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Original Articles

Spatially dependent regularization parameter selection in total generalized variation models for image restoration

, &
Pages 109-123 | Received 17 Feb 2012, Accepted 31 May 2012, Published online: 04 Jul 2012

References

  • Bertalmio , M. , Caselles , V. , Rougé , B. and Solé , A. 2003 . TV based image restoration with local constraints . J. Sci. Comput. , 19 : 95 – 122 . (doi:10.1023/A:1025391506181)
  • Blomgren , P. , Chan , T. F. and Mulet , P. 1997 . “ Extensions to total variation denoising ” . In Proceedings of SPIE 1997 San Diego , CA
  • Bovik , A. 2000 . “ Handbook of Image and Video Processing ” . San Diego : Academic Press .
  • Bredies , K. and Valkonen , T. Inverse problems with second-order total generalized variation constraints . Proceedings of SampTA 2011 – 9th International Conference on Sampling Theory and Applications . Singapore .
  • Bredies , K. , Kunisch , K. and Pock , T. 2010 . Total generalized variation . SIAM J. Imaging Sci. , 3 ( 3 ) : 492 – 526 . (doi:10.1137/090769521)
  • Chambolle , A. and Lions , P.-L. 1997 . Image recovery via total variation minimization and related problems . Numer. Math. , 76 : 167 – 188 . (doi:10.1007/s002110050258)
  • Chambolle , A. and Pock , T. 2011 . A first order primal dual algorithm for convex problems with applications to imaging . J. Math. Imaging Vision , 40 ( 1 ) : 120 – 145 . (doi:10.1007/s10851-010-0251-1)
  • Chan , T. F. , Marquina , A. and Mulet , P. 2000 . Higher order total variation-based image restoration . SIAM J. Sci. Comput. , 22 : 503 – 516 . (doi:10.1137/S1064827598344169)
  • Dong , Y. Q. , Hintermüller , M. and Rincon-Camacho , M. 2011 . Automated regularization parameter selection in multi-scale total variation models for image restoration . J. Math. Imaging Vision , 40 : 82 – 104 . (doi:10.1007/s10851-010-0248-9)
  • Knoll , F. , Bredies , K. , Pock , T. and Stollberger , R. 2011 . Second order total generalized variation (TGV) for MRI . Magn. Reson. Med. , 65 ( 22 ) : 480 – 491 . (doi:10.1002/mrm.22595)
  • Liao , H. , Li , F. and Ng , M. 2009 . Selection of regularization parameter in total variation image restoration . J. Opt. Soc. Am. A , 26 ( 11 ) : 2311 – 2320 . (doi:10.1364/JOSAA.26.002311)
  • Osher , S. , Burger , M. , Goldfarb , D. , Xu , J. and Yin , W. 2005 . An iterative regularization method for total variation-based image restoration . SIAM Multiscale Model. Simul. , 4 : 460 – 489 . (doi:10.1137/040605412)
  • Ring , W. 2000 . Structural properties of solutions to total variation regularization problems . Math. Model. Numer. Anal. , 34 ( 4 ) : 799 – 810 . (doi:10.1051/m2an:2000104)
  • Rudin , L. I. , Osher , S. and Fatemi , E. 1992 . Nonlinear total variation based noise removal algorithms . Phys. D , 60 : 259 – 268 . (doi:10.1016/0167-2789(92)90242-F)
  • Strong , D. and Chan , T. 1996 . “ Spatially and scale adaptive total variation based regularization and anisotropic diffusion in image processing ” . In Tech. Rep , Los Angeles : UCLA .
  • Tadmor , E. , Nezzar , S. and Vese , L. 2004 . A multiscale image representation using hierarchical (BV, L 2) decompositions . Multiscale Model. Simul. , 2 : 554 – 579 . (doi:10.1137/030600448)
  • Temam , R. “ Problèmes Mathématiques en Plasticité [Mathematical Problems in Plasticity] ” . In Méthodes Mathématiques de l'Informatique [Mathematical Methods of Information Science] 12. Gauthier-Villars, Montrouge, 1983 [French].
  • Tikhonov , A. and Arsenin , V. 1977 . “ Solutions of Ill-Posed Problems ” . Washington , DC : Winston and Sons .
  • Vogel , C. R. 2002 . “ Computational Methods for Inverse Problems ” . In Frontiers in Applied Mathematics , Vol. 23 , Philadelphia , PA : SIAM .
  • Wen , Y.-W. and Chan , R. H. 2012 . Parameter selection for total variation based image restoration using discrepancy principle . IEEE Trans. Image Process. , 21 ( 4 ) : 1770 – 1781 . (doi:10.1109/TIP.2011.2181401)

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