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Volumn 8, Issue 1, 2009, Pages 154-189

The TVL1 model: A geometric point of view

Author keywords

Adaptive image denoising; Cheeger sets; Mathematical morphology; Total variation

Indexed keywords

ADAPTIVE FRAMEWORK; ADAPTIVE IMAGES; CHEEGER; CHEEGER SETS; DIGITAL IMAGE; EFFICIENT NUMERICAL SCHEMES; EXACT SOLUTION; GRANULOMETRIES; IMAGE DECOMPOSITION; IMAGE RESTORATION; MATHEMATICAL CONCEPTS; THEORETICAL RESULT; THEORETICAL STUDY; TOTAL VARIATION;

EID: 77953493226     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/090757083     Document Type: Article
Times cited : (77)

References (48)
  • 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
    • 77954956923 scopus 로고    scopus 로고
    • Total variation regularization for image denoising, II. Examples
    • W.K. ALLARD, Total variation regularization for image denoising, II. Examples, SIAM J. Imaging Sci., 1 (2008), pp. 400-417.
    • (2008) SIAM J. Imaging Sci. , vol.1 , pp. 400-417
    • Allard, W.K.1
  • 3
    • 79751482313 scopus 로고    scopus 로고
    • Total variation regularization for image denoising, III. Examples
    • W.K. ALLARD, Total variation regularization for image denoising, III. Examples, SIAM J. Imaging Sci., 2 (2009), pp. 532-568.
    • (2009) SIAM J. Imaging Sci. , vol.2 , pp. 532-568
    • Allard, W.K.1
  • 4
    • 0026883172 scopus 로고
    • Digital filters as absolute norm regularizes
    • S. ALLINEY, Digital filters as absolute norm regularizes, IEEE Trans. Signal Process., 40 (1992), pp. 1548-1562.
    • (1992) IEEE Trans. Signal Process , vol.40 , pp. 1548-1562
    • Alliney, S.1
  • 5
    • 0030169670 scopus 로고    scopus 로고
    • Recursive median filters of increasing order: A variational approach
    • S. ALLINEY, Recursive median filters of increasing order: A variational approach, IEEE Trans. Signal Process., 44 (1996), pp. 1346-1354.
    • (1996) IEEE Trans. Signal Process , vol.44 , pp. 1346-1354
    • Alliney, S.1
  • 7
    • 18244373940 scopus 로고    scopus 로고
    • A characterization of convex calibrable sets in ℝ
    • F. ALTER, V. CASELLES, AND A. CHAMBOLLE, A characterization of convex calibrable sets in ℝ, Math. Ann., 332 (2005), pp. 329-366.
    • (2005) Math. Ann. , vol.332 , pp. 329-366
    • Alter, F.1    Caselles, V.2    Chambolle, A.3
  • 8
    • 15544363597 scopus 로고    scopus 로고
    • Evolution of convex sets in the plane by minimizing the total variation flow
    • F. ALTER, V. CASELLES, AND A. CHAMBOLLE, Evolution of convex sets in the plane by minimizing the 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
  • 10
    • 85014783344 scopus 로고    scopus 로고
    • Corso introduttivo alla teoria geometrica delia misura ed alle superfici minimime
    • Pantograph, Genova, Italy
    • L. AMBROSIO, Corso introduttivo alla teoria geometrica delia misura ed alle superfici minimime, Quad. Scuola Norm. Sup. Pisa, Pantograph, Genova, Italy, 1997.
    • (1997) Quad. Scuola Norm. Sup. Pisa
    • Ambrosio, L.1
  • 11
    • 0003282839 scopus 로고    scopus 로고
    • Functions of bounded variation and free discontinuity problems
    • Oxford University Press, New York
    • L. AMBROSIO, N. FUSCO, AND D. PALLARA, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Oxford University Press, New York, 2000.
    • (2000) Oxford Math. Monogr.
    • Ambrosio, L.1    Fusco, N.2    Pallara, D.3
  • 12
    • 18844398187 scopus 로고    scopus 로고
    • Parabolic quasilinear equations minimizing linear growth functionals
    • Birkhäuser, Basel
    • F. ANDREU-VAILLO, V. CASELLES, AND J.M. MAZÓN, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals, Progr. Math. 223, Birkhäuser, Basel, 2004.
    • (2004) Progr. Math. , vol.223
    • Andreu-Vaillo, F.1    Caselles, V.2    Mazón, J.M.3
  • 13
    • 0000978548 scopus 로고
    • Pairing between measures and bounded functions and compensated compactness
    • G. ANZELLOTTI, Pairing between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4), 135 (1983), pp. 293-318.
    • (1983) Ann. Mat. Pura Appl. , vol.4 , Issue.135 , pp. 293-318
    • Anzellotti, G.1
  • 14
    • 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. 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
  • 15
    • 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. Comput. Vision, 63 (2005), pp. 85-104.
    • (2005) Int. J. Comput. Vision , vol.63 , pp. 85-104
    • Aujol, J.-F.1    Chambolle, A.2
  • 16
    • 33644533840 scopus 로고    scopus 로고
    • Structure-texture image decompositionmodeling, algorithms, and parameter selection
    • J.-F. AUJOL, G. GILBOA, T. CHAN, AND S. OSHER, Structure-texture image decompositionmodeling, algorithms, and parameter selection, Int. J. Comput. Vision, 67 (2006), pp. 111-136.
    • (2006) Int. J. Comput. Vision , vol.67 , pp. 111-136
    • Aujol, J.-F.1    Gilboa, G.2    Chan, T.3    Osher, S.4
  • 17
  • 20
    • 85016548547 scopus 로고    scopus 로고
    • Characterization of facet breaking for nonsmooth mean curvature flow in the convex case
    • G. BELLETTINI, M. NOVAGA, AND M. PAOLINI, Characterization of facet breaking for nonsmooth mean curvature flow in the convex case, Interfaces Free Bound., 3 (2001), pp. 415-446.
    • (2001) Interfaces Free Bound , vol.3 , pp. 415-446
    • Bellettini, G.1    Novaga, M.2    Paolini, M.3
  • 22
    • 34547108563 scopus 로고    scopus 로고
    • On a weighted total variation minimization problem
    • G. CARLIER AND M. COMTE, On a weighted total variation minimization problem, J. Funct. Anal., 250 (2007), pp. 214-226.
    • (2007) J. Funct. Anal. , vol.250 , pp. 214-226
    • Carlier, G.1    Comte, M.2
  • 23
    • 59049094531 scopus 로고    scopus 로고
    • Approximation of maximal Cheeger sets by projection
    • G. CARLIER., M. COMTE, AND G. PEYRÉ, Approximation of maximal Cheeger sets by projection, M2AN Math. Model. Numer. Anal., 43 (2009), pp. 139-150.
    • (2009) M2AN Math. Model. Numer. Anal. , vol.43 , pp. 139-150
    • Carlier, G.1    Comte, M.2    Peyré, G.3
  • 25
    • 55549132662 scopus 로고    scopus 로고
    • Uniqueness of the Cheeger set of a convex body
    • V. CABELLES, A. CHAMBOLLE, AND M. NOVAGA, Uniqueness of the Cheeger set of a convex body, Nonlinear Anal., 370 (2009), pp. 32-44.
    • (2009) Nonlinear Anal. , vol.370 , pp. 32-44
    • Cabelles, V.1    Chambolle, A.2    Novaga, M.3
  • 28
    • 33845482689 scopus 로고    scopus 로고
    • Image restoration with discrete constrained total variation part I: Fast and exact optimization
    • J. DARBON AND M. SIGELLE, Image restoration with discrete constrained total variation part I: Fast and exact optimization, J. Math. Imaging Vision, 26 (2006), pp. 261-276.
    • (2006) J. Math. Imaging Vision , vol.26 , pp. 261-276
    • Darbon, J.1    Sigelle, M.2
  • 30
    • 79751484179 scopus 로고    scopus 로고
    • The TVL1 model: A geometric point of view
    • V. DUVAL, J.-F. AUJOL, AND Y. GOUSSEAU, The TVL1 Model: A Geometric Point of View, Technical report, http://hal.archives-ouvertes.fr/hal-00380195/fr/ (2009).
    • (2009) Technical Report
    • Duval, V.1    Aujol, J.-F.2    Gousseau, Y.3
  • 31
    • 8744270279 scopus 로고    scopus 로고
    • Decomposition of images by the anisotropic Rudin-Osher-Fatemi model
    • S. ESEDOGLU AND S.J. OSHER, Decomposition of images by the anisotropic Rudin-Osher-Fatemi model, Comm. Pure Appl. Math., 57 (2004), pp. 1609-1626.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 1609-1626
    • Esedoglu, S.1    Osher, S.J.2
  • 32
    • 0000236688 scopus 로고
    • On the equation of surfaces of prescribed mean curvature
    • E. GIUSTI, On the equation of surfaces of prescribed mean curvature, Invent. Math., 46 (1978), pp. 111-137.
    • (1978) Invent. Math. , vol.46 , pp. 111-137
    • Giusti, E.1
  • 34
    • 34250215696 scopus 로고    scopus 로고
    • Characterization of Cheeger sets for convex subsets of the plane
    • B. KAWOHL AND T. LACHAND-ROBERT, Characterization of Cheeger sets for convex subsets of the plane, Pacific J. Math., 225 (2006), pp. 103-118.
    • (2006) Pacific J. Math. , vol.225 , pp. 103-118
    • Kawohl, B.1    Lachand-Robert, T.2
  • 37
    • 0011975955 scopus 로고    scopus 로고
    • Scale-space from a level lines tree
    • P. MONASSE AND F. GUICHARD, Scale-space from a level lines tree, J. Vis. Commun. Image R., 11 (2000), pp. 224-236.
    • (2000) J. Vis. Commun. Image R. , vol.11 , pp. 224-236
    • Monasse, P.1    Guichard, F.2
  • 39
    • 1242284980 scopus 로고    scopus 로고
    • A variational approach to remove outliers and impulse noise
    • M. NIKOLOVA, A variational approach to remove outliers and impulse noise, J. Math. Imaging Vision, 20 (2004), pp. 99-120.
    • (2004) J. Math. Imaging Vision , vol.20 , pp. 99-120
    • Nikolova, M.1
  • 41
    • 0004267646 scopus 로고
    • Grundlehren Math. Wiss. 224, Princeton University Press, Princeton, NJ
    • T. ROCKAFELLAR, Convex Analysis, 2nd ed., Grundlehren Math. Wiss. 224, Princeton University Press, Princeton, NJ, 1983.
    • (1983) Convex Analysis, 2nd Ed.
    • Rockafellar, T.1
  • 42
    • 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
  • 43
    • 0001584432 scopus 로고    scopus 로고
    • Anti-extensive connected operators for image and sequence processing
    • P. SALEMBIER., A. OLIVERAS, AND L. GARRIDO, Anti-extensive connected operators for image and sequence processing, IEEE Trans. Image Process., 7 (1998), pp. 555-570.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 555-570
    • Salembier, P.1    Oliveras, A.2    Garrido, L.3
  • 45
    • 0347900511 scopus 로고    scopus 로고
    • Modeling textures with total variation minimization and oscillating patterns in image processing
    • L.A. VESE AND S.J. OSHER, Modeling textures with total variation minimization and oscillating patterns in image processing, J. Sci. Comput., 19 (2003), pp. 553-572.
    • (2003) J. Sci. Comput. , vol.19 , pp. 553-572
    • Vese, L.A.1    Osher, S.J.2
  • 47
    • 34247608671 scopus 로고    scopus 로고
    • A comparison of three total variation based texture extraction models
    • W. YIN, D. GOLDFARB, AND S. OSHER, A comparison of three total variation based texture extraction models, J. Vis. Commun. Image R., 18 (2007), pp. 240-252.
    • (2007) J. Vis. Commun. Image R. , vol.18 , pp. 240-252
    • Yin, W.1    Goldfarb, D.2    Osher, S.3


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