去除乘性噪声的重加权各向异性全变差模型

王旭东; 冯象初; 霍雷刚

doi:10.3724/SP.J.1004.2012.00444

去除乘性噪声的重加权各向异性全变差模型

doi: 10.3724/SP.J.1004.2012.00444

1.
西安电子科技大学理学院应用数学系西安 710071

详细信息

通讯作者:
王旭东, 西安电子科技大学理学院应用数学系博士研究生. 主要研究方向为图像处理的偏微分方程方法.E-mail: xudwang@mail.xidian.edu.cn

计量
- 文章访问数: 2221
- HTML全文浏览量: 54
- PDF下载量: 1328
- 被引次数: 0
出版历程
- 收稿日期: 2011-07-04
- 修回日期: 2011-10-08
- 刊出日期: 2012-03-20

Iteratively Reweighted Anisotropic-TV Based Multiplicative Noise Removal Model

1.
Department of Applied Mathematics, School of Science, Xidian University, Xi'an 710071

摘要

摘要: 恢复含乘性噪声的图像是当前图像处理的重要研究课题. 本文提出基于迭代重加权的各向异性全变差(Total variation, TV)模型. 新模型中, 假定乘性噪声服从Gamma分布. 正则项采用加权的各向异性全变差, 其中, 自适应权函数由期望最大(Expectation maximization, EM)算法得到. 新模型在有效去噪的同时, 较好地保留了图像的边缘和细节信息, 同时能够有效地抑制"阶梯效应". 数值实验验证了新模型的效果.
- 图像去噪 /
- 乘性噪声 /
- 期望最大算法 /
- 全变差 /
- 迭代重加权
Abstract: Multiplicative noise removal is an important research topic on image processing. This paper proposes an iteratively reweighted anisotropic-total variation (TV) based model under the assumption that the multiplicative noise follows a Gamma distribution. The regularization term is the weighted anisotropic-TV regularizer. The weighting function incorporated in the regularization term is derived from the expectation maximization (EM) algorithm. The merits of this model are the preservation of geometrical structures of edges and the restraint of "staircase effect" while removing the noise. Numerical experimental results demonstrate the better performance of the proposed model.
- Image denoising /
- multiplicative noise /
- expectation maximization (EM) algorithms /
- total variation (TV) /
- iteratively reweighted method

HTML全文

参考文献(1)

[1]

Huo Chun-Lei, Cheng Jian, Lu Han-Qing, Zhou Zhi-Xin. Object-level change detection based on multiscale fusion. Acta Automatica Sinica, 2008, 34(3): 251-257(霍春雷, 程健, 卢汉清, 周志鑫. 基于多尺度融合的对象级变化检测新方法. 自动化学报, 2008, 34(3): 251-257)[2] Wu Liang, Hu Yun-An. A survey of automatic road extraction from remote sensing images. Acta Automatica Sinica, 2010, 36(7): 912-922(吴亮, 胡云安. 遥感图像自动道路提取方法综述. 自动化学报, 2010, 36(7): 912-922)[3] Aubert G, Aujol J. A nonconvex model to remove multiplicative noise. In: Proceedings of the 1st International Conference on Scale Space and Variational Methods in Computer Vision. Ischia, Italy: Springer, 2007. 68-79[4] Aubert G, Aujol J. A variational approach to removing multiplicative noise. SIAM Journal on Applied Mathematics, 2008, 68(4): 925-946[5] Jin Z M, Yang X P. Analysis of a new variation model for multiplicative noise removal. Journal of Mathematical Analysis and Applications, 2010, 362(2): 415-426[6] Huang Y M, Ng M K, Wen Y W. A new total variation method for multiplicative noise removal. SIAM Journal on Imaging Sciences, 2009, 2(1): 20-40[7] Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 1992, 60(1-4): 259-268[8] Feng Xiang-Chu, Wang Wei-Wei. Variaitional and Partial Differential Equation Method in Image Processing. Beijing: Science Press, 2009(冯象初, 王卫卫. 图像处理的变分和偏微分方程方法. 北京: 科学出版社, 2009)[9] Rudin L, Lions P L, Osher S. Multiplicative denoising and deblurring: theory and algorithms. Geometric Level Set Methods in Imaging, Vision and Graphics. New York: Springer, 2003. 103-119[10] Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, 6(6): 721-741[11] Li Y Y, Santosa F. A computational algorithm for minimizing total variation in image restoration. IEEE Transactions on Image Processing, 1996, 5(6): 987-995[12] Lin Y Q, Lee D D. Bayesian L1-norm sparse learning. In: International Conference on Acoustics, Speech, and Signal Processing. Toulouse, France: IEEE, 2006. 605-608[13] Nikolova M. Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares. Multiscale Modelling and Simulation, 2005, 4(3): 960-991[14] Nikolova M, Ng M K, Zhang S, Ching W. Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization. SIAM Journal on Image Science, 2008, 1(1): 2-25[15] Nikolova M, Ng M K, Tam C P. Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction. IEEE Transactions on Image Processing, 2010, 19(12): 3073-3088[16] Han Yu, Wang Wei-Wei, Feng Xiang-Chu. Iteratively reweighted method based nonrigid image registration. Acta Automatica Sinica, 2011, 37(9): 1059-1066(韩雨, 王卫卫, 冯象初. 基于迭代重加权的非刚性图像配准. 自动化学报, 2011, 37(9): 1059-1066)[17] Rodriguez P, Wohlberg B. An iteratively reweighted norm algorithm for total variation regularization. In: Proceedings of the 40th Asilomar Conference on Signals, Systems and Computers. Pacific Grove, USA: IEEE, 2006. 892-896[18] Wohlberg B, Rodriguez P. An iteratively reweighted norm algorithm for minimization of total variation functionals. IEEE Signal Processing Letters, 2007, 14(12): 948-951[19] Candes E J, Wakin M, Boyd S P. Enhancing sparsity by reweighted L1 minimization. Journal of Fourier Analysis and Applications, 2008, 14(5): 877-905[20] Daubechies I, DeVore R, Fornasier M, Gunturk C S. Iteratively reweighted least squares minimization for sparse recovery. Communications on Pure and Applied Mathematics, 2010, 63(1): 1-38[21] Foucart S, Lai M J. Sparsest solutions of underdetermined linear systems via L_{q}-minimization for 0 q ≤ 1. Applied and Computational Harmonic Analysis, 2009, 26(3): 395-407[22] Wipf D, Nagarajan S. Iterative reweighted L1 and L2 methods for finding sparse solutions. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2): 317-329

施引文献

资源附件(0)

访问统计