马洁;国凯;

• 1:青岛大学信息工程学院

摘要(Abstract)：

TV去噪模型是基于一阶导数总变差的变分模型,容易在光滑区域出现阶梯效应。通常利用高阶导数信息来使图像扩散更加平滑。Euler弹性项使用光滑的边界对图像进行处理,广泛应用于图像遮挡,修复,分割等领域。本文主要研究基于Euler弹性项的图像去噪模型,并采用Split Bregman算法实现,有效地改善了TV模型的阶梯效应,并用数值实验验证了算法的有效性。

关键词(KeyWords)： 图像去噪;TV模型;Euler弹性项;Split Bregman算法

Abstract:

Keywords:

基金项目(Foundation):

作者(Author): 马洁;国凯;

Email:

DOI:

参考文献(References)：

• [1]P.Perona,J.MALK,Scale-space and edge detection using anisotropic diffusion[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
• [2]L.Rudin,S.Osher,E.fatemi,Nonlinear toatal varation based noise removalalgorithms[J].Physica D,1992,60(11):259-268.
• [3]M.Lysaker,A.Lundervold,and X.C.Tai,Noise removal using fourth-orderpartial differential equation with applications to medical magnetic resonanceimages in space and time[J].IEEE.Trans.Image Process.,2003,12(12):1579-1590.
• [4]]Y.L.You,M.Kaveh,Fourth-order partial differential equations for noiseremoval[J].IEEE Transactions on Image Processing,2000,9(10):1723-1730.
• [5]潘振宽,魏伟波,张海涛,基于梯度和拉普拉斯算子的图像扩散变分模型[J].山东大学学报,2008,43(11):1-6.
• [6]W.Zhu and T.Chan,Image denosing using mean curvature of image surface[J].SIAM J.Imaging Sci.,2012,5(1):1-32.
• [7]]M.Nitzberg,D.Mumford,and T.Shiota,Filtering,segmentation,and depth.Lecturenotes in Comp[Z].SCi.,Berlin:Springer,1993,1-151.
• [8]X.C.Tai,J.Hahn,and G.J.Chung,A Fast Algorithm for Euler’s ElasticaModel Using Augmented Lagrangian Method[J].SIAM Journal on Imaging Sciences,2011,4(1):313-344.
• [9]T.F.Chan,A nonlinear primal-dual method for total variation-based image restoration[J].SIAM J.Sci.Comput.,1999,20(6):1964-1977.
• [10]A.E.H.Love,A Treatise on The Mathematical Theory of Elasticity[M].New York:Dover,1927,1-34.
• [11]D.Mumford.Elastica and computer vision.Algebraic geometry and its application[M].New York:Springer-Verlag,1994,491-506.
• [12]T.F.Chan,J.Shen,Euler’s elastica and curvature based inpainting[J].SIAM J.Appl.Math.2002,63(2):564–592.
• [13]T.Goldstein,S.Osher,The Split Bregman algorithm for L1regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
• [14]J.Yang,W.Yin,Y.Zhang and Y.Wang,A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration[J].SIAM J.Imaging Sci.,2009,2(2):569-592.
• [15]J.Yang,Y.Zhang and W.Yin,An Efficient TV-L1Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise[J].SIAM J.Sci.Comput.,2009,31(4):2842-2865.