메뉴 건너뛰기




Volumn 9, Issue 3, 2011, Pages 797-827

Infimal convolution regularizations with discrete ll-type functionals

Author keywords

Alternating direction method of multipliers; Denoising; Douglas Rachford splitting; Infimal convolution; Primal dual hybrid gradient method; ROF functional; Total generalized variation

Indexed keywords


EID: 79953053495     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2011.v9.n3.a7     Document Type: Article
Times cited : (118)

References (44)
  • 1
    • 14844355103 scopus 로고    scopus 로고
    • Image decomposition into a bounded variation component and an oscillating component
    • J.F. Aujol, G. Aubert, L. Blanc-Féraud, and A. Chambolle, Image decomposition into a bounded variation component and an oscillating component, J. Math. Imag. Vis., 22(1), 71-88, 2005.
    • (2005) J. Math. Imag. Vis. , vol.22 , Issue.1 , pp. 71-88
    • Aujol, J.F.1    Aubert, G.2    Blanc-Féraud, L.3    Chambolle, A.4
  • 2
    • 14844353365 scopus 로고    scopus 로고
    • Dual norms and image decomposition models
    • J.F. Aujol and A. Chambolle, Dual norms and image decomposition models, Int. J. Comp. Vis., 63(1), 85-104, 2005.
    • (2005) Int. J. Comp. Vis. , vol.63 , Issue.1 , pp. 85-104
    • Aujol, J.F.1    Chambolle, A.2
  • 3
    • 70350593691 scopus 로고    scopus 로고
    • Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems
    • A. Beck and M. Teboulle, Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems, IEEE Trans. Imag. Proc., 18(11), 2419-2434, 2009.
    • (2009) IEEE Trans. Imag. Proc. , vol.18 , Issue.11 , pp. 2419-2434
    • Beck, A.1    Teboulle, M.2
  • 4
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-thresholding algorithm for linear inverse problems
    • A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imag. Sci., 2(1), 183-202, 2009.
    • (2009) SIAM J. Imag. Sci. , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 6
    • 0019587748 scopus 로고
    • An iterative row-action method for interval convex programming
    • Y. Censor and A. Lent, An iterative row-action method for interval convex programming, J. Opt. Theo. Appl., 34(3), 321-353, 1981.
    • (1981) J. Opt. Theo. Appl. , vol.34 , Issue.3 , pp. 321-353
    • Censor, Y.1    Lent, A.2
  • 7
    • 1242352408 scopus 로고    scopus 로고
    • An algorithm for total variation minimization and applications
    • A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imag. Vis., 20(1-2), 89-97, 2004.
    • (2004) J. Math. Imag. Vis. , vol.20 , Issue.1-2 , pp. 89-97
    • Chambolle, A.1
  • 8
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • A. Chambolle and P.L. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76, 167-188, 1997.
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.L.2
  • 11
    • 0035074671 scopus 로고    scopus 로고
    • High-order total variation-based image restoration
    • T.F. Chan, A. Marquina, and P. Mulet, High-order total variation-based image restoration, SIAM J. Sci. Comp., 22(2) 503-516 2000.
    • (2000) SIAM J. Sci. Comp. , vol.22 , Issue.2 , pp. 503-516
    • Chan, T.F.1    Marquina, A.2    Mulet, P.3
  • 12
    • 13244295576 scopus 로고    scopus 로고
    • Solving monotone inclusions via compositions of nonexpansive averaged operators
    • P.L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, 53(5-6), 475-504, 2004.
    • (2004) Optimization , vol.53 , Issue.5-6 , pp. 475-504
    • Combettes, P.L.1
  • 13
    • 39449085530 scopus 로고    scopus 로고
    • A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery
    • P.L. Combettes and J.C. Pesquet, A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery, IEEE J. Sel. Top. Sig. Proc., 1(4), 564-574, 2007.
    • (2007) IEEE J. Sel. Top. Sig. Proc. , vol.1 , Issue.4 , pp. 564-574
    • Combettes, P.L.1    Pesquet, J.C.2
  • 15
    • 68949096587 scopus 로고    scopus 로고
    • Properties of higher order nonlinear diffusion filtering
    • S. Didas, J. Weickert, and B. Burgeth, Properties of higher order nonlinear diffusion filtering, J. Math. Imag. Vis., 35, 208-226, 2009.
    • (2009) J. Math. Imag. Vis. , vol.35 , pp. 208-226
    • Didas, S.1    Weickert, J.2    Burgeth, B.3
  • 16
    • 34249837486 scopus 로고
    • On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • J. Eckstein and D.P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Prog., 55, 293-318, 1992.
    • (1992) Math. Prog. , vol.55 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.P.2
  • 17
    • 77949275427 scopus 로고    scopus 로고
    • Applications of Lagrangian-based alternating direction methods and connections to split Bregman
    • UCLA
    • E. Esser, Applications of Lagrangian-based alternating direction methods and connections to split Bregman, CAM Report 09-31, UCLA, 2009.
    • (2009) CAM Report 09-31
    • Esser, E.1
  • 18
    • 76149085420 scopus 로고    scopus 로고
    • A general framework for a class of first order primal-dual algorithms for TV minimization
    • UCLA
    • E. Esser, X. Zhang, and T.F. Chan, A general framework for a class of first order primal-dual algorithms for TV minimization, CAM Report 09-67, UCLA, 2009.
    • (2009) CAM Report 09-67
    • Esser, E.1    Zhang, X.2    Chan, T.F.3
  • 20
    • 0002211517 scopus 로고
    • A dual algorithm for the solution of nonlinear variational problems via finite element approximation
    • D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Comp. Math. Appl., 2, 17-40, 1976.
    • (1976) Comp. Math. Appl. , vol.2 , pp. 17-40
    • Gabay, D.1    Mercier, B.2
  • 21
    • 84969334819 scopus 로고    scopus 로고
    • The Split Bregman method for L1-regularized problems
    • T. Goldstein and S. Osher, The Split Bregman method for L1-regularized problems, SIAM J. Imaging Sciences, 2(2), 323-343, 2009.
    • (2009) SIAM J. Imaging Sciences , vol.2 , Issue.2 , pp. 323-343
    • Goldstein, T.1    Osher, S.2
  • 22
    • 4544249333 scopus 로고    scopus 로고
    • Total bounded variation regularization as a bilaterally constrained optimization problem
    • W. Hintermüller and K. Kunisch, Total bounded variation regularization as a bilaterally constrained optimization problem, SIAM J. Appl. Math., 64(4), 1311-1333, 2004.
    • (2004) SIAM J. Appl. Math. , vol.64 , Issue.4 , pp. 1311-1333
    • Hintermüller, W.1    Kunisch, K.2
  • 23
    • 0031071242 scopus 로고    scopus 로고
    • Natural discretizations for the divergence, gradient, and curl on logically rectangular grids
    • J.M. Hyman and M.J. Shashkov, Natural discretizations for the divergence, gradient, and curl on logically rectangular grids, Comp. Math. Appl., 33(4), 81-104, 1997.
    • (1997) Comp. Math. Appl. , vol.33 , Issue.4 , pp. 81-104
    • Hyman, J.M.1    Shashkov, M.J.2
  • 24
    • 4544278119 scopus 로고    scopus 로고
    • Noise removal using fourth-order partial differential equations with applications to medical magnetic resonance images in space and time
    • M. Lysaker, A. Lundervold, and X. Tai, Noise removal using fourth-order partial differential equations with applications to medical magnetic resonance images in space and time, IEEE Trans. Imag. Proc., 12(12), 1579-1590, 2003.
    • (2003) IEEE Trans. Imag. Proc. , vol.12 , Issue.12 , pp. 1579-1590
    • Lysaker, M.1    Lundervold, A.2    Tai, X.3
  • 25
    • 79953037258 scopus 로고    scopus 로고
    • Curvelet-wavelet regularized split Bregman iteration for compressed sensing
    • accepted
    • J. Ma and G. Plonka-Hoch, Curvelet-wavelet regularized split Bregman iteration for compressed sensing, Int. J. Wavelets, Multires. Inf. Proc., accepted, 2010.
    • (2010) Int. J. Wavelets, Multires. Inf. Proc.
    • Ma, J.1    Plonka-Hoch, G.2
  • 27
    • 0041876673 scopus 로고    scopus 로고
    • Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems
    • D. Potts and G. Steidl, Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems, Lin. Alg. Appl., 281, 265-292, 1998.
    • (1998) Lin. Alg. Appl. , vol.281 , pp. 265-292
    • Potts, D.1    Steidl, G.2
  • 28
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 29
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L.I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60, 259-268, 1992.
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 30
    • 0031653225 scopus 로고    scopus 로고
    • Denoising with higher order derivatives of bounded variation and an application to parameter estimation
    • O. Scherzer, Denoising with higher order derivatives of bounded variation and an application to parameter estimation, Comp., 60, 1-27, 1998.
    • (1998) Comp. , vol.60 , pp. 1-27
    • Scherzer, O.1
  • 33
    • 79953041334 scopus 로고    scopus 로고
    • Operator splittings, Bregman methods and frame shrinkage in image processing
    • accepted
    • S. Setzer, Operator splittings, Bregman methods and frame shrinkage in image processing, Int. J. Comp. Vis., accepted, 2009.
    • (2009) Int. J. Comp. Vis.
    • Setzer, S.1
  • 34
    • 73649084123 scopus 로고    scopus 로고
    • Variational methods with higher order derivatives in image processing
    • M. Neamtu and L.L. Schumaker, (eds.) San Antonio, USA, Nashboro Press, Brentwood
    • S. Setzer and G. Steidl, Variational methods with higher order derivatives in image processing, M. Neamtu and L.L. Schumaker, (eds.), Approximation XII, San Antonio, USA, Nashboro Press, Brentwood, 360-386, 2008.
    • (2008) Approximation XII , pp. 360-386
    • Setzer, S.1    Steidl, G.2
  • 36
    • 27744574209 scopus 로고    scopus 로고
    • Image decomposition: Separation from texture from piecewise smooth content
    • J.L. Starck, M. Elad, and D.L. Donoho, Image decomposition: separation from texture from piecewise smooth content, IEEE Trans. Imag. Proc., 14(10), 1570-1582, 2005.
    • (2005) IEEE Trans. Imag. Proc. , vol.14 , Issue.10 , pp. 1570-1582
    • Starck, J.L.1    Elad, M.2    Donoho, D.L.3
  • 37
    • 0013515106 scopus 로고    scopus 로고
    • The Operation of Infimal Convolution
    • Polska Akademia Nauk, Warszawa, Poland
    • T. Strömberg, The Operation of Infimal Convolution, Ph.D. Thesis. Polska Akademia Nauk, Warszawa, Poland, 1996.
    • (1996) Ph.D. Thesis
    • Strömberg, T.1
  • 38
    • 17444378897 scopus 로고    scopus 로고
    • Cardinal exponential splines: Part I - theory and filtering algorithms
    • M. Unser and T. Blu, Cardinal exponential splines: Part I - theory and filtering algorithms, IEEE Trans. Sig. Proc., 53(4), 1425-1438, 2005.
    • (2005) IEEE Trans. Sig. Proc. , vol.53 , Issue.4 , pp. 1425-1438
    • Unser, M.1    Blu, T.2
  • 39
    • 20544471671 scopus 로고    scopus 로고
    • Generalized smoothing splines and the optimal discretization of the Wiener filter
    • M. Unser and T. Blu, Generalized smoothing splines and the optimal discretization of the Wiener filter, IEEE Trans. Sig. Proc., 53(6), 2146-2159, 2005.
    • (2005) IEEE Trans. Sig. Proc. , vol.53 , Issue.6 , pp. 2146-2159
    • Unser, M.1    Blu, T.2
  • 40
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • Y. Wang, J. Yang, W. Yin, and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction, SIAM J. Imag. Sci., 1(3), 248-272, 2008.
    • (2008) SIAM J. Imag. Sci. , vol.1 , Issue.3 , pp. 248-272
    • Wang, Y.1    Yang, J.2    Yin, W.3    Zhang, Y.4
  • 41
    • 0034298888 scopus 로고    scopus 로고
    • Fourth-order partial differential equations for noise removal
    • Y.L. You and M. Kaveh, Fourth-order partial differential equations for noise removal, IEEE Trans. Imag. Proc., 9(10), 1723-1730, 2000.
    • (2000) IEEE Trans. Imag. Proc. , vol.9 , Issue.10 , pp. 1723-1730
    • You, Y.L.1    Kaveh, M.2
  • 42
    • 54249097825 scopus 로고    scopus 로고
    • Simultaneous higher order optical flow estimation and decomposition
    • J. Yuan, C. Schnörr, and G. Steidl, Simultaneous higher order optical flow estimation and decomposition, SIAM J. Sci. Comp., 29(6), 2283-2304, 2007.
    • (2007) SIAM J. Sci. Comp. , vol.29 , Issue.6 , pp. 2283-2304
    • Yuan, J.1    Schnörr, C.2    Steidl, G.3
  • 43
    • 69049106806 scopus 로고    scopus 로고
    • Total-variation based piecewise affine regularization
    • A. Lie, M. Lysaker, K. Morken, and X.C. Tai (eds.), Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2009, Voss, Norway, June 1-5, 2009. Springer
    • J. Yuan, C. Schnörr, and G. Steidl, Total-variation based piecewise affine regularization, A. Lie, M. Lysaker, K. Morken, and X.C. Tai (eds.), Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2009, Voss, Norway, June 1-5, 2009. Proceedings, Lecture Notes in Computer Science, Springer, 5567, 552-564, 2009.
    • (2009) Proceedings, Lecture Notes in Computer Science , vol.5567 , pp. 552-564
    • Yuan, J.1    Schnörr, C.2    Steidl, G.3
  • 44
    • 67651035078 scopus 로고    scopus 로고
    • An efficient primal-dual hybrid gradient algorithm for total variation image restauration
    • UCLA
    • M. Zhu and T.F. Chan, An efficient primal-dual hybrid gradient algorithm for total variation image restauration, CAM Report 08-34, UCLA, 2008.
    • (2008) CAM Report 08-34
    • Zhu, M.1    Chan, T.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.