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Volumn 46, Issue 1, 2011, Pages 20-46

A unified primal-dual algorithm framework based on Bregman iteration

Author keywords

1 minimization; Bregman iteration; Inexact Uzawa methods; Proximal point iteration; Saddle point

Indexed keywords

ALGORITHM FRAMEWORK; BASIS PURSUITS; BREGMAN ITERATION; EXISTING METHOD; INEXACT UZAWA METHODS; MATRIX COMPLETION; MULTISCALE MODELS; NUMERICAL EXAMPLE; PRIMAL DUAL ALGORITHMS; PROXIMAL POINTS; RICE UNIVERSITY; SADDLE POINT; SIGNAL AND IMAGE PROCESSING;

EID: 78651419159     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-010-9408-8     Document Type: Article
Times cited : (359)

References (53)
  • 6
    • 0001341650 scopus 로고    scopus 로고
    • Analysis of the inexact Uzawa algorithm for saddle point problems
    • 0873.65031 10.1137/S0036142994273343 1451114
    • J.H. Bramble J.E. Pasciak A.T. Vassilev 1997 Analysis of the inexact Uzawa algorithm for saddle point problems SIAM J. Numer. Anal. 34 3 1072 1092 0873.65031 10.1137/S0036142994273343 1451114
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.3 , pp. 1072-1092
    • Bramble, J.H.1    Pasciak, J.E.2    Vassilev, A.T.3
  • 7
    • 49949144765 scopus 로고
    • The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming
    • 10.1016/0041-5553(67)90040-7
    • L. Bregman 1967 The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming USSR Comput. Math. Math Phys. 7 200 217 10.1016/0041-5553(67)90040-7
    • (1967) USSR Comput. Math. Math Phys. , vol.7 , pp. 200-217
    • Bregman, L.1
  • 8
    • 77951291046 scopus 로고    scopus 로고
    • A singular value thresholding algorithm for matrix completion
    • 1201.90155 10.1137/080738970 2600248
    • J.-F. Cai E.J. Candès Z. Shen 2010 A singular value thresholding algorithm for matrix completion SIAM J. Optim. 20 4 1956 1982 1201.90155 10.1137/080738970 2600248
    • (2010) SIAM J. Optim. , vol.20 , Issue.4 , pp. 1956-1982
    • Cai, J.-F.1    Candès, E.J.2    Shen, Z.3
  • 9
    • 70349984018 scopus 로고    scopus 로고
    • 1-norm minimization
    • 1198.65103 10.1090/S0025-5718-09-02242-X 2521281
    • 1-norm minimization Math. Comput. 78 2127 2136 1198.65103 10.1090/S0025-5718-09-02242-X 2521281
    • (2009) Math. Comput. , vol.78 , pp. 2127-2136
    • Cai, J.-F.1    Osher, S.2    Shen, Z.3
  • 10
  • 11
    • 78049353841 scopus 로고    scopus 로고
    • Linearized Bregman iterations for frame-based image deblurring
    • 1175.94010 10.1137/080733371 2486529
    • J.-F. Cai S. Osher Z. Shen 2009 Linearized Bregman iterations for frame-based image deblurring SIAM J. Imag. Sci. 2 1 226 252 1175.94010 10.1137/080733371 2486529
    • (2009) SIAM J. Imag. Sci. , vol.2 , Issue.1 , pp. 226-252
    • Cai, J.-F.1    Osher, S.2    Shen, Z.3
  • 12
    • 77951523456 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • to appear
    • Candès, E.J.; Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. (2008, to appear)
    • (2008) Found. Comput. Math.
    • Candès, E.J.1
  • 13
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • DOI 10.1109/TIT.2005.862083
    • E.J. Candès J. Romberg T. Tao 2006 Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information IEEE Trans. Inf. Theory 52 2 489 509 10.1109/TIT.2005.862083 (Pubitemid 43174093)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.2 , pp. 489-509
    • Candes, E.J.1    Romberg, J.2    Tao, T.3
  • 14
    • 0019587748 scopus 로고
    • An iterative row-action method for interval convex programming
    • 0431.49042 10.1007/BF00934676 628201
    • Y. Censor A. Lent 1981 An iterative row-action method for interval convex programming J. Optim. Theory Appl. 34 3 321 353 0431.49042 10.1007/BF00934676 628201
    • (1981) J. Optim. Theory Appl. , vol.34 , Issue.3 , pp. 321-353
    • Censor, Y.1    Lent, A.2
  • 15
    • 1242352408 scopus 로고    scopus 로고
    • An algorithm for total variation minimization and applications
    • 10.1023/B:JMIV.0000011321.19549.88 2049783
    • A. Chambolle 2004 An algorithm for total variation minimization and applications J. Math. Imag. Vis. 20 89 97 10.1023/B:JMIV.0000011321.19549.88 2049783
    • (2004) J. Math. Imag. Vis. , vol.20 , pp. 89-97
    • Chambolle, A.1
  • 16
    • 0005352194 scopus 로고    scopus 로고
    • A nonlinear primal-dual method for total variation-based image restoration
    • 1430131
    • T.F. Chan G.H. Golub P. Mulet 1996 A nonlinear primal-dual method for total variation-based image restoration Math. Oper. Res. 219 241 252 1430131
    • (1996) Math. Oper. Res. , vol.219 , pp. 241-252
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 17
    • 0000433247 scopus 로고
    • Convergence analysis of a proximal like minimization algorithm using Bregman functions
    • Chen, G.; Teboulle, M.: Convergence analysis of a proximal like minimization algorithm using Bregman functions. SIAM J. Optim.; 3 (1993)
    • (1993) SIAM J. Optim. , vol.3
    • Chen, G.1    Teboulle, M.2
  • 18
    • 0002472542 scopus 로고
    • A proximal-based decomposition method for convex minimization problems
    • 0823.90097 10.1007/BF01582566 1274173
    • G. Chen M. Teboulle 1994 A proximal-based decomposition method for convex minimization problems Math. Program. 64 1 81 101 0823.90097 10.1007/BF01582566 1274173
    • (1994) Math. Program. , vol.64 , Issue.1 , pp. 81-101
    • Chen, G.1    Teboulle, M.2
  • 19
    • 0032131292 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • 10.1137/S1064827596304010 1639094
    • S.S. Chen David L. Donoho M.A. Saunders 1998 Atomic decomposition by basis pursuit SIAM J. Sci. Comput. 20 1 33 61 10.1137/S1064827596304010 1639094
    • (1998) SIAM J. Sci. Comput. , vol.20 , Issue.1 , pp. 33-61
    • Chen, S.S.1    Donoho David, L.2    Saunders, M.A.3
  • 20
  • 22
    • 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
  • 23
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • 10.1109/TIT.2006.871582 2241189
    • D.L. Donoho 2006 Compressed sensing IEEE. Trans. Inf. Theory 52 1289 1306 10.1109/TIT.2006.871582 2241189
    • (2006) IEEE. Trans. Inf. Theory , vol.52 , pp. 1289-1306
    • Donoho, D.L.1
  • 24
    • 78651464899 scopus 로고
    • On the numerical solutions of heat conduction problems in two and three space variables
    • J. Douglas H.H. Rachford 1976 On the numerical solutions of heat conduction problems in two and three space variables Trans. Am. Math. Soc. 1 97 116
    • (1976) Trans. Am. Math. Soc. , vol.1 , pp. 97-116
    • Douglas, J.1    Rachford, H.H.2
  • 25
    • 34249837486 scopus 로고
    • On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • 0765.90073 10.1007/BF01581204 1168183
    • J. Eckstein D.P. Bertsekas 1992 On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators Math. Program. 55 293 318 0765.90073 10.1007/BF01581204 1168183
    • (1992) Math. Program. , vol.55 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.P.2
  • 26
    • 77949275427 scopus 로고    scopus 로고
    • Applications of Lagrangian-based alternating direction methods and connections to split Bregman
    • April
    • Esser, E.: Applications of Lagrangian-based alternating direction methods and connections to split Bregman. CAM Report 09-31, UCLA, April 2009
    • (2009) CAM Report 09-31, UCLA
    • Esser, E.1
  • 27
    • 76149085420 scopus 로고    scopus 로고
    • A general framework for a class of first order primal-dual algorithms for TV minimization
    • UCLA, August
    • Esser, E.; Zhang, X.; Chan, T.: A general framework for a class of first order primal-dual algorithms for TV minimization. CAM Report 09-67, UCLA, August 2009
    • (2009) CAM Report 09-67
    • Esser, E.1    Zhang, X.2    Chan, T.3
  • 28
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
    • DOI 10.1109/JSTSP.2007.910281
    • M.A.T. Figueiredo R.D. Nowak S.J. Wright 2007 Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems IEEE J. Sel. Top. Signal Proces. 1 4 586 597 10.1109/JSTSP.2007.910281 (Pubitemid 351276802)
    • (2007) IEEE Journal on Selected Topics in Signal Processing , vol.1 , Issue.4 , pp. 586-597
    • Figueiredo, M.A.T.1    Nowak, R.D.2    Wright, S.J.3
  • 31
    • 72449187553 scopus 로고    scopus 로고
    • Geometric applications of the split Bregman method: Segmentation and surface reconstruction
    • February
    • Goldstein, T.; Bresson, X.; Osher, S.: Geometric applications of the split Bregman method: segmentation and surface reconstruction. UCLA CAM Report, 09-06, February (2009)
    • (2009) UCLA CAM Report, 09-06
    • Goldstein, T.1    Bresson, X.2    Osher, S.3
  • 34
    • 69649095451 scopus 로고    scopus 로고
    • A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing
    • 1180.65076 10.1137/070698920 2460734
    • E.T. Hale W. Yin Y. Zhang 2008 A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing SIAM J. Optim. 19 1107 1130 1180.65076 10.1137/070698920 2460734
    • (2008) SIAM J. Optim. , vol.19 , pp. 1107-1130
    • Hale, E.T.1    Yin, W.2    Zhang, Y.3
  • 35
    • 0014604308 scopus 로고
    • Multiplier and gradient methods
    • 0174.20705 10.1007/BF00927673 271809
    • M.R. Hestenes 1969 Multiplier and gradient methods J. Optim. Theory Appl. 4 303 320 0174.20705 10.1007/BF00927673 271809
    • (1969) J. Optim. Theory Appl. , vol.4 , pp. 303-320
    • Hestenes, M.R.1
  • 38
    • 77956506829 scopus 로고    scopus 로고
    • 1 minimization with application to compressed sensing; A greedy algorithm
    • 1188.90196 10.3934/ipi.2009.3.487 2557916
    • 1 minimization with application to compressed sensing; a greedy algorithm Inverse Probl. Imaging 3 3 487 503 1188.90196 10.3934/ipi.2009.3.487 2557916
    • (2009) Inverse Probl. Imaging , vol.3 , Issue.3 , pp. 487-503
    • Li, Y.1    Osher, S.2
  • 40
    • 0041356704 scopus 로고
    • Fonctions convexes duales et points proximaux dans un espace hilbertien
    • 0118.10502 144188
    • J.-J. Moreau 1962 Fonctions convexes duales et points proximaux dans un espace hilbertien C. R. Acad. Sci. Paris Ser. A Math. 255 2897 2899 0118.10502 144188
    • (1962) C. R. Acad. Sci. Paris Ser. A Math. , vol.255 , pp. 2897-2899
    • Moreau, J.-J.1
  • 41
    • 19844370110 scopus 로고    scopus 로고
    • An iterative regularization method for total variation-based image restoration
    • DOI 10.1137/040605412
    • S. Osher M. Burger D. Goldfarb J. Xu W. Yin 2005 An iterative regularization method for total variation based image restoration Multiscale Model. Simul. 4 2 460 489 1090.94003 10.1137/040605412 2162864 (Pubitemid 43885248)
    • (2005) Multiscale Modeling and Simulation , vol.4 , Issue.2 , pp. 460-489
    • Osher, S.1    Burger, M.2    Goldfarb, D.3    Xu, J.4    Yin, W.5
  • 42
    • 77349126814 scopus 로고    scopus 로고
    • Fast linearized Bregman iteration for compressive sensing and sparse denoising
    • 1190.49040 2655902
    • S. Osher Y. Mao B. Dong W. Yin 2010 Fast linearized Bregman iteration for compressive sensing and sparse denoising Commun. Math. Sci. 8 1 93 111 1190.49040 2655902
    • (2010) Commun. Math. Sci. , vol.8 , Issue.1 , pp. 93-111
    • Osher, S.1    Mao, Y.2    Dong, B.3    Yin, W.4
  • 43
    • 0002380692 scopus 로고
    • A method for nonlinear constraints in minimization problems
    • Powell, M.J.D.: A method for nonlinear constraints in minimization problems. Optimization (1972)
    • (1972) Optimization
    • Powell, M.J.D.1
  • 44
    • 78651427025 scopus 로고
    • Augmented Lagrangians and applications of the proximal point algorithm in convex programming
    • R.T. Rockafellar 1956 Augmented Lagrangians and applications of the proximal point algorithm in convex programming Math. Oper. Res. 82 421 439
    • (1956) Math. Oper. Res. , vol.82 , pp. 421-439
    • Rockafellar, R.T.1
  • 45
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • 0780.49028
    • L.I. Rudin S. Osher E. Fatemi 1992 Nonlinear total variation based noise removal algorithms Physica D 60 259 268 0780.49028
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 46
    • 69049120535 scopus 로고    scopus 로고
    • Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage
    • K. Morken M. Lysaker K.-A. Lie X.-C. Tai (eds). Springer Berlin. 10.1007/978-3-642-02256-2-39
    • Setzer, S.: Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage. In: Morken, K.; Lysaker, M.; Lie, K.-A.; Tai, X.-C. (eds.) Scale Space and Variational Methods in Computer Vision. LNCS, vol. 5567, pp. 464-476. Springer, Berlin (2009)
    • (2009) Scale Space and Variational Methods in Computer Vision LNCS , vol.5567 , pp. 464-476
    • Setzer, S.1
  • 47
    • 69049111989 scopus 로고    scopus 로고
    • Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model
    • UCLA, January
    • Tai, X.-C.; Wu, C.: Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. CAM Report 09-05, UCLA, January 2009
    • (2009) CAM Report 09-05
    • Tai, X.-C.1    Wu, C.2
  • 48
    • 76149100480 scopus 로고    scopus 로고
    • An efficient TV-L1 algorithm for deblurring multichannel images corrupted by impulsive noise
    • Yang, J.; Zhang, Y.; Yin, W.: An efficient TV-L1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM J. Sci. Comput. 31(4) (2009)
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.4
    • Yang, J.1    Zhang, Y.2    Yin, W.3
  • 49
    • 78651437776 scopus 로고    scopus 로고
    • Analysis and generalizations of the linearized Bregman method
    • Yin, W.: Analysis and generalizations of the linearized Bregman method. CAAM Report, Rice University (2009)
    • (2009) CAAM Report, Rice University
    • Yin, W.1
  • 50
    • 84977895355 scopus 로고    scopus 로고
    • 1 minimization with applications to compressed sensing
    • 05256573 10.1137/070703983 2475828
    • 1 minimization with applications to compressed sensing SIAM J. Imag. Sci. 1 143 168 05256573 10.1137/070703983 2475828
    • (2008) SIAM J. Imag. Sci. , vol.1 , pp. 143-168
    • Yin, W.1    Osher, S.2    Goldfarb, D.3    Darbon, J.4
  • 51
    • 77249161628 scopus 로고    scopus 로고
    • Bregmanized nonlocal regularization for deconvolution and sparse reconstruction
    • January
    • Zhang, X.; Burger, M.; Bresson, X.; Osher, S.: Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. CAM Report 09-03, UCLA, January 2009
    • (2009) CAM Report 09-03, UCLA
    • Zhang, X.1    Burger, M.2    Bresson, X.3    Osher, S.4
  • 52
    • 67651035078 scopus 로고    scopus 로고
    • An efficient primal-dual hybrid gradient algorithm for total variation image restoration
    • UCLA, May
    • Zhu, M.; Chan, T.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. CAM Report 08-34, UCLA, May 2008ry
    • (2008) CAM Report 08-34
    • Zhu, M.1    Chan, T.2
  • 53
    • 67651035078 scopus 로고    scopus 로고
    • An efficient primal-dual hybrid gradient algorithm for total variation image restoration
    • UCLA, May
    • Zhu, M.; Chan, T.: An efficient primal-dual hybrid gradient algorithm for total vari
    • (2008) CAM Report 08-34
    • Zhu, M.1    Chan, T.2


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