l2-total variation image restoration based on subspace optimization

doi:10.3724/SP.J.1087.2013.01112

Journal of Computer Applications ›› 2013, Vol. 33 ›› Issue (04): 1112-1114.DOI: 10.3724/SP.J.1087.2013.01112

• Network and distributed techno • Previous Articles Next Articles

l2-total variation image restoration based on subspace optimization

LIU Xiaoguang¹,GAO Xingbao¹,ZHOU Dongmei²

1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an Shaanxi 710062, China
2. School of Xin Yuan, Chendu Hi-tech Industrial Development Zone, Chengdu Sichuan 610041, China

Received:2012-11-01 Revised:2012-12-09 Online:2013-04-23 Published:2013-04-01
Contact: LIU Xiaoguang

基于子空间优化的l2-总变分图像恢复

刘晓光¹,高兴宝¹,周冬梅²

1. 陕西师范大学数学与信息科学学院，西安 710062
2. 成都高新新源学校，成都 610041

通讯作者: 刘晓光
作者简介:刘晓光(1985-)，男，甘肃定西人，博士研究生，主要研究方向：最优化理论与算法、数字图像处理；高兴宝(1966-)，男，陕西陇县人，教授，博士生导师，主要研究方向：最优化理论与算法、神经网络；周冬梅(1986-)，女，陕西汉中人，硕士研究生，主要研究方向: 偏微分方程及其应用。
基金资助:
中央高校基本科研业务费专项基金资助项目(GK201001002);中央高校基本科研业务费专项基金资助项目(GK201001002)

Abstract

Abstract: The alternating direction method is used widely to deal with the problem of total variation image restoration. A correction method was proposed to solve the problem of inaccuracy in search direction of the alternating direction method, which may influence the efficiency of the algorithm and the quality of the restored images adversely. Combining Taylor expansion of energy function and properties of differentiable function, this subspace-optimization-based method corrected the current direction effectively by utilizing the previous one, and improved the accuracy of search direction. The numerical experiments expound the efficiency of this algorithm and the quality of the restored images by running time and Peak-Signal-to-Noise Ratio (PSNR), respectively.

Key words: neat boundary, Total Variation (TV), alternating direction method, subspace optimization, image restoration

摘要： 交替方向法被广泛用来求解总变分图像恢复问题, 鉴于其搜索方向的不精确性对算法效率和图像恢复质量有着一定影响, 提出了一种矫正方法。该方法以子空间优化为基础,结合能量函数泰勒展式及可微函数性质, 利用先前搜索方向对当前方向进行有效矫正, 提高了搜索方向的精确性。数值实验利用算法运行时间和峰值性噪比分别说明了该修正方法的效率和图像恢复质量。

关键词: 整齐边界, 总变分, 交替方向法, 子空间优化, 图像恢

CLC Number:

TP391

LIU Xiaoguang GAO Xingbao ZHOU Dongmei. l2-total variation image restoration based on subspace optimization[J]. Journal of Computer Applications, 2013, 33(04): 1112-1114.

刘晓光高兴宝周冬梅. 基于子空间优化的l2-总变分图像恢复[J]. 计算机应用, 2013, 33(04): 1112-1114.

References

［1］GONZALEZ R C, WOODS R E. Digital image processing［M］. 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall, 2008.

［2］GUO X X, LI F, NG M K, A fast l1-TV algorithm for image restoration［J］. SIAM Journal Scientific Computing, 2009, 31(3): 2322-2341.

［3］BLACK M J, RANGARAJAN A. On the unification of line processes, outlier rejection, and robust statistics with applications to early vision［J］. International Journal of Computer Vision, 1996, 19(1): 57-91.

［4］RUDIN L I, OSHER S, FATEMI E. Nonlinear total variaion based noise removal algorithm［J］. Physica D: Nonlinear Phenomena, 1992, 60(1/2/3/4): 259-268.

［5］袁亚湘, 孙文瑜, 最优化理论与方法［M］. 北京:科学出版社, 2005.

［6］BOYD S, VANDENBERGHE L. Convex optimization［M］. Cambridge: Cambridge University, 2004.

［7］CHAMBOLLE A. An algorithm for total variation minimization and application［J］. Journal of Mathematical Imaging and Vision, 2004, 20(1/2): 89-97.

［8］NG M K, QI L Q, YANG Y F, et al.On semismooth Newton's methods for total variation minimization［J］. Journal of Mathematical Imaging and Vision,2007, 27(3): 256-276.

［9］LI Y Y, SANTOSA F. A computational algorithm for minimizing total variation in image reconstruction［J］. IEEE Transactions on Image Processing, 1996, 5(6): 987-995.

［10］HUANG Y M, NG M K, WEN Y W. A fast total variation minimization method for image restoration［J］. Multiscale Modeling and Simulation, 2008, 7(2): 774-795.

［11］ELAD M, MATLON B, ZIBULEVSKY M. Coordinate and subspace optimization methods for linear squares with non-quadratic regularization［J］. Applied and Computational Harmonic Analysis, 2007, 23(3): 346-367.

［12］YOUNG D M. Iterative solution of large linear systems［M］. New York: Academic, 1971.

［13］胡家赣. 线性代数方程组的迭代解法［M］. 北京: 科学出版社, 1999: 40-53.

［14］VARGA R S. Matrix iterative analysis［M ］ . 2nd ed. New York: Springer-Verlag, 2000.

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l2-total variation image restoration based on subspace optimization

基于子空间优化的l2-总变分图像恢复

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