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總變分圖像復(fù)原方程的離散化方法

鄒謀炎,  劉小軍

鄒謀炎, 劉小軍. 總變分圖像復(fù)原方程的離散化方法[J]. 電子與信息學(xué)報(bào), 2001, 23(9): 861-867.
引用本文: 鄒謀炎, 劉小軍. 總變分圖像復(fù)原方程的離散化方法[J]. 電子與信息學(xué)報(bào), 2001, 23(9): 861-867.
Zou Mouyan, Liu Xiaojun . A DISCRETIZATION METHOD FOR TOTAL VARIATION BASED IMAGE RESTORATION EQUATION[J]. Journal of Electronics & Information Technology, 2001, 23(9): 861-867.
Citation: Zou Mouyan, Liu Xiaojun . A DISCRETIZATION METHOD FOR TOTAL VARIATION BASED IMAGE RESTORATION EQUATION[J]. Journal of Electronics & Information Technology, 2001, 23(9): 861-867.

總變分圖像復(fù)原方程的離散化方法

A DISCRETIZATION METHOD FOR TOTAL VARIATION BASED IMAGE RESTORATION EQUATION

  • 摘要: 基于總變分的圖像重建和復(fù)原導(dǎo)致一類最小化問(wèn)題,它歸結(jié)為解一個(gè)非線性橢圓型偏微分方程。為了得到數(shù)值解,必須將問(wèn)題線性化和離散化。C.R.Vogel和M.E.Oman等人(1996)的定點(diǎn)迭代是一個(gè)良好的線性化方法。然而文獻(xiàn)中已報(bào)道的離散化方法需要微分方程數(shù)值解的工具,比較繁雜。該文提出一種新的離散化方法,它只需要圖像處理中的常規(guī)技術(shù)。圖像反降晰和噪聲抑制的實(shí)驗(yàn)結(jié)果表明該文的結(jié)果不亞于文獻(xiàn)中報(bào)道的結(jié)果。
    Abstract: Total variation based image restoration and reconstruction lead to a kind of minimization problem that turns out to be a nonlinear integro-differential equation of elliptic type. An effective linearization and. discretization method is essential for solving the problem. The fixed point iteration proposed by C. R. Vogel and M. E. Oman(1996) is an elegant scheme of linearization. For discretization of the problem, however, the reported methods mostly involve the skills in numerical solutions of differential equations that are not amiable for the image processing community. In this paper, a discretization method is presented that needs only con- ventional technique for image processing. The method can simplify the implementation of the fixed point iteration scheme. The experimental results of image restoration and image denoising are used to justify the method.
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  • L.I. Rudin, S. Osher, Feature-oriented image enhancement using shock filters, SIAM J. Num.Anal., 1990, 27, 919-940.[2]L.I. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms.[J]. Phvsica D.1992,60:259-[3]T.F. Chan, H. M. Zhou, R. H. Chan, Continuation method for total variation denoising problems,In SPIE 1995, vol.2563, Advanced Signal Processing Algorithms, F. T. Luk, Ed., San Diego, CA.1995, ［4］Y. Li, F. Santosa, A computational algorithm for minimizing total variation in image restoration,IEEE Trans. on Image Processing, 1996, 5(6), 987-995.[4]C.R. Vogel, M. E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput.,1996, 17(1), 227-238.[5]C.R. Vogel, M. E. Oman, Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Trans. on Image Processing, 1998, 7(6), 813 824.[6]R.E. Ewing, J. Shen, A multigrid algorithm for the cell-centered finite difference scheme, in Proc.6th Copper Mountain Conf. Multigid Methods. NASA Conf. Pub. 3224, April, 1993. ［8］T.F. Chan, Chiu-Kwong, Total variation blind deconvolution, IEEE Trans. on Image Processing,1998, 17(3), 370-375.[7]Zou Mou-yan, R. Unbenhauen, On the computational model of a kind of deconvolution problems,IEEE Trans. on Image Processing, 1995, 4(10), 1464-1467.[8]E.H. Golub, C. F. Van Loan, Matrix Computations, Baltimore, MD: Johns Hopkins Univ. Press,1989. ［11］C. Charalambous, F. K. Ghaddar, K. Kouris, Two iterative image restoration algorithms with application to nuclear medicine, IEEE Trans. on Medical Imaging, 1992, 11(1), 2-8.[9]Zou Mou-yan, Zou Xi, Global optimization: An auxiliary cost function approach, IEEE Trans.on Systems, Man, and Cybernetics, Part A, 2000, 30(3), 347-354.
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出版歷程
  • 收稿日期:  2000-01-21
  • 修回日期:  2000-09-14
  • 刊出日期:  2001-09-19

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