Electrical Flow Algorithms for Total Variation Minimization

作者: Aleksander Madry , Richard Peng , Gary L. Miller

DOI:

关键词:

摘要: The total variation (TV) minimization framework is a very popular method for wide variety of image restoration problems. This comes in two variants: anisotropic, where the “smoothness” denoised measured by L1-difference neighboring pixel; and isotropic, measure based on computing localized L2-differences thus rotationally invariant. There was lot work obtaining efficient algorithms computingTV denoising. Most this effort focused anisotropic variant as it possible to exploit its connection maximum flow problem. In case isotropic variant, no longer holds context rely convex programming techniques, which results much slower running time. paper we develop an approach TV that electrical flows builds upon introduced [CKM + 11]. encompasses natural way both variants obtains times versions are essentially same. On with n pixels m relations, our algorithm produces solution that’s within 1 ǫ optimum time ˜

参考文章(16)
Tony F. Chan, Jianhong (Jackie) Shen, Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. ,(2005) , 10.1137/1.9780898717877
Shantanu H. Joshi, Antonio Marquina, Stanley J. Osher, Ivo Dinov, John D. Van Horn, Arthur W. Toga, Edge-Enhanced Image Reconstruction Using (TV) Total Variation and Bregman Refinement international conference on scale space and variational methods in computer vision. pp. 389- 400 ,(2009) , 10.1007/978-3-642-02256-2_33
Brendt Wohlberg, Paul Rodriguez, An Iteratively Reweighted Norm Algorithm for Minimization of Total Variation Functionals IEEE Signal Processing Letters. ,vol. 14, pp. 948- 951 ,(2007) , 10.1109/LSP.2007.906221
Wotao Yin, Stanley Osher, Donald Goldfarb, Jerome Darbon, Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing Siam Journal on Imaging Sciences. ,vol. 1, pp. 143- 168 ,(2008) , 10.1137/070703983
Stephen Boyd, Kwangmoo Koh, Seung-Jean Kim, An Interior-Point Method for Large-Scale l 1 -Regularized Logistic Regression Journal of Machine Learning Research. ,vol. 8, pp. 1519- 1555 ,(2007)
Donald Goldfarb, Wotao Yin, Second-order Cone Programming Methods for Total Variation-Based Image Restoration SIAM Journal on Scientific Computing. ,vol. 27, pp. 622- 645 ,(2005) , 10.1137/040608982
Ioannis Koutis, Gary L. Miller, A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians symposium on discrete algorithms. pp. 1002- 1011 ,(2007) , 10.5555/1283383.1283491
Erik G. Boman, Bruce Hendrickson, Support Theory for Preconditioning SIAM Journal on Matrix Analysis and Applications. ,vol. 25, pp. 694- 717 ,(2003) , 10.1137/S0895479801390637
Jian-Feng Cai, Stanley Osher, Zuowei Shen, Split Bregman Methods and Frame Based Image Restoration Multiscale Modeling & Simulation. ,vol. 8, pp. 337- 369 ,(2010) , 10.1137/090753504
Andrew V. Goldberg, Satish Rao, Beyond the flow decomposition barrier Journal of the ACM. ,vol. 45, pp. 783- 797 ,(1998) , 10.1145/290179.290181