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Volumn 193, Issue 1, 2004, Pages 40-66

Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINED OPTIMIZATION; EQUATIONS OF MOTION; GEOMETRY; LAGRANGE MULTIPLIERS; NUMERICAL METHODS; ROTATIONAL FLOW; SET THEORY;

EID: 0344550387     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.08.003     Document Type: Article
Times cited : (172)

References (46)
  • 1
    • 0036609140 scopus 로고    scopus 로고
    • Refinement and coarsening indicators for adaptive parametrization: Application to the estimation of hydraulic transmissivities
    • H. Ben Ameur, Guy Chavent, Jerome Jaffré, Refinement and coarsening indicators for adaptive parametrization: application to the estimation of hydraulic transmissivities, Inverse Problems 18 (2002) 775-794.
    • (2002) Inverse Problems , vol.18 , pp. 775-794
    • Ben Ameur, H.1    Chavent, G.2    Jaffré, J.3
  • 2
    • 0034497171 scopus 로고    scopus 로고
    • Basis norm rescaling for nonlinear parameter estimation
    • (electronic)
    • K. Brusdal, T. Mannseth, Basis norm rescaling for nonlinear parameter estimation, SIAM J. Sci. Comput. 21 (6) (2000) 2114-2125 (electronic).
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.6 , pp. 2114-2125
    • Brusdal, K.1    Mannseth, T.2
  • 3
    • 0035473388 scopus 로고    scopus 로고
    • A level set method for inverse problems
    • M. Burger, A level set method for inverse problems, Inverse problems 17 (2001) 1327-1356.
    • (2001) Inverse Problems , vol.17 , pp. 1327-1356
    • Burger, M.1
  • 4
    • 85189849723 scopus 로고    scopus 로고
    • A framework for the construction of level set methods for shape optimization and reconstruction
    • preprint
    • M. Burger, A framework for the construction of level set methods for shape optimization and reconstruction, preprint, 2002.
    • (2002)
    • Burger, M.1
  • 5
    • 0345655616 scopus 로고    scopus 로고
    • Augmented Lagrangian and total variation methods for recovering discontinuous coefficients from elliptic equations
    • M. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Periaux, M.F. Wheeler (Eds.), Wiley, New York
    • T.F. Chan, X-C. Tai, Augmented Lagrangian and total variation methods for recovering discontinuous coefficients from elliptic equations, in: M. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Periaux, M.F. Wheeler (Eds.), Computational Science for the 21st Century, Wiley, New York, 1997, pp. 597-607.
    • (1997) Computational Science for the 21st Century , pp. 597-607
    • Chan, T.F.1    Tai, X.-C.2
  • 6
    • 85189847960 scopus 로고    scopus 로고
    • Identification of discontinuous coefficients in elliptic problems using total variation regularization
    • (to appear). Available at
    • T.F. Chan, X.-C. Tai. Identification of discontinuous coefficients in elliptic problems using total variation regularization, SIAM J. Sci. Comput. (to appear). Available at .
    • SIAM J. Sci. Comput.
    • Chan, T.F.1    Tai, X.-C.2
  • 7
    • 0012956922 scopus 로고    scopus 로고
    • Image segmentation using level sets and the piecewise constant Mumford-Shah model
    • Technical Report, CAM Report 00-14, UCLA, Math. Dept., April 2000, Revised December
    • T.F. Chan, L.A.Vese, Image segmentation using level sets and the piecewise constant Mumford-Shah model, Technical Report, CAM Report 00-14, UCLA, Math. Dept., April 2000, Revised December 2000.
    • (2000)
    • Chan, T.F.1    Vese, L.A.2
  • 8
    • 0033077273 scopus 로고    scopus 로고
    • Estimation of relative permeabilities in three-phase flow in porous media. conference on inverse problems, control and shape optimization (carthage, 1998)
    • G. Chavent, J. Jaffré, S. Jan-Jégou, Estimation of relative permeabilities in three-phase flow in porous media. conference on inverse problems, control and shape optimization (carthage, 1998), Inverse Problems 15 (1999) 33-39.
    • (1999) Inverse Problems , vol.15 , pp. 33-39
    • Chavent, G.1    Jaffré, J.2    Jan-Jégou, S.3
  • 9
    • 84996143333 scopus 로고    scopus 로고
    • Regularization of linear least squares problems by total bounded variation
    • (electronic)
    • G. Chavent, K. Kunisch, Regularization of linear least squares problems by total bounded variation, ESAIM Control Optim. Calc. Var. 2 (1997) 359-376 (electronic).
    • (1997) ESAIM Control Optim. Calc. Var. , vol.2 , pp. 359-376
    • Chavent, G.1    Kunisch, K.2
  • 10
    • 0032633972 scopus 로고    scopus 로고
    • An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems
    • (electronic)
    • Z. Chen, J. Zou, An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems, SIAM J. Control Optim. 37 (3) (1999) 892-910 (electronic).
    • (1999) SIAM J. Control Optim. , vol.37 , Issue.3 , pp. 892-910
    • Chen, Z.1    Zou, J.2
  • 11
    • 0002621641 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • (electronic)
    • M. Cheney, D. Isaacson, J.C. Newell, Electrical impedance tomography, SIAM Rev. 41 (1) (1999) 85-101 (electronic).
    • (1999) SIAM Rev. , vol.41 , Issue.1 , pp. 85-101
    • Cheney, M.1    Isaacson, D.2    Newell, J.C.3
  • 13
    • 0001341095 scopus 로고
    • An image enhancement technique for electrical impedance tomography
    • D.C. Dobson, F. Santosa, An image enhancement technique for electrical impedance tomography, Inverse Problems 10 (1994) 317-334.
    • (1994) Inverse Problems , vol.10 , pp. 317-334
    • Dobson, D.C.1    Santosa, F.2
  • 14
    • 0034292566 scopus 로고    scopus 로고
    • A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets
    • Electromagnetic imaging and inversion of the Earth's subsurface
    • O. Dorn, E.L. Miller, C.M. Rappaport, A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets, Inverse Problems 16 (5) (2000) 1119-1156, Electromagnetic imaging and inversion of the Earth's subsurface.
    • (2000) Inverse Problems , vol.16 , Issue.5 , pp. 1119-1156
    • Dorn, O.1    Miller, E.L.2    Rappaport, C.M.3
  • 18
    • 0026138893 scopus 로고
    • A class of parameter estimation techniques for fluid flow in porous media
    • Parameter identification in ground water flow, transport, and related processes
    • R.E. Ewing, T. Lin, A class of parameter estimation techniques for fluid flow in porous media, Adv. Water Res. 14 (2) (1991) 89-97, Parameter identification in ground water flow, transport, and related processes, Part I.
    • (1991) Adv. Water Res. , vol.14 , Issue.2 PART 1 , pp. 89-97
    • Ewing, R.E.1    Lin, T.2
  • 19
    • 0005316834 scopus 로고    scopus 로고
    • A mixed least-squares method for an inverse problem of a nonlinear beam equation
    • Conference on Inverse Problems, Control and Shape Optimization (Carthage, 1998)
    • R.E. Ewing, T. Lin, Y. Lin, A mixed least-squares method for an inverse problem of a nonlinear beam equation, Inverse Problems 15 (1) (1999) 19-32, Conference on Inverse Problems, Control and Shape Optimization (Carthage, 1998).
    • (1999) Inverse Problems , vol.15 , Issue.1 , pp. 19-32
    • Ewing, R.E.1    Lin, T.2    Lin, Y.3
  • 20
    • 84966231637 scopus 로고
    • Falk, Error estimates for the numerical identification of a variable coefficient
    • Richard S. Falk, Error estimates for the numerical identification of a variable coefficient, Math. Comp. 40 (162) (1983) 537-546.
    • (1983) Math. Comp. , vol.40 , Issue.162 , pp. 537-546
    • Richard, S.1
  • 22
    • 0002215984 scopus 로고    scopus 로고
    • The determination of a discontinuity in a conductivity from a single boundary measurement
    • F. Hettlich, W. Rundell, The determination of a discontinuity in a conductivity from a single boundary measurement, Inverse Problems 14 (1) (1998) 67-82.
    • (1998) Inverse Problems , vol.14 , Issue.1 , pp. 67-82
    • Hettlich, F.1    Rundell, W.2
  • 23
    • 0344361062 scopus 로고    scopus 로고
    • A second order shape optimization approach for image segmentation
    • (to appear)
    • M. Hintermuller, W. Ring, A second order shape optimization approach for image segmentation, SIAM J. Appl. Math. (to appear).
    • SIAM J. Appl. Math.
    • Hintermuller, M.1    Ring, W.2
  • 24
    • 0025208790 scopus 로고
    • The augmented Lagrangian method for parameter estimation in elliptic systems
    • K. Ito, K. Kunisch, The augmented Lagrangian method for parameter estimation in elliptic systems, SIAM J. Control Optim. 28 (1990) 113-136.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 113-136
    • Ito, K.1    Kunisch, K.2
  • 25
    • 0035473295 scopus 로고    scopus 로고
    • Level-set function approach to an inverse interface problem
    • K. Ito, K. Kunisch, Z. Li, Level-set function approach to an inverse interface problem, Inverse Problems 17 (5) (2001) 1225-1242.
    • (2001) Inverse Problems , vol.17 , Issue.5 , pp. 1225-1242
    • Ito, K.1    Kunisch, K.2    Li, Z.3
  • 26
    • 0022027469 scopus 로고
    • Identification of parameters in distributed parameter systems by regularization
    • C. Kravaris, J.H. Seinfeld, Identification of parameters in distributed parameter systems by regularization, SIAM J. Control Optim. 23 (2) (1985) 217-241.
    • (1985) SIAM J. Control Optim. , vol.23 , Issue.2 , pp. 217-241
    • Kravaris, C.1    Seinfeld, J.H.2
  • 27
    • 0002501641 scopus 로고    scopus 로고
    • Sequential and parallel splitting methods for bilinear control problems in Hilbertspaces
    • K. Kunisch, X.-C. Tai, Sequential and parallel splitting methods for bilinear control problems in Hilbertspaces, SIAM J. Numer. Anal. 34 (1997) 91-118.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 91-118
    • Kunisch, K.1    Tai, X.-C.2
  • 28
    • 0041672593 scopus 로고
    • Parameter estimation for distributed systems arising in fluid flow problems via time series methods
    • Birkhäuser, Basel
    • T. Lin, R. Ewing, Parameter estimation for distributed systems arising in fluid flow problems via time series methods, in: Inverse Problems (Oberwolfach, 1986), Birkhäuser, Basel, 1986, pp. 117-126.
    • (1986) Inverse Problems (Oberwolfach, 1986) , pp. 117-126
    • Lin, T.1    Ewing, R.2
  • 29
    • 0000386587 scopus 로고    scopus 로고
    • Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set
    • A. Litman, D. Lesselier, F. Santosa, Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set, Inverse Problems 14 (3) (1998) 685-706.
    • (1998) Inverse Problems , vol.14 , Issue.3 , pp. 685-706
    • Litman, A.1    Lesselier, D.2    Santosa, F.3
  • 31
    • 0141534420 scopus 로고    scopus 로고
    • Existence for shape optimization problems in arbitrary dimension
    • W. Liu, P. Neittaanmäki, D. Tiba, Existence for shape optimization problems in arbitrary dimension, SIAM J. Control Optim. 41 (2003) 1440-1454.
    • (2003) SIAM J. Control Optim. , vol.41 , pp. 1440-1454
    • Liu, W.1    Neittaanmäki, P.2    Tiba, D.3
  • 32
    • 0042392221 scopus 로고
    • Unique recovery of a coefficient in an elliptic equation from input sources
    • B.D. Lowe, W. Rundell, Unique recovery of a coefficient in an elliptic equation from input sources, Inverse Problems 11 (1) (1995) 211-215.
    • (1995) Inverse Problems , vol.11 , Issue.1 , pp. 211-215
    • Lowe, B.D.1    Rundell, W.2
  • 33
    • 0030164824 scopus 로고    scopus 로고
    • The determination of a coefficient in an elliptic equation from average flux data
    • B.D. Lowe, W. Rundell, The determination of a coefficient in an elliptic equation from average flux data, J. Comput. Appl. Math. 70 (1) (1996) 173-187.
    • (1996) J. Comput. Appl. Math. , vol.70 , Issue.1 , pp. 173-187
    • Lowe, B.D.1    Rundell, W.2
  • 34
    • 0003761554 scopus 로고    scopus 로고
    • Level set methods
    • Technical Report, CAM Report 00-08, UCLA, Math. Dept., February
    • S. Osher, R.R. Fedkiw, Level set methods, Technical Report, CAM Report 00-08, UCLA, Math. Dept., February 2000.
    • (2000)
    • Osher, S.1    Fedkiw, R.R.2
  • 35
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on Hamilton Jacobi formulations
    • S. Osher, J.A. Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton Jacobi formulations, J. Comput. Phys. 79 (1988) 12-49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 36
    • 0000653948 scopus 로고    scopus 로고
    • Level set methods for optimization problems involving geometry and constraints. I. Frequencies of a two-density inhomogeneous drum
    • S.J. Osher, F. Santosa, Level set methods for optimization problems involving geometry and constraints. I. Frequencies of a two-density inhomogeneous drum, J. Comput. Phys. 171 (1) (2001) 272-288.
    • (2001) J. Comput. Phys. , vol.171 , Issue.1 , pp. 272-288
    • Osher, S.J.1    Santosa, F.2
  • 39
    • 84996143735 scopus 로고
    • A level-set approach for inverse problems involving obstacles
    • (electronic)
    • F. Santosa, A level-set approach for inverse problems involving obstacles, ESAIM Control Optim. Calc. Var. 1 (1995/96) 17-33 (electronic).
    • (1995) ESAIM Control Optim. Calc. Var. , vol.1 , pp. 17-33
    • Santosa, F.1
  • 40
    • 0002893662 scopus 로고    scopus 로고
    • Overlapping domain decomposition and multigrid methods for inverse problems
    • Domain Decomposition Methods, 10 (Boulder, CO, 1997), American Mathematical Society, Providence, RI, See also URL
    • X.-C. Tai, J. Froyen, M.S. Espedal, T.F. Chan. Overlapping domain decomposition and multigrid methods for inverse problems, Domain Decomposition Methods, 10 (Boulder, CO, 1997), Contemp. Math., vol. 218, American Mathematical Society, Providence, RI, 1998, pp. 523-529. See also URL: http://www.mi.uib.no/~tai/.
    • (1998) Contemp. Math. , vol.218 , pp. 523-529
    • Tai, X.-C.1    Froyen, J.2    Espedal, M.S.3    Chan, T.F.4
  • 41
    • 0345223780 scopus 로고
    • Identification of a nonlinear parameter in a parabolic equation from a linear equation
    • X-C. Tai, T. Karkainen, Identification of a nonlinear parameter in a parabolic equation from a linear equation, Comput. Appl. Math. 14 (1995) 157-184.
    • (1995) Comput. Appl. Math. , vol.14 , pp. 157-184
    • Tai, X.-C.1    Karkainen, T.2
  • 42
    • 0345223789 scopus 로고
    • Error estimates for numerical identification of distributed parameters
    • X.-C. Tai, P. Neittaanmaki, Error estimates for numerical identification of distributed parameters, J. Comp. Math. Suppl. (1992) 66-78.
    • (1992) J. Comp. Math. Suppl. , pp. 66-78
    • Tai, X.-C.1    Neittaanmaki, P.2
  • 43
    • 0344361059 scopus 로고    scopus 로고
    • Pointwise error estimates for distributed parameter identification
    • D. Bainov (Ed.), International Science Publishers, The Netherlands
    • X.-C. Tai, P. Neittaanmaki, Pointwise error estimates for distributed parameter identification, in: D. Bainov (Ed.), Proceedings of the Seventh International Colloqium on Differential Equations, International Science Publishers, The Netherlands, 1997, pp. 455-468.
    • (1997) Proceedings of the Seventh International Colloqium on Differential Equations , pp. 455-468
    • Tai, X.-C.1    Neittaanmaki, P.2
  • 44
    • 0036891794 scopus 로고    scopus 로고
    • A new multiphase level set framework for image segmentation via the Mumford and Shah model
    • L.A. Vese, T.F. Chan, A new multiphase level set framework for image segmentation via the Mumford and Shah model, Int. J. Comput. Vision 50 (2002) 271-293.
    • (2002) Int. J. Comput. Vision , vol.50 , pp. 271-293
    • Vese, L.A.1    Chan, T.F.2
  • 45
    • 0344792927 scopus 로고    scopus 로고
    • The level set method links active contours, Mumford-Shah segmentation, and total variation restoration
    • UCLA, Math. Dept., CAM-Report 02-05
    • L.A. Vese, S.Osher, The level set method links active contours, Mumford-Shah segmentation, and total variation restoration, UCLA, Math. Dept., CAM-Report 02-05 2002.
    • (2002)
    • Vese, L.A.1    Osher, S.2
  • 46
    • 0004095766 scopus 로고
    • Springer, New York, Sobolev spaces and functions of bounded variation Graduate Texts in Mathematics
    • W.P. Ziemer, Weakly Differentiable Functions, Graduate Texts in Mathematics, vol. 120, Springer, New York, 1989, Sobolev spaces and functions of bounded variation.
    • (1989) Weakly Differentiable Functions , vol.120
    • Ziemer, W.P.1


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