Fractional Total Variation Denoising Model Based on Adaptive Projection Algorithm
ZHANG Guimei1, SUN Xiaoxu1, LIU Jianxin2
1.Key Laboratory of Jiangxi Province for Image Processing and Pattern Recognition, Nanchang Hangkong University, Nanchang 330063 2.School of Mechanical Engineering, Xihua University, Chengdu 610039
Abstract To preserve weak edges and texture details of an image during image denoising, a fractional order total variation denoising model is presented based on adaptive projection algorithm. Firstly, Grünwald-Letnikov fractional order differential is used as a substitute for the first order derivative in the regularization term of total variation model. Secondly, the image is projected to a total variation ball to handle the optimization problem. The image is divided into the texture area and the non-texture area according to the local information of the image, and thus soft threshold values can be calculated adaptively. Both theoretical analysis and experimental results show that the proposed method eliminates the block effect as well as preserves the texture details effectively for removing noise.
Fund:Supported by National Natural Science Foundation of China (No.61462065,61263046), Natural Science Foundation of Jiangxi Province (No.20151BAB207036)
About author:: ZHANG Guimei, born in 1970, Ph.D., professor. Her research interests include computer vision, image processing and pattern recognition. SUN Xiaoxu, born in 1992, master student. His research interests include computer vision, image processing and pattern recognition. LIU JianxinCorresponding author, born in 1969, Ph.D., professor. His research interests include computer vision and intelligent robot.
[1] GONZALEZ R C, WOODS R E. Digital Image Processing. Upper Saddle River, USA: Prentice Hall, 2007. [2] LIN T C. A New Adaptive Center Weighted Median Filter for Su-ppressing Impulsive Noise in Images. Information Sciences, 2007, 177(4): 1073-1087. [3] MARTIN-FERNANDEZ M, ALBEROLA-LOPEZ C, RUIZ-ALZOLA J, et al. Sequential Anisotropic Wiener Filtering Applied to 3D MRI Data. Magnetic Resonance Imaging, 2007, 25(2): 278-292. [4] JIANG S, HAO X. Hybrid Fourier-Wavelet Image Denoising. Electronics Letters, 2007, 43(20): 1081-1082. [5] OTHMAN H, QIAN S E. Noise Reduction of Hyperspectral Imagery Using Hybrid Spatial-Spectral Derivative-Domain Wavelet Shrin-kage. IEEE Trans on Geoscience and Remote Sensing, 2006, 44(2): 397-408. [6] GUO K H, KUTYNIOK G, LABATE D. Sparse Multidimensional Representations Using Anisotropic Dilation and Shear Operators [C/OL].[2016-03-05].http://www.math.uh.edu/~dlabate/Athens.pdf. [7] RUDIN L I, OSHER S, FATEMI E. Nonlinear Total Variation Based Noise Removal Algorithms. Physica D(Nonlinear Phenomena), 1992, 60(1/2/3/4): 259-268. [8] YOU Y L, KAVEH M. Fourth-Order Partial Differential Equations for Noise Removal. IEEE Trans on Image Processing, 2000, 9(10): 1723-1730. [9] BRITO-LOEZA C, CHEN K. Multigrid Algorithm for High Order Denoising. SIAM Journal on Imaging Sciences, 2010, 3(3): 363-389. [10] LYSAKER M, LUNDERVOLD A, TAI X C. Noise Removal Using Fourth-Order Partial Differential Equation with Applications to Medical Magnetic Resonance Images in Space and Time. IEEE Trans on Image Processing, 2003, 12(12): 1579-1590. [11] BAI J, FENG X C. Fractional-Order Anisotropic Diffusion for Image Denoising. IEEE Trans on Image Processing, 2007, 16(10): 2492-2502. [12] ZHANG J, WEI Z H. Fractional Variational Model and Algorithm for Image Denoising // Proc of the 4th International Conference on Natural Computation. New York, USA: IEEE, 2008, V: 524-528. [13] PU Y F, Siarry P, ZHOU J L, et al. Fractional Partial Differential Equation Denoising Models for Texture Image. Science China (Information Sciences), 2014, 57(7): 1-19. [14] CHEN D L, CHEN Y Q, XUE D Y. Fractional-Order Total Variation Image Denoising Based on Proximity Algorithm. Applied Mathematics and Computation, 2015, 257: 537-545. [15] 黄 果,许 黎,陈庆利,等.基于空间分数阶偏微分方程的图像去噪模型研究.四川大学学报(工程科学版), 2012, 44(2): 91-98. (HUANG G, XU L, CHEN Q L, et al. Research on Image Denoising Based on Space Fractional Partial Differential Equations. Journal of Sichuan University(Engineering Science Edition), 2012, 44(2): 91-98.) [16] ZHANG J, WEI Z H. A Class of Fractional-Order Multi-scale Va-riational Models and Alternating Projection Algorithm for Image Denoising. Applied Mathematical Modelling, 2011, 35(5): 2516-2528. [17] CHAMBOLLE A. An Algorithm for Total Variation Minimization and Applications. Journal of Mathematical Imaging and Vision, 2004, 20(1): 89-97. [18] FADILI J M, PEYR G. Total Variation Projection with First Order Schemes. IEEE Trans on Image Processing, 2011, 20(3): 657-669. [19] 蒲亦非,王卫星.数字图像的分数阶微分掩模及其数值运算规则.自动化学报, 2007, 33(11): 1128-1135. (PU Y F, WANG W X. Fractional Differential Masks of Digital Image and Their Numerical Implementation Algorithms. Acta Automatica Sinica, 2007, 33(11): 1128-1135. ) [20] GILBOA G, SOCHEN N, ZEEVI Y Y. Variational Denoising of Partly Textured Images by Spatially Varying Constraints. IEEE Trans on Image Processing, 2006, 15(8): 2281-2289.
2016, Vol. 29 
