메뉴 건너뛰기




Volumn 4, Issue 1, 2011, Pages 277-299

An upwind finite-difference method for total variation–based image smoothing

Author keywords

Finite difference schemes; Image denoising; Multiscale methods; Total variation; Upwind schemes

Indexed keywords

IMAGE DENOISING; NUMERICAL METHODS; RADIO COMMUNICATION;

EID: 79957451716     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/090752754     Document Type: Article
Times cited : (77)

References (29)
  • 1
    • 48249125815 scopus 로고    scopus 로고
    • Total variation regularization for image denoising, I. Geometric theory
    • W. K. Allard, Total variation regularization for image denoising, I. Geometric theory, SIAM J. Math. Anal., 39 (2007), pp. 1150–1190.
    • (2007) SIAM J. Math. Anal. , vol.39 , pp. 1150-1190
    • Allard, W.K.1
  • 2
    • 15544363597 scopus 로고    scopus 로고
    • Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow
    • F. Alter, V. Caselles, and A. Chambolle, Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow, Interfaces Free Bound., 7 (2005), pp. 29–53.
    • (2005) Interfaces Free Bound. , vol.7 , pp. 29-53
    • Alter, F.1    Caselles, V.2    Chambolle, A.3
  • 3
    • 17444417799 scopus 로고    scopus 로고
    • Global ly optimal geodesic active contours
    • B. Appleton and H. Talbot, Global ly optimal geodesic active contours, J. Math. Imaging Vision, 23 (2005), pp. 67–86.
    • (2005) J. Math. Imaging Vision , vol.23 , pp. 67-86
    • Appleton, B.1    Talbot, H.2
  • 5
    • 14844355103 scopus 로고    scopus 로고
    • Image decomposition into a bounded variation component and an oscil lating component
    • J.-F. Aujol, G. Aubert, L. Blanc-Féraud, and A. Chambolle, Image decomposition into a bounded variation component and an oscil lating component, J. Math. Imaging Vision, 22 (2005), pp. 71–88.
    • (2005) J. Math. Imaging Vision , vol.22 , pp. 71-88
    • Aujol, J.-F.1    Aubert, G.2    Blanc-Féraud, L.3    Chambolle, A.4
  • 7
    • 0026905465 scopus 로고
    • Bayesian estimation of transmission tomograms using segmentation based optimization
    • C. Bouman and K. Sauer, Bayesian estimation of transmission tomograms using segmentation based optimization, IEEE Trans. Nuclear Sci., 39 (1992), pp. 1144–1152.
    • (1992) IEEE Trans. Nuclear Sci. , vol.39 , pp. 1144-1152
    • Bouman, C.1    Sauer, K.2
  • 11
    • 50949131499 scopus 로고    scopus 로고
    • The discontinuity set of solutions of the TV denoising problem and some extensions
    • V. Caselles, A. Chambolle, and M. Novaga, The discontinuity set of solutions of the TV denoising problem and some extensions, Multiscale Model. Simul., 6 (2007), pp. 879–894.
    • (2007) Multiscale Model. Simul. , vol.6 , pp. 879-894
    • Caselles, V.1    Chambolle, A.2    Novaga, M.3
  • 12
    • 84856771727 scopus 로고    scopus 로고
    • Regularity for solutions of the total variation denoising problem
    • V. Caselles, A. Chambolle, and M. Novaga, Regularity for solutions of the total variation denoising problem, Rev. Mat. Iberoamericana, 27 (2010), pp. 233–252.
    • (2010) Rev. Mat. Iberoamericana , vol.27 , pp. 233-252
    • Caselles, V.1    Chambolle, A.2    Novaga, M.3
  • 13
    • 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. Imaging Vision, 20 (2004), pp. 89–97.
    • (2004) J. Math. Imaging Vision , vol.20 , pp. 89-97
    • Chambolle, A.1
  • 15
    • 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 (1997), pp. 167–188.
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 16
    • 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 (2004), pp. 475–504.
    • (2004) Optimization , vol.53 , pp. 475-504
    • Combettes, P.L.1
  • 17
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), pp. 1168–1200.
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 1168-1200
    • Combettes, P.L.1    Wajs, V.R.2
  • 18
    • 35048895256 scopus 로고    scopus 로고
    • Exact optimization of discrete constrained total variation minimization problems
    • Springer, Berlin
    • J. Darbon and M. Sigelle, Exact optimization of discrete constrained total variation minimization problems, in Combinatorial Image Analysis, Lecture Notes in Comput. Sci. 3322, Springer, Berlin, 2004, pp. 548–557.
    • (2004) Combinatorial Image Analysis, Lecture Notes in Comput. Sci. 3322 , pp. 548-557
    • Darbon, J.1    Sigelle, M.2
  • 20
    • 84880683689 scopus 로고
    • Iteration methods for convexly constrained il l-posed problems in Hilbert space
    • B. Eicke, Iteration methods for convexly constrained il l-posed problems in Hilbert space, Numer. Funct. Anal. Optim., 13 (1992), pp. 413–429.
    • (1992) Numer. Funct. Anal. Optim. , vol.13 , pp. 413-429
    • Eicke, B.1
  • 21
    • 0003244186 scopus 로고
    • Convex Analysis and Variational Problems
    • North– Holland, Amsterdam
    • I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Stud. Math. Appl. 1, North– Holland, Amsterdam, 1976.
    • (1976) Stud. Math. Appl. , vol.1
    • Ekeland, I.1    Temam, R.2
  • 22
    • 33645038355 scopus 로고    scopus 로고
    • Second-order cone programming methods for total variation-based image restoration
    • D. Goldfarb and W. Yin, Second-order cone programming methods for total variation-based image restoration, SIAM J. Sci. Comput., 27 (2005), pp. 622–645.
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 622-645
    • Goldfarb, D.1    Yin, W.2
  • 24
    • 84968481460 scopus 로고
    • Weak convergence of the sequence of successive approximations for nonexpansive mappings
    • Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), pp. 591–597.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 591-597
    • Opial, Z.1
  • 25
    • 19844370110 scopus 로고    scopus 로고
    • An iterative regularization method for total variation-based image restoration
    • S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul., 4 (2005), pp. 460–489.
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 460-489
    • Osher, S.1    Burger, M.2    Goldfarb, D.3    Xu, J.4    Yin, W.5
  • 26
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), pp. 12–49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 27
    • 0034412757 scopus 로고    scopus 로고
    • Structural properties of solutions to total variation regularization problems, M2AN Math
    • W. Ring, Structural properties of solutions to total variation regularization problems, M2AN Math. Model. Numer. Anal., 34 (2000), pp. 799–810.
    • (2000) Model. Numer. Anal. , vol.34 , pp. 799-810
    • Ring, W.1
  • 28
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259–268.
    • (1992) Phys. D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 29
    • 85053695949 scopus 로고    scopus 로고
    • Error bounds for finite difference methods for Rudin–Osher–Fatemi image smoothing
    • to appear
    • J. Wang and B. J. Lucier, Error bounds for finite difference methods for Rudin–Osher–Fatemi image smoothing, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal
    • Wang, J.1    Lucier, B.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.