메뉴 건너뛰기




Volumn 33, Issue 5, 2011, Pages 2972-2994

Iterative parameter-choice and multigrid methods for anisotropic diffusion denoising

Author keywords

Anisotropic diffusion; Brent's method; Normalized cumulative periodogram; Parameter choice; Regularization; Robust multigrid

Indexed keywords

DIFFUSION; ITERATIVE METHODS; OPTICAL ANISOTROPY; PARAMETER ESTIMATION; PARAMETERIZATION;

EID: 81555213050     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/100796066     Document Type: Conference Paper
Times cited : (28)

References (44)
  • 1
    • 0032023714 scopus 로고    scopus 로고
    • Multigrid anisotropic diffusion
    • S. Acton, Multigrid anisotropic diffusion, IEEE Trans. Image Process., 7 (1998), pp. 280-290.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 280-290
    • Acton, S.1
  • 2
    • 0000014842 scopus 로고
    • The multi-grid method for the diffusion equation with strongly discontinuous coefficients
    • R. E. Alcouffe, A. Brandt, J. E. Dendy, Jr., and J. W. Painter, The multi-grid method for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 430-454.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 430-454
    • Alcouffe, R.E.1    Brandt, A.2    Dendy Jr., J.E.3    Painter, J.W.4
  • 5
    • 23044527717 scopus 로고    scopus 로고
    • An Accurate Operator Splitting Scheme for Nonlinear Diffusion Filtering
    • D. Barash, M. Israeli, and R. Kimmel, An accurate operator splitting scheme for nonlinear diffusion filtering, in Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision, Springer-Verlag, London, UK, 2001, pp. 281-289. (Pubitemid 33303190)
    • (2001) Lecture Notes in Computer Science , Issue.2106 , pp. 281-289
    • Barash, D.1    Israeli, M.2    Kimmel, R.3
  • 6
    • 0002438068 scopus 로고
    • Algebraic multigrid (AMG) for sparse matrix equations
    • D. J. Evans, ed., Cambridge University Press, Cambridge, UK
    • A. Brandt, S. McCormick, and J. Ruge, Algebraic multigrid (AMG) for sparse matrix equations, in Sparsity and Its Applications, D. J. Evans, ed., Cambridge University Press, Cambridge, UK, 1985, pp. 257-284.
    • (1985) Sparsity and Its Applications , pp. 257-284
    • Brandt, A.1    McCormick, S.2    Ruge, J.3
  • 8
    • 34748877593 scopus 로고    scopus 로고
    • Technical report, CMLA (Centre de Mathematiques et de Leurs Applications), Cachen, France
    • A. Buades, B. Coll, and J. M. Morel, On Image Denoising Methods, Technical report, CMLA (Centre de Mathematiques et de Leurs Applications), Cachen, France, 2004.
    • (2004) On Image Denoising Methods
    • Buades, A.1    Coll, B.2    Morel, J.M.3
  • 9
    • 0022808786 scopus 로고
    • A computational approach to edge detection
    • J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell., 8 (1986), pp. 679-698.
    • (1986) IEEE Trans. Pattern Anal. Mach. Intell. , vol.8 , pp. 679-698
    • Canny, J.1
  • 10
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29 (1992), pp. 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
  • 11
    • 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
  • 12
    • 34250902982 scopus 로고    scopus 로고
    • An accelerated algebraic multigrid algorithm for total-variation denoising
    • K. Chen and J. Savage, An accelerated algebraic multigrid algorithm for total-variation denoising, BIT, 47 (2007), pp. 277-296.
    • (2007) BIT , vol.47 , pp. 277-296
    • Chen, K.1    Savage, J.2
  • 14
    • 0001677218 scopus 로고
    • Black box multigrid
    • J. Dendy, Black box multigrid, J. Comput. Phys., 48 (1982), pp. 366-386.
    • (1982) J. Comput. Phys. , vol.48 , pp. 366-386
    • Dendy, J.1
  • 15
    • 69049097417 scopus 로고    scopus 로고
    • Multi-scale total variation with automated regularization parameter selection for color image restoration
    • Lecture Notes in Comput. Sci. Springer, Berlin/Heidelberg
    • Y. Dong and M. Hintermüller, Multi-scale total variation with automated regularization parameter selection for color image restoration, in Scale Space and Variational Methods in Computer Vision, Lecture Notes in Comput. Sci. 5567, Springer, Berlin/Heidelberg, 2009, pp. 271-281.
    • (2009) Scale Space and Variational Methods in Computer Vision , vol.5567 , pp. 271-281
    • Dong, Y.1    Hintermüller, M.2
  • 16
    • 48849106119 scopus 로고    scopus 로고
    • Multiscale representation and segmentation of hyperspectral imagery using geometric partial differential equations and algebraic multigrid methods
    • J.M. Duarte-Carvajalino, G. Sapiro, M. Velez-Reyes, and P.E. Castillo, Multiscale representation and segmentation of hyperspectral imagery using geometric partial differential equations and algebraic multigrid methods, IEEE Trans. Geosci. Remote Sensing, 46 (2008), pp. 2418-2434.
    • (2008) IEEE Trans. Geosci. Remote Sensing , vol.46 , pp. 2418-2434
    • Duarte-Carvajalino, J.M.1    Sapiro, G.2    Velez-Reyes, M.3    Castillo, P.E.4
  • 18
    • 56549118623 scopus 로고    scopus 로고
    • Nonlinear scale space with spatially varying stopping time
    • G. Gilboa, Nonlinear scale space with spatially varying stopping time, IEEE Trans. Pattern Anal. Mach. Intell., 30 (2008), pp. 2175-2187.
    • (2008) IEEE Trans. Pattern Anal. Mach. Intell. , vol.30 , pp. 2175-2187
    • Gilboa, G.1
  • 19
    • 33645036956 scopus 로고    scopus 로고
    • Exploiting residual information in the parameter choice for discrete ill-posed problems
    • DOI 10.1007/s10543-006-0042-7
    • P. Hansen, M. Kilmer, and R. Kjeldsen, Exploiting residual information in the parameter choice for discrete ill-posed problems, BIT, 46 (2006), pp. 41-59. (Pubitemid 43417398)
    • (2006) BIT Numerical Mathematics , vol.46 , Issue.1 , pp. 41-59
    • Hansen, P.C.1    Kilmer, M.E.2    Kjeldsen, R.H.3
  • 20
    • 0031256990 scopus 로고    scopus 로고
    • The Perona-Malik paradox
    • S. Kichenassamy, The Perona-Malik paradox, SIAM J. Appl. Math., 57 (1997), pp. 1328-1342.
    • SIAM J. Appl. Math. , vol.57 , Issue.1997 , pp. 1328-1342
    • Kichenassamy, S.1
  • 21
    • 0042430619 scopus 로고    scopus 로고
    • An algebraic multigrid approach for image analysis
    • R. Kimmel and I. Yavneh, An algebraic multigrid approach for image analysis, SIAM J. Sci. Comput., 24 (2003), pp. 1218-1231.
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 1218-1231
    • Kimmel, R.1    Yavneh, I.2
  • 23
    • 84937421180 scopus 로고    scopus 로고
    • Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering
    • P. Mrázek, Selection of optimal stopping time for nonlinear diffusion filtering, in Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision, Scale-Space 01, Springer-Verlag, Berlin, New York, 2001, pp. 290-298. (Pubitemid 33303191)
    • (2001) Lecture Notes in Computer Science , Issue.2106 , pp. 290-298
    • Mrazek, P.1
  • 25
    • 33745125969 scopus 로고    scopus 로고
    • A cross-validatory statistical approach to scale selection for image denoising by nonlinear diffusion
    • DOI 10.1109/CVPR.2005.21, 1467326, Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
    • G. Papandreou and P. Maragos, A cross-validatory statistical approach to scale selection for image denoising by nonlinear diffusion, in Proceedings of the IEEE Computer Vision and Pattern Recognition, IEEE Press, Piscataway, NJ, 2005, pp. 625-630. (Pubitemid 43897252)
    • (2005) Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005 , vol.I , pp. 625-630
    • Papandreou, G.1    Maragos, P.2
  • 26
    • 33847740315 scopus 로고    scopus 로고
    • Multigrid geometric active contour models
    • DOI 10.1109/TIP.2006.884952
    • G. Papandreou and P. Maragos, Multigrid geometric active contour models, IEEE Trans. Image Process., 16 (2007), pp. 229-240. (Pubitemid 46437485)
    • (2007) IEEE Transactions on Image Processing , vol.16 , Issue.1 , pp. 229-240
    • Papandreou, G.1    Maragos, P.2
  • 30
    • 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
  • 31
    • 0001885411 scopus 로고
    • Algebraic multigrid
    • S. F. McCormick, ed., SIAM, Philadelphia
    • J. Ruge and K. Stüben, Algebraic multigrid, in Multigrid Methods, S. F. McCormick, ed., SIAM, Philadelphia, 1987, pp. 73-130.
    • (1987) Multigrid Methods , pp. 73-130
    • Ruge, J.1    Stüben, K.2
  • 32
    • 44449162474 scopus 로고    scopus 로고
    • Residual periodograms for choosing regularization parameters for ill-posed problems
    • B. Rust and D. O'Leary, Residual periodograms for choosing regularization parameters for ill-posed problems, Inverse Problems, 24 (2008), 034005.
    • (2008) Inverse Problems , vol.24 , pp. 034005
    • Rust, B.1    O'Leary, D.2
  • 33
    • 33847761438 scopus 로고    scopus 로고
    • Scale recognition, regularization parameter selection, and Meyer's G norm in total variation regularization
    • DOI 10.1137/040621624
    • D. M. Strong, J.-F. Aujol, and T. F. Chan, Scale recognition, regularization parameter selection, and Meyer's G norm in total variation regularization, Multiscale Model. Simul., 5 (2006), pp. 273-303. (Pubitemid 46380331)
    • (2006) Multiscale Modeling and Simulation , vol.5 , Issue.1 , pp. 273-303
    • Strong, D.M.1    Aujol, J.-F.2    Chan, T.F.3
  • 34
    • 71649109807 scopus 로고    scopus 로고
    • The use of Kolmogorov-Smirnov test in event-by-event analysis
    • B. Tomasik, I. Melo, G. Torrieri, S. Vogel, and M. Bleicher, The use of Kolmogorov-Smirnov test in event-by-event analysis, Nucl. Phys., A830 (2009), pp. 195c-198c.
    • (2009) Nucl. Phys. , vol.A830
    • Tomasik, B.1    Melo, I.2    Torrieri, G.3    Vogel, S.4    Bleicher, M.5
  • 36
    • 85032751127 scopus 로고    scopus 로고
    • Mean squared error: Love it or leave it? A new look at signal fidelity measures
    • Z. Wang and A.C. Bovik, Mean squared error: Love it or leave it? A new look at signal fidelity measures, IEEE Signal Process. Mag., 26 (2009), pp. 98-117.
    • (2009) IEEE Signal Process. Mag. , vol.26 , pp. 98-117
    • Wang, Z.1    Bovik, A.C.2
  • 37
    • 1942436689 scopus 로고    scopus 로고
    • Image quality assessment: From error visibility to structural similarity
    • Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Trans. Image Process., 13 (2004), pp. 600-612.
    • (2004) IEEE Trans. Image Process. , vol.13 , pp. 600-612
    • Wang, Z.1    Bovik, A.2    Sheikh, H.3    Simoncelli, E.4
  • 38
  • 39
    • 84957681902 scopus 로고    scopus 로고
    • A review of nonlinear diffusion filtering
    • Scale-Space Theory in Computer Vision
    • J. Weickert, A review of nonlinear diffusion filtering, in SCALE-SPACE '97: Proceedings of the First International Conference on Scale-Space Theory in Computer Vision, Springer-Verlag, London, 1997, pp. 3-28. (Pubitemid 127097428)
    • (1997) Lecture Notes in Computer Science , Issue.1252 , pp. 3-28
    • Weickert, J.1
  • 40
    • 0033100270 scopus 로고    scopus 로고
    • Coherence-enhancing diffusion of colour images
    • J. Weickert, Coherence-enhancing diffusion of colour images, Image Vision Comput., 17 (1999), pp. 201-212.
    • (1999) Image Vision Comput. , vol.17 , pp. 201-212
    • Weickert, J.1
  • 41
    • 0002236989 scopus 로고    scopus 로고
    • A semidiscrete nonlinear scale-space theory and its relation to the Perona-Malik paradox
    • F. Solina, ed., Springer, Berlin, New York
    • J. Weickert and B. Benhamouda, A semidiscrete nonlinear scale-space theory and its relation to the Perona-Malik paradox, in Advances in Computer Vision, F. Solina, ed., Springer, Berlin, New York, 1997, pp. 1-10.
    • (1997) Advances in Computer Vision , pp. 1-10
    • Weickert, J.1    Benhamouda, B.2
  • 43
    • 0036501337 scopus 로고    scopus 로고
    • A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance
    • DOI 10.1006/jvci.2001.0495
    • J. Weickert and H. Scharr, A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance, J. Visual Commun. Image Representation, 13 (2002), pp. 103-118. (Pubitemid 34278486)
    • (2002) Journal of Visual Communication and Image Representation , vol.13 , Issue.1-2 , pp. 103-118
    • Weickert, J.1    Scharr, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.