210003)

基金项目:

国家自然科学基金(61501251, 61271335, 61271240)，江苏省自然科学基金项目(BK20140891)，南京邮电大学引进人才科研启动基金资助项目(NY214191)

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- 被引次数: 0
出版历程
- 收稿日期: 2016-06-21
- 修回日期: 2017-01-03
- 刊出日期: 2017-05-19

A Total Variational Approach Based on Meridian Norm for Restoring Noisy Images with Alpha-stable Noise

2.
(Center for Visual Cognitive Computation and Application, Nanjing University of Posts and Telecommunications, Nanjing 210023, China)

Funds:

The National Natural Science Foundation of China (61501251, 61271335, 61271240), The Natural Science Foundation of Jiangsu Province (BK20140891), The Science Foundation of Nanjing University of Posts and Telecommunications (NY214191)

摘要

摘要: 在实际应用中，噪声不可避免，因此，图像去噪一直是图像处理领域研究的重点，并且近年来受到越来越多的研究者的青睐。该文首先基于Meridian分布和全变分(Total Variational, TV)的统计特性，提出一种全变分模型来复原alpha稳态噪声环境下的含噪声图像。此外，为了保证模型解的唯一性，对提出的全变分模型添加了一个二次惩罚项，得到一个严格凸的全变分模型，然后，使用原始-对偶算法对提出的全变分模型进行求解，并证明了该算法的收敛性。最后，进行了仿真实验，并对实验结果进行了分析，实验结果验证了提出模型的可行性与有效性。
- 图像处理 /
- Meridian范数 /
- Alpha稳态噪声 /
- 原始-对偶算法 /
- 全变分
Abstract: In actual applications, noises may inevitably exist, and thus to study the denoising method for images is great significant task in image processing filed that attracts much attention in recent years. In this paper, based on the statistical property of Meridian distributed and the Total Variational (TV), a total variational method is proposed for restoring images degraded by alpha-stable noise. Besides, in order to obtain a strictly convex model, a quadratic penalty term is added, which guarantees the uniqueness of the solution. For solving the novel convex variational model, a primal-dual algorithm is employed to solve the above model, and the convergence of the algorithm is proved. The experimental results demonstrate that the feasibility and effectiveness of the proposed model for the noisy images with alpha-stable noise.
- Image processing /
- Meridian norm /
- Alpha-stable noise /
- Primal-dual algorithm /
- Total Variational (TV)

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参考文献(23)

CHANG S G, YU B, and VETTERLI M. Adaptive wavelet thresholding for image denoising and compression[J]. IEEE Transactions on Image Processing, 2000, 9(9): 1532-1546. doi: 10.1109/83. 862633.

RAFAEL C G and RICHARD E W. Digital Image Processing[M]. 2nd Edition, Upper Saddle River, USA, Prentice Hall, 2002: 220-275.

NODES T and GALLAGHER N Jr. Median filter: Some modifications and their properties[J]. IEEE Transactions on Acoustics, Speech and Signal, Processing, 1982, 30(5): 739-746. doi: 10.1109/TASSP.1982.1163951.

BARBU T, BARBU V, BIGA V, et al. A PDE variational approach to image denoising and restoration[J]. Nonlinear Analysis: Real World Applications, 2009, 10(3): 1351-1361.

RUDIN L, OSHER S, and FATEMI E. Nonlinear total variation based noise removal algorithms[J]. Physica D: Nonlinear Phenomena, 1992, 60(1/4): 259-268. doi: 10.1016/ 0167-2789(92)90242-F.

CHAMBOLLE A. An algorithm for total variation minimization and applications[J]. Journal of Mathematical Imaging and Vision, 2004, 20(1): 89-97. doi: 10.1023/B:JMIV. 0000011325.36760.1e.

CHAN R, DONG Y, and HINTERMULLER M. An efficient two-phase L1-TV method for restoring blurred images with impulse noise[J]. IEEE Transactions on Image Processing, 2010, 19(7): 1731-1739. doi: 10.1109/TIP.2010.2045148.

YANG J, ZHANG Y, and YIN W. An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise[J]. SIAM Journal on Scientific Computing, 2009, 31(4): 2842-2865. doi: 10.1137/080732894.

金正猛, 杨燕. 基于框式约束的快速全变差图像泊松去噪算法[J]. 电子与信息学报, 2014, 36(8): 1866-1871. doi: 10.3724 /SP.J.1146.2014.00154.

JIN Zhengmeng and YANG Yan. A fast total variation algorithm based on box constraint for Possion noise removal [J]. Journal of Electronics Information Technology, 2014, 36(8): 1866-1871. doi: 10.3724/SP.J.1146.2014.00154.

SCIACCHITANO F, DONG Y, and ZENG T. Variational approach for restoring blurred images with Cauchy noise[J]. SIAM Journal on Imaging Sciences, 2015, 8(3): 1894-1922. doi: 10.1137/140997816.

AUBERT G and AUJOL J. A variational approach to removing multiplicative noise[J]. SIAM Journal on Applied Mathematics, 2008, 68(4): 925-946. doi: 10.1137/060671814.

DONG Y and ZENG T. A convex variational model for restoring blurred images with multiplicative noise[J]. SIAM Journal on Imaging Sciences, 2013, 6(3): 1598-1625. doi: 10.1137/120870621.

CHEN L and ZENG T. A convex variational model for restoring blurred images with large Rician noise[J]. Journal of Mathematical Imaging and Vision, 2015, 53(1): 92-111. doi: 10.1007/s10851-014-0551-y.

NOLAN J. Stable Distributions-Models for Heavy Tailed Data[M]. Birkhauser Boston, 2015: 3-24.

ZOZOR S, BROSSIER J, and AMBLARD P O. A parametric approach to suboptimal signal detection in alpha-stable noise[J]. IEEE Transactions on Signal Processing, 2006, 54(12): 4497-4509. doi: 10.1109/TSP.2006. 882066.

SADREAZAMI H, AHMAD M O, and SWAMY M N S. Contourlet domain image denoising using the alpha-stable distribution[C]. IEEE 57th International Midwest Symposium on Circuits and Systems, College Station, Texas, USA, 2014: 141-144. doi: 10.1109/MWSCAS.2014.6908372.

AYSAL T C and BARNER K E. Meridian filtering for robust signal processing[J]. IEEE Transactions on Signal Processing, 2007, 55(8): 3949-3962. doi: 10.1109/TSP.2007.894383.

KORNPROBST P, DERICHE R, and AUBERT G. Image sequence analysis via partial differential equations[J]. Journal of Mathematical Imaging and Vision, 1999, 11(1): 5-26. doi: 10.1023/A:1008318126505.

CHAMBOLLE A and POCK T. A first-order primal-dual algorithm for convex problems with applications to imaging [J]. Journal of Mathematical Imaging and Vision, 2011, 40(1): 120-145. doi: 10.1007/s10851-010-0251-1.

WEI K, TAI X, CHAN T, et al. Primal-dual method for continuous max-flow approaches[C]. Proceedings of 5th Eccomas Thematic Conference on Computational Vision and Medical Image Processing, UK, 2016: 17-24. doi: 10.1201/ b19241-5.

CARRILLO R E, BARNER K E, and AYSAL T C. Robust sampling and reconstruction methods for sparse signal in the presence of impulsive noise[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2): 392-408. doi: 10.1109 /JSTSP.2009.2039177.

ZHOU W, BOVIK A, SHEIKH H, et al. Image quality assessment: From error visibility to structural similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4): 600-612. doi: 10.1109/TIP.2003.819861.

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