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Volumn 33, Issue 2, 2009, Pages 135-148

(Φ,Φ*) Image decomposition models and minimization algorithms

Author keywords

BV duality; Functional minimization; Image decomposition; Image restoration

Indexed keywords

DIFFERENTIAL EQUATIONS; EQUATIONS OF MOTION; EULER EQUATIONS; GROWTH (MATERIALS); IMAGE RECONSTRUCTION; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; OPTIMIZATION; REPAIR; RESTORATION;

EID: 59849109623     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-008-0130-1     Document Type: Article
Times cited : (6)

References (43)
  • 1
    • 36149030663 scopus 로고
    • Analysis of bounded variation penalty methods for ill-posed problems
    • 6
    • R. Acar C.R. Vogel 1994 Analysis of bounded variation penalty methods for ill-posed problems Inverse Probl. 10 6 1217 1229
    • (1994) Inverse Probl. , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.R.2
  • 2
  • 3
    • 0026883886 scopus 로고
    • Image selective smoothing and edge detection by non-linear diffusion 2
    • 3
    • L. Alvarez P.-L. Lions J.-M. Morel 1992 Image selective smoothing and edge detection by non-linear diffusion 2 SIAM J. Numer. Anal. 29 3 845 866
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 845-866
    • Alvarez, L.1    Lions, P.-L.2    Morel, J.-M.3
  • 5
    • 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 (2004)
    • (2004) Progress in Mathematics , vol.223
    • Andreu-Vaillo, F.1    Caselles, V.2    Mazon, J.M.3
  • 6
    • 17444396382 scopus 로고    scopus 로고
    • Modeling very oscillating signals. Application to image processing
    • 2
    • G. Aubert J.-F. Aujol 2005 Modeling very oscillating signals. Application to image processing Appl. Math. Optim. 51 2 163 182
    • (2005) Appl. Math. Optim. , vol.51 , pp. 163-182
    • Aubert, G.1    Aujol, J.-F.2
  • 7
    • 0011235023 scopus 로고    scopus 로고
    • A variational method in image recovery
    • 5
    • G. Aubert L. Vese 1997 A variational method in image recovery SIAM J. Numer. Anal. 34 5 1948 1979
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1948-1979
    • Aubert, G.1    Vese, L.2
  • 8
    • 14844353365 scopus 로고    scopus 로고
    • Dual norms and image decomposition models
    • 1
    • J.-F. Aujol A. Chambolle 2005 Dual norms and image decomposition models Int. J. Comput. Vis. 3 1 85 104
    • (2005) Int. J. Comput. Vis. , vol.3 , pp. 85-104
    • Aujol, J.-F.1    Chambolle, A.2
  • 9
    • 35248822315 scopus 로고    scopus 로고
    • Image decomposition application to SAR images
    • Aujol, J.-F., Aubert, G., Blanc-Féraud, L., Chambolle, A.: Image decomposition application to SAR images. In: LNCS, vol. 2695, pp. 297-312 (2003)
    • (2003) LNCS , vol.2695 , pp. 297-312
    • Aujol, J.-F.1    Aubert, G.2    Blanc-Féraud, L.3    Chambolle, A.4
  • 10
    • 14844355103 scopus 로고    scopus 로고
    • Image decomposition into a bounded variation component and an oscillating component
    • 1
    • J.-F. Aujol G. Aubert L. Blanc-Féraud A. Chambolle 2005 Image decomposition into a bounded variation component and an oscillating component J. Math. Imaging Vis. 22 1 71 88
    • (2005) J. Math. Imaging Vis. , vol.22 , pp. 71-88
    • Aujol, J.-F.1    Aubert, G.2    Blanc-Féraud, L.3    Chambolle, A.4
  • 11
    • 0037386021 scopus 로고    scopus 로고
    • On the equation div∈Y=f and application to control of phases
    • J. Bourgain H. Brezis 2003 On the equation div∈Y=f and application to control of phases J. Am. Math. Soc. 16 393 426
    • (2003) J. Am. Math. Soc. , vol.16 , pp. 393-426
    • Bourgain, J.1    Brezis, H.2
  • 12
    • 0026821645 scopus 로고
    • Image selective smoothing and edge-detection by nonlinear diffusion
    • 1
    • F. Catté P.-L. Lions J.-M. Morel T. Coll 1992 Image selective smoothing and edge-detection by nonlinear diffusion SIAM J. Numer. Anal. 29 1 182 193
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 182-193
    • Catté, F.1    Lions, P.-L.2    Morel, J.-M.3    Coll, T.4
  • 13
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • 2
    • A. Chambolle P.-L. Lions 1997 Image recovery via total variation minimization and related problems Numer. Math. 76 2 167 188
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 15
    • 20144365032 scopus 로고    scopus 로고
    • Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising
    • 1
    • I. Daubechies G. Teschke 2005 Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising Appl. Comput. Harmon. Anal. 19 1 1 16
    • (2005) Appl. Comput. Harmon. Anal. , vol.19 , pp. 1-16
    • Daubechies, I.1    Teschke, G.2
  • 17
    • 0001020536 scopus 로고
    • Convex functions of a measure and applications
    • 5
    • F. Demengel R. Témam 1984 Convex functions of a measure and applications Indiana Univ. Math. J. 33 5 673 709
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 673-709
    • Demengel, F.1    Témam, R.2
  • 19
    • 0003346795 scopus 로고
    • Measure Theory and Fine Properties of Functions
    • CRC Press Boca Raton
    • Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1992)
    • (1992) Studies in Advanced Mathematics
    • Evans, L.C.1    Gariepy, R.F.2
  • 20
    • 34249800358 scopus 로고    scopus 로고
    • Image decompositions using bounded variation and homogeneous Besov spaces
    • J.B. Garnett T.M. Le Y. Meyer L.A. Vese 2007 Image decompositions using bounded variation and homogeneous Besov spaces Appl. Comput. Harmon. Anal. 23 25 56
    • (2007) Appl. Comput. Harmon. Anal. , vol.23 , pp. 25-56
    • Garnett, J.B.1    Le, T.M.2    Meyer, Y.3    Vese, L.A.4
  • 23
    • 0029341230 scopus 로고
    • Nonlinear image recovery with half-quadratic regularization
    • 7
    • D. Geman C. Yang 1995 Nonlinear image recovery with half-quadratic regularization IEEE Trans. Image Process. 4 7 932 946
    • (1995) IEEE Trans. Image Process. , vol.4 , pp. 932-946
    • Geman, D.1    Yang, C.2
  • 27
    • 33645696337 scopus 로고    scopus 로고
    • Image decomposition using total variation and div(BMO)
    • 2
    • T.M. Le L.A. Vese 2005 Image decomposition using total variation and div(BMO) Multiscale Model. Simul. 4 2 390 423
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 390-423
    • Le, T.M.1    Vese, L.A.2
  • 28
    • 33645695107 scopus 로고    scopus 로고
    • An adaptive variational model for image decomposition
    • Rangarajan, A., Vemuri, B., Yuille, A.L. (eds.) Energy Minimization Methods in Computer Vision and Pattern Recognition. 5th International Workshop, EMMCVPR 2005, St. Augustine, FL, 9-11 November 2005
    • Levine, S.E.: An adaptive variational model for image decomposition. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds.) Energy Minimization Methods in Computer Vision and Pattern Recognition. 5th International Workshop, EMMCVPR 2005, St. Augustine, FL, 9-11 November 2005. LNCS, vol. 3757, pp. 382-397. Springer, Berlin (2005)
    • (2005) LNCS , vol.3757 , pp. 382-397
    • Levine, S.E.1
  • 29
    • 51849090507 scopus 로고    scopus 로고
    • Image restoration and decomposition via bounded total variation and negative Hilbert-Sobolev spaces
    • L. Lieu L. Vese 2008 Image restoration and decomposition via bounded total variation and negative Hilbert-Sobolev spaces Appl. Math. Optim. 58 167 193
    • (2008) Appl. Math. Optim. , vol.58 , pp. 167-193
    • Lieu, L.1    Vese, L.2
  • 30
    • 22844455863 scopus 로고    scopus 로고
    • A new time dependent model based on level set motion for nonlinear deblurring and noise removal
    • Marquina, A., Osher, S.: A new time dependent model based on level set motion for nonlinear deblurring and noise removal. In: LNCS, vol. 1682, pp. 429-434 (1999)
    • (1999) LNCS , vol.1682 , pp. 429-434
    • Marquina, A.1    Osher, S.2
  • 31
    • 0035075370 scopus 로고    scopus 로고
    • Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal
    • 2
    • A. Marquina S. Osher 2000 Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal SIAM J. Sci. Comput. 22 2 387 405
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 387-405
    • Marquina, A.1    Osher, S.2
  • 32
    • 0038508524 scopus 로고    scopus 로고
    • Oscillating Patterns in Image Processing and Nonlinear Evolution Equations
    • Am. Math. Soc. Providence
    • Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. University Lecture Series, vol. 22. Am. Math. Soc., Providence (2001)
    • (2001) University Lecture Series , vol.22
    • Meyer, Y.1
  • 34
    • 0035281916 scopus 로고    scopus 로고
    • Stochastic models for generic images
    • 1
    • D. Mumford B. Gidas 2001 Stochastic models for generic images Q. Appl. Math. 59 1 85 111
    • (2001) Q. Appl. Math. , vol.59 , pp. 85-111
    • Mumford, D.1    Gidas, B.2
  • 35
    • 84990602490 scopus 로고
    • Optimal approximations by piecewise-smooth functions and associated variational problems
    • 5
    • D. Mumford J. Shah 1989 Optimal approximations by piecewise-smooth functions and associated variational problems Commun. Pure Appl. Math. 42 5 577 685
    • (1989) Commun. Pure Appl. Math. , vol.42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 37
  • 38
    • 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
  • 39
    • 84996774871 scopus 로고
    • Total variation based image restoration with free local constraints
    • Rudin, L.I., Osher, S.: Total variation based image restoration with free local constraints. In: Proceedings of IEEE ICIP-94, vol. 1, pp. 31-35 (1994)
    • (1994) Proceedings of IEEE ICIP-94 , vol.1 , pp. 31-35
    • Rudin, I.L.1    Osher, S.2
  • 40
    • 0039472976 scopus 로고
    • ∞ and approximation of vector fields in the plane
    • Fujita, H., Lax, P., and Strang, G. (eds.) Nonlinear Partial Differential Equations in Applied Science
    • ∞ and approximation of vector fields in the plane. In: Fujita, H., Lax, P., and Strang, G. (eds.) Nonlinear Partial Differential Equations in Applied Science. Lecture Notes in Num. Appl. Anal., vol. 5, pp. 273-288 (1982)
    • (1982) Lecture Notes in Num. Appl. Anal. , vol.5 , pp. 273-288
    • Strang, G.1
  • 41
    • 0011021531 scopus 로고    scopus 로고
    • A study in the BV space of a denoising-deblurring variational problem
    • 2
    • L. Vese 2001 A study in the BV space of a denoising-deblurring variational problem Appl. Math. Optim. 44 2 131 161
    • (2001) Appl. Math. Optim. , vol.44 , pp. 131-161
    • Vese, L.1
  • 42
    • 0347900511 scopus 로고    scopus 로고
    • Modeling textures with total variation minimization and oscillating patterns in image processing
    • 13
    • L. Vese S. Osher 2003 Modeling textures with total variation minimization and oscillating patterns in image processing J. Sci. Comput. 19 13 553 572
    • (2003) J. Sci. Comput. , vol.19 , pp. 553-572
    • Vese, L.1    Osher, S.2
  • 43
    • 1242265490 scopus 로고    scopus 로고
    • Image denoising and decomposition with total variation minimization and oscillatory functions
    • L.A. Vese S.J. Osher 2004 Image denoising and decomposition with total variation minimization and oscillatory functions J. Math. Imaging Vis. 20 7 18
    • (2004) J. Math. Imaging Vis. , vol.20 , pp. 7-18
    • Vese, L.A.1    Osher, S.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.