메뉴 건너뛰기




Volumn , Issue , 2004, Pages 153-158

Discretization schemes and numerical approximations of PDE impainting models and a comparative evaluation on novel real world MRI reconstruction applications

Author keywords

Diffusion PDEs; Image Impainting; MRI Reconstruction; PDE Discretization; Variational PDEs

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ERROR ANALYSIS; FUNCTIONS; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; NUMERICAL METHODS;

EID: 15844402365     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (5)

References (38)
  • 1
    • 3042758075 scopus 로고    scopus 로고
    • Variational PDE models in image processing
    • T. Chan, J. Shen and L. Vese, "Variational PDE Models in Image Processing", Notic. of the AMS Journal, Vol. 50, n. 1, pp. 14-26, 2003.
    • (2003) Notic. of the AMS Journal , vol.50 , Issue.1 , pp. 14-26
    • Chan, T.1    Shen, J.2    Vese, L.3
  • 3
    • 0036301838 scopus 로고    scopus 로고
    • Mathematical models for local nontexture inpaintings
    • T. F. Chan and J. Shen. "Mathematical models for local nontexture inpaintings", SIAM J. Appl. Math., 62(3):1019-1043, 2002.
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.3 , pp. 1019-1043
    • Chan, T.F.1    Shen, J.2
  • 4
    • 0025465145 scopus 로고
    • Scale-space and edge detection using anisotropic diffusion
    • P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion". IEEE Trans. Pattern Anal. Machine Intell., 12:629-639, 1990.
    • (1990) IEEE Trans. Pattern Anal. Machine Intell. , vol.12 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 5
    • 84990602490 scopus 로고
    • Optimal approximations by piecewise smooth functions and associated variational problems
    • D. Mumford and J. Shah, "Optimal approximations by piecewise smooth functions and associated variational problems", Comm. Pure and Applied Mathematics, 42, pp. 577-684, 1989.
    • (1989) Comm. Pure and Applied Mathematics , vol.42 , pp. 577-684
    • Mumford, D.1    Shah, J.2
  • 6
    • 44049111982 scopus 로고
    • Nonlinear Total Variation (TV) based noise removal algorithms
    • L. Rudin, S. Osher, and E. Fatemi, "Nonlinear Total Variation (TV) based noise removal algorithms", Physica D, 60:259-268, 1992.
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 8
    • 15844366832 scopus 로고    scopus 로고
    • Low curvature image simplifiera: Global regularity of smooth solutions and Laplacian limiting schemes
    • October
    • A L. Bertozzi and J. B. Greer. "Low curvature image simplifiera: global regularity of smooth solutions and Laplacian limiting schemes", Comm. Pure App. Math., October 2003.
    • (2003) Comm. Pure App. Math.
    • Bertozzi, A.L.1    Greer, J.B.2
  • 9
    • 84988310135 scopus 로고    scopus 로고
    • LCIS: A boundary hierarchy for detail-preserving contrast reduction
    • August 8-13, 1999, Los Angeles, CA USA
    • J. Tumblin and G. Turk., "LCIS: A boundary hierarchy for detail-preserving contrast reduction". In Proceedings of the SIGGRAPH 1999, August 8-13, 1999, Los Angeles, CA USA, pages 83-90, 1999.
    • (1999) Proceedings of the SIGGRAPH 1999 , pp. 83-90
    • Tumblin, J.1    Turk, G.2
  • 10
    • 0034298888 scopus 로고    scopus 로고
    • Fourth-order partial differential equations for noise removal
    • Yu-Li You and M. Kaveh,. "Fourth-order partial differential equations for noise removal", IEEE Trans. Im. Process., 9(10):1723-1730, 2000.
    • (2000) IEEE Trans. Im. Process. , vol.9 , Issue.10 , pp. 1723-1730
    • You, Y.-L.1    Kaveh, M.2
  • 12
    • 15844416036 scopus 로고    scopus 로고
    • Travelling wave solutions of fourth order PDEs for image processing
    • October
    • J. B. Greer and A. L. Bertozzi, "Travelling wave solutions of fourth order PDEs for image processing. SIAM J. Math. Anal., October 2003.
    • (2003) SIAM J. Math. Anal.
    • Greer, J.B.1    Bertozzi, A.L.2
  • 13
    • 0000708355 scopus 로고    scopus 로고
    • Positivity preserving numerical schemes for lubrication-type equations
    • L. Zhoraitskaya and Andrea L. Bertozzi, "Positivity preserving numerical schemes for lubrication-type equations", S.I.A.M. J. Num Anal., 37(2):523-555, 2000.
    • (2000) S.I.A.M. J. Num Anal. , vol.37 , Issue.2 , pp. 523-555
    • Zhoraitskaya, L.1    Bertozzi, A.L.2
  • 14
    • 0037401623 scopus 로고    scopus 로고
    • ADI schemes for higher-order nonlinear diffusion equations
    • T. P. Witelski and M. Bowen, "ADI schemes for higher-order nonlinear diffusion equations", Appl. Numer. Math., 45(2-3):331-351, 2003.
    • (2003) Appl. Numer. Math. , vol.45 , Issue.2-3 , pp. 331-351
    • Witelski, T.P.1    Bowen, M.2
  • 15
    • 0035892970 scopus 로고    scopus 로고
    • A discrete model for an ill-posed nonlinear parabolic PDE
    • T. P. Witelski, et al. "A discrete model for an ill-posed nonlinear parabolic PDE", Phys. D, 160(3-4): 189-221, 2001.
    • (2001) Phys. D , vol.160 , Issue.3-4 , pp. 189-221
    • Witelski, T.P.1
  • 16
    • 0021136434 scopus 로고
    • The structure of images
    • J.J. Koenderink, "The structure of images", Biol. Cybern., vol. 50, pp. 363-370, 1984.
    • (1984) Biol. Cybern. , vol.50 , pp. 363-370
    • Koenderink, J.J.1
  • 18
    • 0030169399 scopus 로고    scopus 로고
    • Differential morphology and image processing
    • June
    • P. Maragos, "Differential Morphology and Image Processing", IEEE Trans. Image Processing, vol. IP-5, pp. 922-937, June 1996.
    • (1996) IEEE Trans. Image Processing , vol.IP-5 , pp. 922-937
    • Maragos, P.1
  • 19
    • 15844399978 scopus 로고    scopus 로고
    • Partial differential equations in image analysis: Continuous modeling, discrete processing
    • Greece
    • P. Maragos, "Partial Differential Equations in Image Analysis: Continuous Modeling, Discrete Processing", Proceedings of EUSIPCO-98, Greece, 1998.
    • (1998) Proceedings of EUSIPCO-98
    • Maragos, P.1
  • 20
    • 0012393656 scopus 로고    scopus 로고
    • Advances in differential morphology: Image segmentation via eikonal PDE & curve evolution and reconstruction via constrained dilation flow
    • P. Maragos and M. A. Butt, "Advances in Differential Morphology: Image Segmentation via Eikonal PDE & Curve Evolution and Reconstruction via Constrained Dilation Flow", Math. Morphology and its Applic. to Image & Signal Proc., pp. 167-173, 1998.
    • (1998) Math. Morphology and Its Applic. to Image & Signal Proc. , pp. 167-173
    • Maragos, P.1    Butt, M.A.2
  • 21
    • 33745471444 scopus 로고    scopus 로고
    • Differential morphology
    • (Eds. S.K. Mitra and G. Sicuranza), Academic Press Series in Communications, Networking and Multimedia, ISBN: 1-12-500451-6, Academic Press, San Diego, CA
    • P. Maragos, "Differential Morphology", in Nonlinear Image Processing, (Eds. S.K. Mitra and G. Sicuranza), Academic Press Series in Communications, Networking and Multimedia, ISBN: 1-12-500451-6, Academic Press, San Diego, CA, 2001.
    • (2001) Nonlinear Image Processing
    • Maragos, P.1
  • 23
    • 0025210711 scopus 로고
    • A scattered data approximation scheme with applications to computational fluid dynamics-II Solutions to parabolic, hyperbolic and elliptic partial differential equations
    • E.J. Kansa and Y.C. Hon, "A scattered data approximation scheme with applications to computational fluid dynamics-II Solutions to parabolic, hyperbolic and elliptic partial differential equations", Comput. Math. Applic., vol. 19, pp. 147-161, 1990.
    • (1990) Comput. Math. Applic. , vol.19 , pp. 147-161
    • Kansa, E.J.1    Hon, Y.C.2
  • 24
    • 0031076132 scopus 로고    scopus 로고
    • The partition of unity method
    • I. Babuska and M. Melenk, "The partition of unity method", Int J. Numer. Methods, vol. 40, pp. 727-758, 1997.
    • (1997) Int J. Numer. Methods , vol.40 , pp. 727-758
    • Babuska, I.1    Melenk, M.2
  • 26
    • 0002635575 scopus 로고    scopus 로고
    • A fast adaptive wavelet collocation algorithm for multidimensional PDEs
    • O.V. Vasilyev and S. Paolucci, "A fast adaptive wavelet collocation algorithm for multidimensional PDEs", J. Comput. Physics, vol. 138, pp. 16-56, 1997.
    • (1997) J. Comput. Physics , vol.138 , pp. 16-56
    • Vasilyev, O.V.1    Paolucci, S.2
  • 28
    • 0001018295 scopus 로고
    • Multiquadratic equations of topography and other irregular surfaces
    • R.L. Hardy, "Multiquadratic equations of topography and other irregular surfaces", J. Geophys. Res., vol. 76, pp. 1905-1915, 1971.
    • (1971) J. Geophys. Res. , vol.76 , pp. 1905-1915
    • Hardy, R.L.1
  • 29
    • 38249001569 scopus 로고
    • Solution and control of PDE via global optimization methods
    • E.A. Galperin, and Q. Zheng, "Solution and control of PDE via global optimization methods", Comput. Math. Applic., vol. 25, No. 10/11, pp.103-118, 1993.
    • (1993) Comput. Math. Applic. , vol.25 , Issue.10-11 , pp. 103-118
    • Galperin, E.A.1    Zheng, Q.2
  • 30
    • 0348189600 scopus 로고
    • Application of global optimization to implicit solution of partial differential equations
    • E.A. Galperin, Z. Pan and Q. Zheng, "Application of global optimization to implicit solution of partial differential equations", Comput. Math. Applic., vol. 25, No. 10/11, pp. 119-124, 1993.
    • (1993) Comput. Math. Applic. , vol.25 , Issue.10-11 , pp. 119-124
    • Galperin, E.A.1    Pan, Z.2    Zheng, Q.3
  • 31
    • 0002114455 scopus 로고
    • Numerical experiments with one-dimensional adaptive cubic algorithm
    • A. Ferrari and E.A. Galperin,"Numerical experiments with one-dimensional adaptive cubic algorithm", Comput. Math. Applic., vol. 25, No. 10/11, pp. 47-56, 1993.
    • (1993) Comput. Math. Applic. , vol.25 , Issue.10-11 , pp. 47-56
    • Ferrari, A.1    Galperin, E.A.2
  • 33
    • 0022669613 scopus 로고
    • Wave digital filters: Theory and practice
    • A. Fettweis, "Wave digital filters: theory and practice", Proc. IEEE, vol. 74, pp. 270-327, 1986.
    • (1986) Proc. IEEE , vol.74 , pp. 270-327
    • Fettweis, A.1
  • 34
    • 0026909211 scopus 로고
    • Multidimensional wave digital filters for discrete-time modelling of Maxwell's equations
    • A. Fettweis, "Multidimensional wave digital filters for discrete-time modelling of Maxwell's equations", Int J. Numerical Modelling, vol. 5, pp. 1-29, 1992.
    • (1992) Int J. Numerical Modelling , vol.5 , pp. 1-29
    • Fettweis, A.1
  • 35
    • 0026898873 scopus 로고
    • Discrete modelling of lossless fluid dynamic systems
    • A. Fettweis, "Discrete modelling of lossless fluid dynamic systems", AEU, vol. 46, No. 4, pp. 209-218, 1992.
    • (1992) AEU , vol.46 , Issue.4 , pp. 209-218
    • Fettweis, A.1
  • 36
    • 4344678271 scopus 로고
    • Discrete passive modelling of physical systems described by partial differential equations
    • C.R. Rao, editor, chapter 7
    • A. Fettweis, "Discrete passive modelling of physical systems described by partial differential equations", Multivariate Analysis: Future Directions, C.R. Rao, editor, chapter 7, pp. 115-B 130, 1993.
    • (1993) Multivariate Analysis: Future Directions
    • Fettweis, A.1
  • 37
    • 0026155137 scopus 로고
    • Transformation approach to numerically integrating PDEs by means of WDF principles
    • A. Fettweis and G. Niteche, "Transformation approach to numerically integrating PDEs by means of WDF principles", Multidimensional Systems and Signal Processingl, vol. 2, pp. 127-159, 1991.
    • (1991) Multidimensional Systems and Signal Processingl , vol.2 , pp. 127-159
    • Fettweis, A.1    Niteche, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.