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一种基于L曲线准则的正则化图像复原算法

Keywords: 偏差函数,正则化函数,正则化参数,L曲线准则

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Abstract:

针对因大气湍流而引起的模糊图像的复原问题,通过对偏差函数添加正则函数以使得要求解的方程组是适定的.以偏差函数和正则化函数为坐标,得到复原图像关于正则化参数的参数曲线,用三次多项式拟合了该曲线的左端部分,并以该曲线的最大曲率点对应的参数为最优正则化参数.当图像边界满足周期性条件时,利用傅里叶矩阵可以将分块循环矩阵对角化,进而利用二维离散傅里叶变化和反变换求解线性方程组而得到复原图像.实验结果表明,当噪声方差较小时,可得到比较满意的复原结果.

References

[1]  Vogel C R. Computational methods for inverse problems [M]. [S.l.]: SIAM, 2002.
[2]  Dorota K, Marek R. Regularization parameter selection in discrete ill-posed problems-the use of the U-curve[J]. Int J Appl Math Comput Sci, 2007,17(2):157-164.
[3]  Hansen P C, Oleary D P. The use of the L-curve in the regularization of discrete ill-posed problems[J]. SIAM Sci Comput, 1993,14(6):1487-1503.
[4]  Hansen P C. Analysis of discrete ill-posed problems by means of the L-curve[J]. SIAM Rev, 1992,34(4):561-580.
[5]  Rodriguz G, Seatzu S, Theis D. A new technique for ill-conditional linear systems[J]. Numerical Algorithms, 2003,33:433-442.
[6]  徐新禹,李建成,王正涛,等.Tikhonov 正则化方法在GOCE 重力场求解中的模拟研究[J].测绘学报,2010,39(5):465-470.Xu Xinyu, Li Jiancheng, Wang Zhengtao, et al. The simulation research on the Tikhonov regularization applied in gravity field determination of GOCE satellite mission[J]. Acta Geodaetica et Cartographica Sinica, 2010,39(5):465-470. (in Chinese)
[7]  盛琳阳,解凯,张田文.超分辨率图像复原中的快速L-曲线估计[J].小型微型计算机系统,2006,27(6):1120-1123. Sheng Linyang, Xie Kai, Zhang Tianwen. Efficient parameter estimation with L-curve in super-resolution image reconstruction[J]. Mini Micro Systems, 2006,27(6):1120-1123. (in Chinese)
[8]  李绍新,许晓安,徐军发,等.基于L曲线法正则参数优化反演光子相关光谱[J].华中科技大学学报:自然科学版,2010,38(6):102-106.Li Shaoxin, Xu Xiaoan, Xu Junfa, et al. Inversion of photon correlation spectroscopy by means of L-curve optimizing regular parameters[J]. J Huazhong Univ of Sci & Tech: Natural Science ed, 2010,38(6):102-106. (in Chinese)
[9]  吴国丽,李维国. L-曲线估计确定正则参数的双网格迭代法[J].数学理论与应用,2006,26(4):8-12.Wu Guoli, Li Weiguo. L-curve curvature bounds in two-grid iterative methods[J]. Mathematical Theory and Applications, 2006,26(4):8-12. (in Chinese)[ZK)]
[10]  汉语,伍凡,万勇建,等.Tikhonov正则化在Zernike多项式拟合中的应用[J].光电工程,2010,37(7):60-63. Han Yu, Wu Fan, Wan Yongjian, et al. Application of Tikhonov regularization method in Zernike polynomials fitting[J]. Opto-Electronic Engineering, 2010,37(7):60-63. (in Chinese)
[11]  张路寅,张玉海,钱坤明.关于不适定问题的迭代Tikhonov正则化方法[J].山东大学学报,2011,46(4):29-33.Zhang Luyin, Zhang Yuha, Qian Kunming. On the iterated Tikhonov regularization for ill-posed problems[J]. Journal of Shandong University, 2011,46(4):29-3. (in Chinese)
[12]  霍智勇,朱秀昌.用于图象复原的离散L-曲线自适应算法[J].南京邮电大学学报,2008,28(4):27-33.Huo Zhiyong, Zhu Xiuchang. An adaptive discrete L-curve algorithm for image restoration[J]. Journal of Nanjing University of Posts and Telecommunications, 2008,28(4):27-33. (in Chinese)

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