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Volumn 43, Issue 3, 2012, Pages 167-179

A fast fixed point algorithm for total variation deblurring and segmentation

Author keywords

Fixed point; Image deblurring; Image segmentation; Proximity operator

Indexed keywords

DEBLURRING; FIXED POINTS; FIXED-POINT ALGORITHMS; IMAGE DEBLURRING; MINIMIZATION PROBLEMS; NUMERICAL ALGORITHMS; NUMERICAL EXPERIMENTS; PROXIMITY OPERATOR; STATE-OF-THE-ART ALGORITHMS; TOTAL VARIATION;

EID: 84859433768     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-011-0298-7     Document Type: Article
Times cited : (33)

References (34)
  • 1
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • 0780.49028 10.1016/0167-2789(92)90242-F
    • L.I. Rudin S. Osher E. Fatemi 1992 Nonlinear total variation based noise removal algorithms Physica D 60 259 268 0780.49028 10.1016/0167-2789(92)90242-F
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 2
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • DOI 10.1007/s002110050258
    • A. Chambolle P.L. Lions 1997 Image recovery via total variation minimization and related problems Numer. Math. 76 167 188 1440119 0874.68299 10.1007/s002110050258 (Pubitemid 127056405)
    • (1997) Numerische Mathematik , vol.76 , Issue.2 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 3
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • DOI 10.1002/cpa.20042
    • I. Daubechies M. Defrise C. De Mol 2004 An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Commun. Pure Appl. Math. 57 11 1413 1457 1077.65055 10.1002/cpa.20042 (Pubitemid 39427442)
    • (2004) Communications on Pure and Applied Mathematics , vol.57 , Issue.11 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 5
    • 84990602490 scopus 로고
    • Optimal approximation by piecewise smooth functions and associated variational problems
    • 997568 0691.49036 10.1002/cpa.3160420503
    • D. Mumford J. Shah 1989 Optimal approximation by piecewise smooth functions and associated variational problems Commun. Pure Appl. Math. 42 577 685 997568 0691.49036 10.1002/cpa.3160420503
    • (1989) Commun. Pure Appl. Math. , vol.42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 6
    • 0032096686 scopus 로고    scopus 로고
    • Fast, robust total variation-based reconstruction of noisy, blurred images
    • PII S1057714998040020
    • C. Vogel M. Oman 1998 Fast, robust total variation-based reconstruction of noisy, blurring images IEEE Trans. Image Process. 7 813 824 1667392 0993.94519 10.1109/83.679423 (Pubitemid 128745393)
    • (1998) IEEE Transactions on Image Processing , vol.7 , Issue.6 , pp. 813-824
    • Vogel, C.R.1    Oman, M.E.2
  • 7
    • 0033295350 scopus 로고    scopus 로고
    • A nonlinear primal-dual method for total variation-based image restoration
    • 1694649 0929.68118 10.1137/S1064827596299767
    • T.F. Chan G.H. Golub P. Mulet 1999 A nonlinear primal-dual method for total variation-based image restoration SIAM J. Sci. Comput. 20 1964 1977 1694649 0929.68118 10.1137/S1064827596299767
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1964-1977
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 8
    • 33645038355 scopus 로고    scopus 로고
    • Second-order cone programming methods for total variation-based image restoration
    • 2202237 10.1137/040608982
    • D. Goldforb W. Yin 2005 Second-order cone programming methods for total variation-based image restoration SIAM J. Sci. Comput. 27 2 622 645 2202237 10.1137/040608982
    • (2005) SIAM J. Sci. Comput. , vol.27 , Issue.2 , pp. 622-645
    • Goldforb, D.1    Yin, W.2
  • 9
    • 70350593691 scopus 로고    scopus 로고
    • Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems
    • 2722312 10.1109/TIP.2009.2028250
    • A. Beck M. Teboulle 2009 Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems IEEE Trans. Image Process. 18 11 2419 2434 2722312 10.1109/TIP.2009.2028250
    • (2009) IEEE Trans. Image Process. , vol.18 , Issue.11 , pp. 2419-2434
    • Beck, A.1    Teboulle, M.2
  • 10
    • 34247549668 scopus 로고    scopus 로고
    • On semismooth Newton's methods for total variation minimization
    • DOI 10.1007/s10851-007-0650-0
    • M.K. Ng L.Q. Qi Y.F. Yang Y.M. Huang 2007 On semismooth newton's methods for total variation minimization J. Math. Imaging Vis. 27 3 265 276 2325853 10.1007/s10851-007-0650-0 (Pubitemid 46664095)
    • (2007) Journal of Mathematical Imaging and Vision , vol.27 , Issue.3 , pp. 265-276
    • Ng, M.K.1    Qi, L.2    Yang, Y.-F.3    Huang, Y.-M.4
  • 12
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • 2486032 1187.68665
    • Y. Wang J. Yang W. Yin Y. Zhang 2008 A new alternating minimization algorithm for total variation image reconstruction J. Imag. Sci. 1 3 248 272 2486032 1187.68665
    • (2008) J. Imag. Sci. , vol.1 , Issue.3 , pp. 248-272
    • Wang, Y.1    Yang, J.2    Yin, W.3    Zhang, Y.4
  • 13
    • 84969334819 scopus 로고    scopus 로고
    • The split Bergman method for l1 regularized problems
    • 2496060 1177.65088 10.1137/080725891
    • T. Goldstein S. Osher 2009 The split Bergman method for l1 regularized problems J. Imag. Sci. 2 2 323 343 2496060 1177.65088 10.1137/080725891
    • (2009) J. Imag. Sci. , vol.2 , Issue.2 , pp. 323-343
    • Goldstein, T.1    Osher, S.2
  • 14
    • 77955783919 scopus 로고    scopus 로고
    • Fast image recovery using variable splitting and constrained optimization
    • 2798930 10.1109/TIP.2010.2047910
    • M. Afonso J. Bioucas-Dias M. Figueiredo 2010 Fast image recovery using variable splitting and constrained optimization IEEE Trans. Image Process. 19 9 2345 2356 2798930 10.1109/TIP.2010.2047910
    • (2010) IEEE Trans. Image Process. , vol.19 , Issue.9 , pp. 2345-2356
    • Afonso, M.1    Bioucas-Dias, J.2    Figueiredo, M.3
  • 15
    • 36348991574 scopus 로고    scopus 로고
    • A primal-dual active-set method for non-negativity constrained total variation deblurring problems
    • DOI 10.1109/TIP.2007.908079
    • D. Krishnan P. Lin A.M. Yip 2007 A primal-dual active-set method for non-negativity constrained total variation deblurring problems IEEE Trans. Image Process. 16 11 2766 2777 2472418 10.1109/TIP.2007.908079 (Pubitemid 350141849)
    • (2007) IEEE Transactions on Image Processing , vol.16 , Issue.11 , pp. 2766-2777
    • Krishnan, D.1    Lin, P.2    Yip, A.M.3
  • 16
    • 67349259329 scopus 로고    scopus 로고
    • A primal-dual active-set algorithm for bilaterally constrained total variation deblurring and piecewise constant Mumford-shah segmentation problems
    • 2511581 1169.94005 10.1007/s10444-008-9101-8
    • D. Krishnan Q.V. Pham A.M. Yip 2009 A primal-dual active-set algorithm for bilaterally constrained total variation deblurring and piecewise constant Mumford-shah segmentation problems Adv. Comput. Math. 31 1-3 237 266 2511581 1169.94005 10.1007/s10444-008-9101-8
    • (2009) Adv. Comput. Math. , vol.31 , Issue.13 , pp. 237-266
    • Krishnan, D.1    Pham, Q.V.2    Yip, A.M.3
  • 17
    • 0035248865 scopus 로고    scopus 로고
    • Active contours without edges
    • DOI 10.1109/83.902291
    • T.F. Chan L.A. Vese 2001 Active contours without edges IEEE Trans. Image Process. 10 2 266 277 1039.68779 10.1109/83.902291 (Pubitemid 32254596)
    • (2001) IEEE Transactions on Image Processing , vol.10 , Issue.2 , pp. 266-277
    • Chan, T.F.1    Vese, L.A.2
  • 18
    • 57049189180 scopus 로고    scopus 로고
    • A multi-resolution stochastic level set method for Mumford-Shah image segmentation
    • 2517432 10.1109/TIP.2008.2005823
    • Y.N. Law H.K. Lee A.M. Yip 2008 A multi-resolution stochastic level set method for Mumford-Shah image segmentation IEEE Trans. Image Process. 17 12 2289 2300 2517432 10.1109/TIP.2008.2005823
    • (2008) IEEE Trans. Image Process. , vol.17 , Issue.12 , pp. 2289-2300
    • Law, Y.N.1    Lee, H.K.2    Yip, A.M.3
  • 20
    • 77956186438 scopus 로고    scopus 로고
    • Geometric applications of the split Bergman method: Segmentation and surface reconstruction
    • 2679800 1203.65044 10.1007/s10915-009-9331-z
    • T. Goldstein X. Bresson S. Osher 2010 Geometric applications of the split Bergman method: segmentation and surface reconstruction J. Sci. Comput. 45 1-3 272 293 2679800 1203.65044 10.1007/s10915-009-9331-z
    • (2010) J. Sci. Comput. , vol.45 , Issue.13 , pp. 272-293
    • Goldstein, T.1    Bresson, X.2    Osher, S.3
  • 21
    • 77954087952 scopus 로고    scopus 로고
    • A fast algorithm for the total variation model of image denoising
    • 2659588 1191.94017 10.1007/s10444-009-9128-5
    • R.Q. Jia H. Zhao 2010 A fast algorithm for the total variation model of image denoising Adv. Comput. Math. 33 231 241 2659588 1191.94017 10.1007/s10444-009-9128-5
    • (2010) Adv. Comput. Math. , vol.33 , pp. 231-241
    • Jia, R.Q.1    Zhao, H.2
  • 22
    • 79953645045 scopus 로고    scopus 로고
    • Proximity algorithms for image models: Denoising
    • Micchelli, C.A., Shen, L.X., Xu, Y.S.: Proximity algorithms for image models: denoising. Inverse Probl. 27(4) (2011)
    • (2011) Inverse Probl. , vol.27 , Issue.4
    • Micchelli, C.A.1    Shen, L.X.2    Xu, Y.S.3
  • 23
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace Hilbertien
    • 201952 0136.12101
    • J.J. Moreau 1965 Proximité et dualité dans un espace Hilbertien Bull. Soc. Math. Fr., Mém. 93 273 299 201952 0136.12101
    • (1965) Bull. Soc. Math. Fr., Mém. , vol.93 , pp. 273-299
    • Moreau, J.J.1
  • 24
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • 2203849 10.1137/050626090
    • P. Combettes V. Wajs 2006 Signal recovery by proximal forward-backward splitting Multiscale Model. Simul. 4 4 1168 1200 2203849 10.1137/050626090
    • (2006) Multiscale Model. Simul. , vol.4 , Issue.4 , pp. 1168-1200
    • Combettes, P.1    Wajs, V.2
  • 25
    • 84968481460 scopus 로고
    • Weak convergence of the sequence of successive approximations for nonexpansive mappings
    • 211301 0179.19902 10.1090/S0002-9904-1967-11761-0
    • Z. Opial 1967 Weak convergence of the sequence of successive approximations for nonexpansive mappings Bull. Am. Math. Soc. 73 591 597 211301 0179.19902 10.1090/S0002-9904-1967-11761-0
    • (1967) Bull. Am. Math. Soc. , vol.73 , pp. 591-597
    • Opial, Z.1
  • 26
    • 77952921188 scopus 로고    scopus 로고
    • Split Bregman methods and frame based image restoration
    • 2581025 10.1137/090753504
    • J.F. Cai S. Osher Z. Shen 2009 Split Bregman methods and frame based image restoration Multiscale Model. Simul. 8 2 337 369 2581025 10.1137/090753504
    • (2009) Multiscale Model. Simul. , vol.8 , Issue.2 , pp. 337-369
    • Cai, J.F.1    Osher, S.2    Shen, Z.3
  • 27
    • 39449085530 scopus 로고    scopus 로고
    • A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery
    • DOI 10.1109/JSTSP.2007.910264
    • P.L. Combettes J.C. Pesquet 2007 A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery IEEE J. Sel. Top. Signal Process. 1 564 574 10.1109/JSTSP.2007.910264 (Pubitemid 351266623)
    • (2007) IEEE Journal on Selected Topics in Signal Processing , vol.1 , Issue.4 , pp. 564-574
    • Combettes, P.L.1    Pesquet, J.-C.2
  • 28
    • 79251599898 scopus 로고    scopus 로고
    • Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
    • 2763184 1207.94006 10.1016/j.cam.2010.11.028
    • D.Q. Chen L.Z. Cheng F. Su 2011 Restoration of images based on subspace optimization accelerating augmented Lagrangian approach J. Comput. Appl. Math. 235 8 2766 2774 2763184 1207.94006 10.1016/j.cam.2010.11.028
    • (2011) J. Comput. Appl. Math. , vol.235 , Issue.8 , pp. 2766-2774
    • Chen, D.Q.1    Cheng, L.Z.2    Su, F.3
  • 29
    • 80052211668 scopus 로고    scopus 로고
    • Operator splittings, Bregman methods and frame shrinkage in image processing
    • 2780769 10.1007/s11263-010-0357-3
    • S. Setzer 2011 Operator splittings, Bregman methods and frame shrinkage in image processing Int. J. Comput. Vis. 92 3 265 280 2780769 10.1007/s11263-010-0357-3
    • (2011) Int. J. Comput. Vis. , vol.92 , Issue.3 , pp. 265-280
    • Setzer, S.1
  • 30
    • 33750153530 scopus 로고    scopus 로고
    • Algorithms for finding global minimizers of image segmentation and denoising models
    • DOI 10.1137/040615286
    • T.F. Chan S. Esedolglu M. Nikolova 2006 Algorithms for finding global minimizers of image segmentation and denoising models SIAM J. Appl. Math. 66 1632 1648 2246072 1117.94002 10.1137/040615286 (Pubitemid 44599935)
    • (2006) SIAM Journal on Applied Mathematics , vol.66 , Issue.5 , pp. 1632-1648
    • Chan, T.F.1    Esedoglu, S.2    Nikolova, M.3
  • 31
    • 17444406259 scopus 로고    scopus 로고
    • Smooth minimization of non-smooth functions
    • DOI 10.1007/s10107-004-0552-5
    • Y. Nesterov 2005 Smooth minimization of non-smooth functions Math. Program. 103 127 152 2166537 1079.90102 10.1007/s10107-004-0552-5 (Pubitemid 40537674)
    • (2005) Mathematical Programming , vol.103 , Issue.1 , pp. 127-152
    • Nesterov, Yu.1
  • 32
    • 77949265482 scopus 로고    scopus 로고
    • Removing multiplicative noise by Douglas-Rachford splitting methods
    • 2585850 10.1007/s10851-009-0179-5
    • G. Steidl T. Teuber 2010 Removing multiplicative noise by Douglas-Rachford splitting methods J. Math. Imaging Vis. 36 2 168 184 2585850 10.1007/s10851-009-0179-5
    • (2010) J. Math. Imaging Vis. , vol.36 , Issue.2 , pp. 168-184
    • Steidl, G.1    Teuber, T.2


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