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Volumn 27, Issue 3, 2006, Pages 831-849

A multigrid method for a fourth-order diffusion equation with application to image processing

Author keywords

Biharmonic equation; Finite differences; Image processing; Multigrid methods; Nonlinear diffusion equation

Indexed keywords

DIFFUSION; FINITE DIFFERENCE METHOD; IMAGE PROCESSING; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS);

EID: 33646598675     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040611124     Document Type: Article
Times cited : (42)

References (27)
  • 1
    • 0001039561 scopus 로고    scopus 로고
    • Multigrid solution of automatically generated high-order discretizations for the biharmonic equation
    • I. ALTAS, J. DYM, M. M. GUPTA, AND R. P. MANOHAR, Multigrid solution of automatically generated high-order discretizations for the biharmonic equation, SIAM J. Sci. Comput., 19 (1998), pp. 1575-1585.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1575-1585
    • Altas, I.1    Dym, J.2    Gupta, M.M.3    Manohar, R.P.4
  • 3
    • 84979130379 scopus 로고
    • On the boundary value problem of the biharmonic operator on domains with angular corners
    • H. BLUM AND R. RANNACHER, On the boundary value problem of the biharmonic operator on domains with angular corners, Math. Methods Appl. Sci., 2 (1980), pp. 556-581.
    • (1980) Math. Methods Appl. Sci. , vol.2 , pp. 556-581
    • Blum, H.1    Rannacher, R.2
  • 5
    • 0012613191 scopus 로고
    • An optimal-order nonconforming multigrid method for the biharmonic equation
    • S. BRENNER, An optimal-order nonconforming multigrid method for the biharmonic equation, SIAM J. Numer. Anal., 26 (1989), pp. 1124-1138.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1124-1138
    • Brenner, S.1
  • 6
    • 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
  • 7
    • 0033295350 scopus 로고    scopus 로고
    • A nonlinear primal-dual method for total variation-based image restoration
    • T. F. CHAN, G. H. GOLUB, AND P. MULET, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comput., 20 (1999), pp. 1964-1977.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1964-1977
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 8
    • 3042758075 scopus 로고    scopus 로고
    • Variational PDE models in image processing
    • T. CHAN, J. SHEN, AND L. VESE, Variational PDE models in image processing, Notices Amer. Math. Soc., 50 (2003), pp. 14-26.
    • (2003) Notices Amer. Math. Soc. , vol.50 , pp. 14-26
    • Chan, T.1    Shen, J.2    Vese, L.3
  • 10
    • 0000165266 scopus 로고
    • On an alternating direction method for solving the plate problem with mixed boundary conditions
    • S. D. CONTE AND R. T. DAMES, On an alternating direction method for solving the plate problem with mixed boundary conditions, J. ACM, 7 (1960), pp. 264-273.
    • (1960) J. ACM , vol.7 , pp. 264-273
    • Conte, S.D.1    Dames, R.T.2
  • 11
    • 0016567049 scopus 로고
    • Some difference schemes for the biharmonic equation
    • L. W. EHRLICH AND M. M. GUPTA, Some difference schemes for the biharmonic equation, SIAM J. Numer. Anal., 12 (1975), pp. 773-790.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 773-790
    • Ehrlich, L.W.1    Gupta, M.M.2
  • 14
    • 0141714099 scopus 로고
    • Direct solution of the biharmonic equation using noncoupled approaches
    • M. GUPTA AND R. MANOHAR, Direct solution of the biharmonic equation using noncoupled approaches, J. Comput. Phys., 33 (1979), pp. 236-248.
    • (1979) J. Comput. Phys. , vol.33 , pp. 236-248
    • Gupta, M.1    Manohar, R.2
  • 15
    • 0016518840 scopus 로고
    • Discretization error estimates for certain splitting procedures for solving first biharmonic boundary value problems
    • M. M. GUPTA, Discretization error estimates for certain splitting procedures for solving first biharmonic boundary value problems, SIAM J. Numer. Anal., 12 (1975), pp. 364-377.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 364-377
    • Gupta, M.M.1
  • 17
    • 0003606909 scopus 로고
    • Elliptic Differential Equations. Theory and Numerical Treatment
    • Springer-Verlag, Berlin
    • W. HACKBUSCH, Elliptic Differential Equations. Theory and Numerical Treatment, Springer Ser. Comput. Math. 18, Springer-Verlag, Berlin, 1992.
    • (1992) Springer Ser. Comput. Math. , vol.18
    • Hackbusch, W.1
  • 18
    • 0027543238 scopus 로고
    • Multigrid preconditioning for the biharmonic Dirichlet problem
    • M. R. HANISCH, Multigrid preconditioning for the biharmonic Dirichlet problem, SIAM J. Numer. Anal., 30 (1993), pp. 184-214.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 184-214
    • Hanisch, M.R.1
  • 19
    • 0036341612 scopus 로고    scopus 로고
    • Iterative multigrid regularization techniques for image matching
    • S. HENN AND K. WITSCH, Iterative multigrid regularization techniques for image matching, SIAM J. Sci. Comput., 23 (2001), pp. 1077-1093.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 1077-1093
    • Henn, S.1    Witsch, K.2
  • 20
    • 33646545510 scopus 로고    scopus 로고
    • Image registration based on multiscale energy information
    • S. HENN AND K. WITSCH, Image registration based on multiscale energy information, Multiscale Model. Simul., 4 (2005), pp. 584-609.
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 584-609
    • Henn, S.1    Witsch, K.2
  • 21
    • 0004252812 scopus 로고
    • Multigrid Methods
    • S. F. MCCORMICK, ED., SIAM, Philadelphia
    • S. F. MCCORMICK, ED., Multigrid Methods, Frontiers Appl. Math. 3, SIAM, Philadelphia, 1987.
    • (1987) Frontiers Appl. Math. , vol.3
  • 22
    • 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
  • 23
    • 0001822668 scopus 로고
    • Multigrid methods: Fundamental algorithms, model problem analysis and applications
    • Multigrid Methods, Springer-Verlag, Berlin, New York
    • K. STÜBEN AND U. TROTTENBERG, Multigrid methods: Fundamental algorithms, model problem analysis and applications, in Multigrid Methods, Lecture Notes in Math. 960, Springer-Verlag, Berlin, New York, 1982.
    • (1982) Lecture Notes in Math. , vol.960
    • Stüben, K.1    Trottenberg, U.2
  • 25
    • 0003417587 scopus 로고
    • Computational Frameworks for the Fast Fourier Transform
    • SIAM, Philadelphia
    • C. VAN LOAN, Computational Frameworks for the Fast Fourier Transform, Frontiers Appl. Math. 10, SIAM, Philadelphia, 1992.
    • (1992) Frontiers Appl. Math. , vol.10
    • Van Loan, C.1
  • 26
    • 0013110835 scopus 로고    scopus 로고
    • Computational Methods for Inverse Problems
    • SIAM, Philadelphia
    • C. R. VOGEL, Computational Methods for Inverse Problems, Frontiers Appl. Math., 23, SIAM, Philadelphia, 2002.
    • (2002) Frontiers Appl. Math. , vol.23
    • Vogel, C.R.1
  • 27
    • 0001556589 scopus 로고    scopus 로고
    • Iterative methods for total variation denoising
    • C. R. VOGEL AND M. E. OMAN, Iterative methods for total variation denoising, SIAM J. Sci. Comput., 17 (1996), pp. 227-238.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 227-238
    • Vogel, C.R.1    Oman, M.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.