메뉴 건너뛰기




Volumn 34, Issue 3, 2009, Pages 307-327

Some first-order algorithms for total variation based image restoration

Author keywords

Algorithms; Duality; Image restoration; Total variation regularization

Indexed keywords

DUALITY; EFFICIENT ALGORITHM; FIRST-ORDER; FIRST-ORDER ALGORITHMS; IMAGE RESTORATION; NUMERICAL EXAMPLE; NUMERICAL SCHEME; PROJECTION ALGORITHMS; TOTAL VARIATION; TOTAL VARIATION REGULARIZATION;

EID: 67651033716     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-009-0149-y     Document Type: Article
Times cited : (129)

References (54)
  • 1
    • 36149030663 scopus 로고
    • Analysis of total variation penalty methods for ill-posed problems
    • R. Acar C. Vogel 1994 Analysis of total variation penalty methods for ill-posed problems Inverse Probl. 10 1217 1229
    • (1994) Inverse Probl. , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.2
  • 3
    • 0003282839 scopus 로고    scopus 로고
    • Functions of bounded variations and free discontinuity problems
    • Oxford University Press London
    • Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variations and Free Discontinuity Problems, Oxford mathematical monographs. Oxford University Press, London (2000)
    • (2000) Oxford Mathematical Monographs
    • Ambrosio, L.1    Fusco, N.2    Pallara, D.3
  • 4
    • 18844398187 scopus 로고    scopus 로고
    • Parabolic quasilinear equations minimizing linear growth functionals
    • Birkhäuser Basel
    • Andreu-Vaillo, F., Caselles, V., Mazon, J.M.: Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Progress in Mathematics, vol. 223. Birkhäuser, Basel (2002)
    • (2002) Progress in Mathematics , vol.223
    • Andreu-Vaillo, F.1    Caselles, V.2    Mazon, J.M.3
  • 5
    • 85049184544 scopus 로고    scopus 로고
    • Mathematical problems in image processing
    • Springer New York
    • Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing. Applied Mathematical Sciences, vol. 147. Springer, New York (2002)
    • (2002) Applied Mathematical Sciences , vol.147
    • Aubert, G.1    Kornprobst, P.2
  • 6
    • 67651053616 scopus 로고    scopus 로고
    • Some algorithms for total variation based image restoration
    • Aujol, J.-F.: Some algorithms for total variation based image restoration. CMLA Report 08-21 (2008). http://hal.archives-ouvertes.fr/hal- 00260494/fr/
    • (2008) CMLA Report 08-21
    • Aujol, J.-F.1
  • 7
    • 33751529245 scopus 로고    scopus 로고
    • Constrained and SNR-based solutions for TV-Hilbert space image denoising
    • DOI 10.1007/s10851-006-7801-6
    • J.-F. Aujol G. Gilboa 2006 Constrained and SNR-based solutions for TV-Hilbert space image denoising J. Math. Imaging Vis. 26 1-2 217 237 (Pubitemid 44832629)
    • (2006) Journal of Mathematical Imaging and Vision , vol.26 , Issue.1-2 , pp. 217-237
    • Aujol, J.-F.1    Gilboa, G.2
  • 10
    • 0002220733 scopus 로고
    • Duality methods for solving variational inequalities
    • A. Bermùdez C. Moreno 1981 Duality methods for solving variational inequalities Comput. Math. Appl. 7 43 58
    • (1981) Comput. Math. Appl. , vol.7 , pp. 43-58
    • Bermùdez, A.1    Moreno, C.2
  • 11
  • 12
    • 41449101407 scopus 로고    scopus 로고
    • A generalized conditional gradient method for nonlinear operator equations with sparsity constraints
    • T. Bonesky K. Bredies D. Lorenz P. Mass 2009 A generalized conditional gradient method for nonlinear operator equations with sparsity constraints Inverse Probl. 23 2041 2048
    • (2009) Inverse Probl. , vol.23 , pp. 2041-2048
    • Bonesky, T.1    Bredies, K.2    Lorenz, D.3    Mass, P.4
  • 13
    • 69049096192 scopus 로고    scopus 로고
    • Fast minimization of the vectorial total variation norm nd applications to color image processing
    • Bresson, X., Chan, T.: Fast minimization of the vectorial total variation norm and applications to color image processing. UCLA CAM report, 07-25 (2007)
    • (2007) UCLA CAM Report , pp. 07-25
    • Bresson, X.1    Chan, T.2
  • 16
    • 1242352408 scopus 로고    scopus 로고
    • An algorithm for total variation minimization and applications
    • A. Chambolle 2004 An algorithm for total variation minimization and applications J. Math. Imaging Vis. 20 89 97
    • (2004) J. Math. Imaging Vis. , vol.20 , pp. 89-97
    • Chambolle, A.1
  • 18
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • A. Chambolle P.L. Lions 1997 Image recovery via total variation minimization and related problems Numer. Math. 76 3 167 188
    • (1997) Numer. Math. , vol.76 , Issue.3 , pp. 167-188
    • Chambolle, A.1    Lions, P.L.2
  • 19
    • 0000668458 scopus 로고    scopus 로고
    • On the convergence of the lagged diffusivity fixed point method in total variation image restoration
    • PII S0036142997327075
    • T. Chan P. Mulet 1999 On the convergence of the lagged diffusity fixed point method in total variation image restoration SIAM J. Numer. Anal. 36 2 354 367 (Pubitemid 129582569)
    • (1999) SIAM Journal on Numerical Analysis , vol.36 , Issue.2 , pp. 354-367
    • Chan, T.F.1    Mulet, P.2
  • 21
    • 0033295350 scopus 로고    scopus 로고
    • Nonlinear primal-dual method for total variation-based image restoration
    • T. Chan G. Golub P. Mulet 1999 A nonlinear primal-dual method for total variation-based image restoration SIAM J. Sci. Comput. 20 6 1964 1977 (Pubitemid 30895588)
    • (1999) SIAM Journal of Scientific Computing , vol.20 , Issue.6 , pp. 1964-1977
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 24
    • 4344685262 scopus 로고    scopus 로고
    • Image restoration subject to a total variation constraint
    • P.L. Combettes J. Pesquet 2004 Image restoration subject to a total variation constraint IEEE Trans. Image Process. 13 9 1213 1222
    • (2004) IEEE Trans. Image Process. , vol.13 , Issue.9 , pp. 1213-1222
    • Combettes, P.L.1    Pesquet, J.2
  • 25
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • DOI 10.1137/050626090
    • P.L. Combettes V. Wajs 2005 Signal recovery by proximal forward-backward splitting SIAM J. Multiscale Model. Simul. 4 4 1168 1200 (Pubitemid 44932287)
    • (2005) Multiscale Modeling and Simulation , vol.4 , Issue.4 , pp. 1168-1200
    • Combettes, P.L.1    Wajs, V.R.2
  • 26
    • 33845482689 scopus 로고    scopus 로고
    • Image restoration with discrete constrained total variation part I: Fast and exact optimization
    • J. Darbon M. Sigelle 2006 Image restoration with discrete constrained total variation part I: Fast and exact optimization J. Math. Imaging Vis. 26 3 277 291
    • (2006) J. Math. Imaging Vis. , vol.26 , Issue.3 , pp. 277-291
    • Darbon, J.1    Sigelle, M.2
  • 27
    • 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 1413 1457 (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
  • 28
    • 0000427927 scopus 로고    scopus 로고
    • Convergence of an iterative method for total variation denoising
    • D. Dobson C. Vogel 1997 Convergence of an iterative method for total variation denoising SIAM J. Numer. Anal. 34 1779 1791 (Pubitemid 127463570)
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , Issue.5 , pp. 1779-1791
    • Dobson, D.C.1    Vogel, C.R.2
  • 30
    • 67651019366 scopus 로고    scopus 로고
    • Projected gradient based color image decomposition
    • Duval, V., Aujol, J.-F., Vese, L.: Projected gradient based color image decomposition. In: SSVM 09 (2009)
    • (2009) SSVM 09
    • Duval, V.1    Aujol, J.-F.2    Vese, L.3
  • 34
    • 33751208047 scopus 로고    scopus 로고
    • Efficient minimization methods of mixed l1-l1 and l2-l1 norms for image restoration
    • H. Fu M. Ng M. Nikolova J. Barlow 2006 Efficient minimization methods of mixed l1-l1 and l2-l1 norms for image restoration SIAM J. Sci. Comput. 27 6 1881 1902
    • (2006) SIAM J. Sci. Comput. , vol.27 , Issue.6 , pp. 1881-1902
    • Fu, H.1    Ng, M.2    Nikolova, M.3    Barlow, J.4
  • 35
    • 33645038355 scopus 로고    scopus 로고
    • Second-order cone programming methods for total variation based image restoration
    • D. Goldfarb W. Yin 2005 Second-order cone programming methods for total variation based image restoration SIAM J. Sci. Comput. 27 2 622 645
    • (2005) SIAM J. Sci. Comput. , vol.27 , Issue.2 , pp. 622-645
    • Goldfarb, D.1    Yin, W.2
  • 36
    • 67651195543 scopus 로고    scopus 로고
    • The split bregman algorithm for L1 regularized problems
    • April 2008
    • Goldstein, T., Osher, S.: The split Bregman algorithm for L1 regularized problems. UCLA CAM Report, April 2008
    • UCLA CAM Report
    • Goldstein, T.1    Osher, S.2
  • 39
    • 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. (A) 103 1 127 152 (Pubitemid 40537674)
    • (2005) Mathematical Programming , vol.103 , Issue.1 , pp. 127-152
    • Nesterov, Yu.1
  • 42
    • 34249073050 scopus 로고    scopus 로고
    • The equivalence of half-quadratic minimization and the gradient linearization iteration
    • DOI 10.1109/TIP.2007.896622
    • M. Nikolova R. Chan 2007 The equivalence of half-quadratic minimization and the gradient linearization iteration IEEE Trans. Image Process. 16 6 1623 1627 (Pubitemid 46796057)
    • (2007) IEEE Transactions on Image Processing , vol.16 , Issue.6 , pp. 1623-1627
    • Nikolova, M.1    Chan, R.H.2
  • 43
    • 0012964910 scopus 로고
    • On the asymptotic behavior of iterates of nonexpansive mappings in Hilbert space
    • A. Pazy 1977 On the asymptotic behavior of iterates of nonexpansive mappings in Hilbert space Isr. J. Math. 26 197 204
    • (1977) Isr. J. Math. , vol.26 , pp. 197-204
    • Pazy, A.1
  • 44
    • 0003316678 scopus 로고
    • Semigroups of Linear Operators and Applications to Partial Differential Equations
    • Springer New York
    • Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol. 44. Springer, New York (1983)
    • (1983) Applied Mathematical Sciences , vol.44
    • Pazy, A.1
  • 46
    • 33748848713 scopus 로고    scopus 로고
    • A Tikhonov-based projection iteration for nonlinear Ill-posed problems with sparsity constraints
    • DOI 10.1007/s00211-006-0016-3
    • R. Ramlau G. Teschke 2006 A Tikhonov-based projection iteration for nonlinear ill-posed problems with sparsity constraints Numer. Math. 104 177 203 (Pubitemid 44421163)
    • (2006) Numerische Mathematik , vol.104 , Issue.2 , pp. 177-203
    • Ramlau, R.1    Teschke, G.2
  • 47
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. Rudin S. Osher E. Fatemi 1992 Nonlinear total variation based noise removal algorithms Physica D 60 259 268
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 49
    • 0000281286 scopus 로고
    • Sur le point pour lequel la somme des distances de points donnés est minimum
    • E. Weisfeld 1937 Sur le point pour lequel la somme des distances de points donnés est minimum Tôhoku Math. J. 43 355 386
    • (1937) Tôhoku Math. J. , vol.43 , pp. 355-386
    • Weisfeld, E.1
  • 51
    • 67651044298 scopus 로고    scopus 로고
    • Efficient schemes for total variation minimization under constraints in image processing
    • in press
    • Weiss, P., Aubert, G., Blanc-Feraud, L.: Efficient schemes for total variation minimization under constraints in image processing. SIAM J. Sci. Comput. (2009, in press)
    • (2009) SIAM J. Sci. Comput.
    • Weiss, P.1    Aubert, G.2    Blanc-Feraud, L.3
  • 52
    • 59949104853 scopus 로고    scopus 로고
    • Convex Hodge decomposition and regularization of image flows
    • J. Yuan C. Schnörr G. Steidl 2009 Convex Hodge decomposition and regularization of image flows J. Math. Imaging Vis. 33 2 169 177
    • (2009) J. Math. Imaging Vis. , vol.33 , Issue.2 , pp. 169-177
    • Yuan, J.1    Schnörr, C.2    Steidl, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.