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Robust Estimation Based Hybrid Variational Model for Image Restoration and Application


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Robust Estimation Based Hybrid Variational Model for Image Restoration and Application
XIAO Liang1WU Hui-Zhong1WEI Zhi-Hui2
1.School of Computer Science and Technology;2.School of Sciences,NUST,Nanjing 210094,China
im age restoration max imum a posteriori robust estim ation variat iona lmethod part ial differential equations
The connection betw een a class o f variational functionalmode ls and Bayesianmethod for image restorat ion is established from the v iewpoint ofmax imum a posteriori (MAP) estim ation. Assum ing that the gradient o f images is amember o fE-contam inated norm al distribution, a least favo rab le distribution comb in ing a quadratic w ith a linear function is derived, then a hybrid mode l in the form of tota l variational integra l and D irichlet integral is proposed. The ex istence of the variational problem is discussed and aw e igh ted grad ient descent flow for image deno ising w ith an iterative algorithm is also deve loped. Exper imenta l resu lts show that our model has good performance in image restoration.


[ 1] Cobson D, Voge lC. Convergence of an iterative m ethod fo r tota l var ia tion denoising [ J]. SIAM Journa l o f Num er ica lAna lysis, 1997, 34 ( 5): 1 779- 1 791.
[ 2] Rudin L, Osher S, Fatem i E. Nonlinear tota l var ia tion based no ise remove l algor ithm s [ J] . Phys ica D, 1992, 60: 259- 268.
[ 3] 汪凯宇, 肖亮, 韦志辉. 基于图像整体变分和分数 阶奇异性提取的图像恢复模型[ J]. 南京理工大学 学报, 2003, 27( 4) : 400- 404.
[ 4] 肖亮, 吴慧中, 韦志辉, 汤淑春. 新型梯度倒数加权 滤波器及其性质[ J] . 南京理工大学学报, 2003, 27 ( 4): 390- 394.
[ 5] Huber P. Robust statistics[M ]. New York:W iley, 1981.
[ 6] Geman S, Geman D. Stochastic re laxation, G ibbs distr ibutions and the Bayes in restoration o f im ages [ J ]. IEEE Trans PAM I, 1984, 6 ( 6): 721- 741.
[ 7] H am za B A, H am id K, Go zde B U. Un ify ing probab-i listic and var iationa l estim ation [ J]. IEEE S igna l ProcessingM agazine, 2002, 19 ( 9): 37- 47.
[ 8] 张恭庆. 泛函分析[M ]. 北京: 北京大学出版 社, 2001.
[ 9] M a rqu ina A, O sher S. A new tim e dependent m ode l based on leve l set m o tion for non linear deb lurr ing and no ise remova l [ J]. Lecture No tes in Com puter Sc-i ence, 1999, 1 682: 429- 434.
[ 10] 张贤达. 现代信号处理[M ]. 北京: 清华大学出版 社(第二版), 2002.
[ 11] Chan T, Shen Jianhong. M a them aticalm ode ls fo r loca l non- texture inpa inting [ J]. SIAM Journa l o f Applied M athem atica,l 2001, 62 ( 3) : 1 019- 1 043.
[ 12] 肖亮, 吴慧中, 韦志辉. 面向彩色图像恢复与边缘 检测Mum ford-Shah推广模型研究[ J] . 计算机学 报, 2006, 29( 2): 286- 299.


Last Update: 2007-08-30