메뉴 건너뛰기




Volumn 25, Issue 3, 2009, Pages

On multiple level-set regularization methods for inverse problems

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE AND STABILITY; EXISTENCE RESULTS; FIRST-ORDER OPTIMALITY CONDITION; MULTIPLE LEVELS; MULTIPLE OBJECTS; NUMERICAL EXPERIMENTS; PIECEWISE CONSTANT; POTENTIAL PROBLEMS; REGULARIZATION METHODS; TIKHONOV FUNCTIONAL; TIKHONOV METHOD;

EID: 69049120372     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/3/035004     Document Type: Article
Times cited : (37)

References (52)
  • 1
    • 36149030663 scopus 로고
    • Analysis of bounded variation penalty methods for ill-posed problems
    • Acar R and Vogel C R 1994 Analysis of bounded variation penalty methods for ill-posed problems Inverse Problems 10 1217-29
    • (1994) Inverse Problems , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.R.2
  • 3
    • 33746286478 scopus 로고    scopus 로고
    • On effective methods for implicit piecewise smooth surface recovery
    • Ascher U M, Haber E and Huang H 2006 On effective methods for implicit piecewise smooth surface recovery SIAM J. Sci. Comput. 28 339-58
    • (2006) SIAM J. Sci. Comput. , vol.28 , pp. 339-358
    • Ascher, U.M.1    Haber, E.2    Huang, H.3
  • 4
    • 23844524180 scopus 로고    scopus 로고
    • A survey on level set methods for inverse problems and optimal design
    • Burger M and Osher S J 2005 A survey on level set methods for inverse problems and optimal design Eur. J. Appl. Math. 16 263-301
    • (2005) Eur. J. Appl. Math. , vol.16 , pp. 263-301
    • Burger, M.1    Osher, S.J.2
  • 5
    • 33750153530 scopus 로고    scopus 로고
    • Algorithms for finding global minimizers of image segmentation and denoising models
    • Chan T F, Esedoglu S and Nikolova M 2006 Algorithms for finding global minimizers of image segmentation and denoising models SIAM J. Appl. Math. 66 1632-48
    • (2006) SIAM J. Appl. Math. , vol.66 , pp. 1632-1648
    • Chan, T.F.1    Esedoglu, S.2    Nikolova, M.3
  • 7
    • 2942612639 scopus 로고    scopus 로고
    • Identification of discontinuous coefficients in elliptic problems using total variation regularization
    • Chan T F and Tai X C 2003 Identification of discontinuous coefficients in elliptic problems using total variation regularization SIAM J. Sci. Comput. 25 881-904
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 881-904
    • Chan, T.F.1    Tai, X.C.2
  • 8
    • 0344550387 scopus 로고    scopus 로고
    • Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients
    • Chan T F and Tai X C 2004 Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients J. Comput. Phys. 193 40-66
    • (2004) J. Comput. Phys. , vol.193 , pp. 40-66
    • Chan, T.F.1    Tai, X.C.2
  • 9
    • 0032633972 scopus 로고    scopus 로고
    • An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems
    • Chen Z and Zou J 1999 An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems SIAM J. Control Optim. 37 892-910
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 892-910
    • Chen, Z.1    Zou, J.2
  • 10
    • 16844364446 scopus 로고    scopus 로고
    • Electrical impedance tomography using level set representation and total variational regularization
    • Chung E T, Chan T F and Tai X C 2005 Electrical impedance tomography using level set representation and total variational regularization J. Comput. Phys. 205 357-72
    • (2005) J. Comput. Phys. , vol.205 , pp. 357-372
    • Chung, E.T.1    Chan, T.F.2    Tai, X.C.3
  • 11
    • 33746284514 scopus 로고    scopus 로고
    • Level set methods for inverse scattering
    • Dorn O and Lesselier D 2006 Level set methods for inverse scattering Inverse Problems 22 R67-R131
    • (2006) Inverse Problems , vol.22
    • Dorn, O.1    Lesselier, D.2
  • 12
    • 0034292566 scopus 로고    scopus 로고
    • A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets
    • Dorn O, Miller E and Rappaport C 2000 A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets Inverse Problems 16 1119-56
    • (2000) Inverse Problems , vol.16 , pp. 1119-1156
    • Dorn, O.1    Miller, E.2    Rappaport, C.3
  • 13
    • 33947416683 scopus 로고    scopus 로고
    • Nonlinear integral equations for the inverse electrical impedance problem
    • Eckel H and Kress R 2007 Nonlinear integral equations for the inverse electrical impedance problem Inverse Problems 23 475-91
    • (2007) Inverse Problems , vol.23 , pp. 475-491
    • Eckel, H.1    Kress, R.2
  • 15
    • 36149030945 scopus 로고
    • Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems
    • Engl H W, Kunisch K and Neubauer A 1989 Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems Inverse Problems 5 523-40
    • (1989) Inverse Problems , vol.5 , pp. 523-540
    • Engl, H.W.1    Kunisch, K.2    Neubauer, A.3
  • 16
    • 0003346795 scopus 로고
    • Measure theory and fine properties of functions
    • (Boca Raton, FL: CRC Press)
    • Evans L C and Gariepy R F 1992 Measure theory and fine properties of functions Studies in Advanced Mathematics (Boca Raton, FL: CRC Press)
    • (1992) Studies in Advanced Mathematics
    • Evans, L.C.1    Gariepy, R.F.2
  • 17
    • 34247591357 scopus 로고    scopus 로고
    • Multi-phase permittivity reconstruction in electrical capacitance tomography by level-set methods
    • Fang W F 2007 Multi-phase permittivity reconstruction in electrical capacitance tomography by level-set methods Inverse Problems Sci. Eng. 15 213-47
    • (2007) Inverse Problems Sci. Eng. , vol.15 , pp. 213-247
    • Fang, W.F.1
  • 18
    • 27744433287 scopus 로고    scopus 로고
    • Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators
    • Frühauf F, Scherzer O and Leito A 2005 Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators SIAM J. Numer. Anal. 43 767-86
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 767-786
    • Frühauf, F.1    Scherzer, O.2    Leito, A.3
  • 19
    • 42449106892 scopus 로고    scopus 로고
    • Equation error approach for elliptic inverse problems with an application to the identification of lame parameters
    • Gockenbach M S, Jadamba B and Khan A A 2008 Equation error approach for elliptic inverse problems with an application to the identification of lame parameters Inverse Problems Sci. Eng. 16 349-67
    • (2008) Inverse Problems Sci. Eng. , vol.16 , pp. 349-367
    • Gockenbach, M.S.1    Jadamba, B.2    Khan, A.A.3
  • 20
    • 34447283331 scopus 로고    scopus 로고
    • An abstract framework for elliptic inverse problems: Part 1. An output least-squares approach
    • Gockenbach M S and Khan A A 2007 An abstract framework for elliptic inverse problems: part 1. An output least-squares approach Math. Mech. Solids 12 259-76
    • (2007) Math. Mech. Solids , vol.12 , pp. 259-276
    • Gockenbach, M.S.1    Khan, A.A.2
  • 21
    • 0025482307 scopus 로고
    • Identification of discontinuous parameters in flow equations
    • Gutman S 1990 Identification of discontinuous parameters in flow equations SIAM J. Control Optim. 28 1049-60
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 1049-1060
    • Gutman, S.1
  • 22
    • 0000298487 scopus 로고    scopus 로고
    • Iterative methods for the reconstruction of an inverse potential problem
    • Hettlich F and Rundell W 1996 Iterative methods for the reconstruction of an inverse potential problem Inverse Problems 12 251-66 (Pubitemid 126658373)
    • (1996) Inverse Problems , vol.12 , Issue.3 , pp. 251-266
    • Hettlich, F.1    Rundell, W.2
  • 23
    • 0003323928 scopus 로고
    • Inverse source problems
    • Providence, RI: American Mathematical Society
    • Isakov V 1990 Inverse source problems Mathematical Surveys and Monographs vol 34 (Providence, RI: American Mathematical Society)
    • (1990) Mathematical Surveys and Monographs , vol.34
    • Isakov, V.1
  • 24
    • 0035473295 scopus 로고    scopus 로고
    • Level-set function approach to an inverse interface problem
    • Ito K, Kunisch K and Li Z 2001 Level-set function approach to an inverse interface problem Inverse Problems 17 1225-42
    • (2001) Inverse Problems , vol.17 , pp. 1225-1242
    • Ito, K.1    Kunisch, K.2    Li, Z.3
  • 25
    • 33748996511 scopus 로고    scopus 로고
    • Phase boundary estimation in electrical resistance tomography with weighted multi-layered neural networks and front point approach
    • Kim J H et al 2006 Phase boundary estimation in electrical resistance tomography with weighted multi-layered neural networks and front point approach Meas. Sci. Technol. 17 2731-9
    • (2006) Meas. Sci. Technol. , vol.17 , pp. 2731-2739
    • Kim, J.H.1
  • 26
    • 34247131866 scopus 로고    scopus 로고
    • Moving interfacial boundary estimation in stratified flow of two immiscible liquids using electrical resistance tomography
    • Kim S et al 2007 Moving interfacial boundary estimation in stratified flow of two immiscible liquids using electrical resistance tomography Meas. Sci. Technol. 18 1257-69
    • (2007) Meas. Sci. Technol. , vol.18 , pp. 1257-1269
    • Kim, S.1
  • 27
    • 42649137589 scopus 로고    scopus 로고
    • Piecewise constant level set method for multiphase motion
    • Li H and Tai X C 2007 Piecewise constant level set method for multiphase motion Int. J. Numer. Anal. Modelling 4 291-305
    • (2007) Int. J. Numer. Anal. Modelling , vol.4 , pp. 291-305
    • Li, H.1    Tai, X.C.2
  • 28
    • 33746291689 scopus 로고    scopus 로고
    • A variant of the level set method and applications to image segmentation
    • Lie J, Lysaker M and Tai X C 2006 A variant of the level set method and applications to image segmentation Math. Comput. 75 1155-74
    • (2006) Math. Comput. , vol.75 , pp. 1155-1174
    • Lie, J.1    Lysaker, M.2    Tai, X.C.3
  • 29
    • 28544445605 scopus 로고    scopus 로고
    • Reconstruction by level sets of n-ary scattering obstacles
    • Litman A 2005 Reconstruction by level sets of n-ary scattering obstacles Inverse Problems 21 S131-52
    • (2005) Inverse Problems , vol.21
    • Litman, A.1
  • 30
    • 37349038483 scopus 로고    scopus 로고
    • Level set method for optimal shape design of mram core micromagnetic approach
    • Melicher V, Cirarak I and Van Keer R 2008 Level set method for optimal shape design of mram core micromagnetic approach Phisica B:Condens. Matter. 403 308-11
    • (2008) Phisica B:Condens. Matter. , vol.403 , pp. 308-311
    • Melicher, V.1    Cirarak, I.2    Van Keer, R.3
  • 31
    • 36749089673 scopus 로고    scopus 로고
    • A projection-based level-set approach to enhance conductivity anomaly reconstruction in electrical resistance tomography
    • Miled M K B H and Miller E L 2007 A projection-based level-set approach to enhance conductivity anomaly reconstruction in electrical resistance tomography Inverse Problems 23 2375-400
    • (2007) Inverse Problems , vol.23 , pp. 2375-2400
    • Miled, M.K.B.H.1    Miller, E.L.2
  • 32
    • 53349171499 scopus 로고    scopus 로고
    • A nonlinear iterative reconstruction and analysis approach to shape-based approximate electromagnetic tomography
    • Naik N, Eriksson J, de Groen P and Sahli H 2008 A nonlinear iterative reconstruction and analysis approach to shape-based approximate electromagnetic tomography IEEE Trans. Geosci. Remote Sens. 46 1558-74
    • (2008) IEEE Trans. Geosci. Remote Sens. , vol.46 , pp. 1558-1574
    • Naik, N.1    Eriksson, J.2    De Groen, P.3    Sahli, H.4
  • 33
    • 0032165154 scopus 로고    scopus 로고
    • Least squares and bounded variation regularization with nondifferentiable functionals
    • Nashed M Z and Scherzer O 1998 Least squares and bounded variation regularization with nondifferentiable functionals Numer. Funct. Anal. Optim. 19 873-901
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , pp. 873-901
    • Nashed, M.Z.1    Scherzer, O.2
  • 34
    • 38049120696 scopus 로고    scopus 로고
    • A binary level set model for elliptic inverse problems with discontinuous coefficients
    • Nielsen L K, Tai X C, Aanonsen S I and Espedal M 2007 A binary level set model for elliptic inverse problems with discontinuous coefficients Int. J. Numer. Anal. Modelling 4 75-100
    • (2007) Int. J. Numer. Anal. Modelling , vol.4 , pp. 75-100
    • Nielsen, L.K.1    Tai, X.C.2    Aanonsen, S.I.3    Espedal, M.4
  • 35
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • Osher S and Sethian J A 1988 Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations J. Comput. Phys. 79 12-49
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 36
    • 33846386077 scopus 로고    scopus 로고
    • A mumford-shah level-set approach for the inversion and segmentation of x-ray tomography data
    • Ramlau R and Ring W 2007 A mumford-shah level-set approach for the inversion and segmentation of x-ray tomography data J. Comput. Phys. 221 539-57
    • (2007) J. Comput. Phys. , vol.221 , pp. 539-557
    • Ramlau, R.1    Ring, W.2
  • 37
    • 0029323644 scopus 로고
    • Identification of a core from boundary data
    • Ring W 1995 Identification of a core from boundary data SIAM J. Appl. Math. 55 677-706
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 677-706
    • Ring, W.1
  • 38
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Rudin L, Osher S and Fatemi E 1992 Nonlinear total variation based noise removal algorithms Physica D 60 259-68
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 39
    • 84996143735 scopus 로고
    • A level-set approach for inverse problems involving obstacles
    • Santosa F 1995/96 A level-set approach for inverse problems involving obstacles ESAIM Controle Optim. Calc. Var. 1 17-33
    • (1995) ESAIM Controle Optim. Calc. Var. , vol.1 , pp. 17-33
    • Santosa, F.1
  • 40
    • 0000027929 scopus 로고
    • Well-posedness and convergence of some regularisation methods for nonlinear ill-posed problems
    • Seidman T I and Vogel C R 1989 Well-posedness and convergence of some regularisation methods for nonlinear ill-posed problems Inverse Problems 5 227-38
    • (1989) Inverse Problems , vol.5 , pp. 227-238
    • Seidman, T.I.1    Vogel, C.R.2
  • 41
    • 33746298774 scopus 로고    scopus 로고
    • A narrow-band level set method applied to eit in brain for cryosurgery monitoring
    • Soleimani M, Dorn O and Lionheart W R B 2006 A narrow-band level set method applied to eit in brain for cryosurgery monitoring IEEE Trans. Biomed. Eng. 53 2257-64
    • (2006) IEEE Trans. Biomed. Eng. , vol.53 , pp. 2257-2264
    • Soleimani, M.1    Dorn, O.2    Lionheart, W.R.B.3
  • 42
    • 25644447578 scopus 로고    scopus 로고
    • Nonlinear image reconstruction for electrical capacitance tomography using experimental data
    • Soleimani M and Lionheart W R B 2005 Nonlinear image reconstruction for electrical capacitance tomography using experimental data Meas. Sci. Technol. 16 1987-96
    • (2005) Meas. Sci. Technol. , vol.16 , pp. 1987-1996
    • Soleimani, M.1    Lionheart, W.R.B.2
  • 43
    • 30544449867 scopus 로고    scopus 로고
    • Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data
    • Soleimani M, Lionheart W R B and Dorn O 2006 Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data Inverse Problems Sci. Eng. 14 193-210
    • (2006) Inverse Problems Sci. Eng. , vol.14 , pp. 193-210
    • Soleimani, M.1    Lionheart, W.R.B.2    Dorn, O.3
  • 44
    • 33646421136 scopus 로고    scopus 로고
    • A three-dimensional inverse finite-element method applied to experimental eddy-current imaging data
    • Soleimani M et al 2006 A three-dimensional inverse finite-element method applied to experimental eddy-current imaging data IEEE Trans. Magn. 42 1560-7
    • (2006) IEEE Trans. Magn. , vol.42 , pp. 1560-1567
    • Soleimani, M.1
  • 45
    • 24644508476 scopus 로고    scopus 로고
    • A survey on multiple level set methods with applications for identifying piecewise constant functions
    • Tai X C and Chan T F 2004 A survey on multiple level set methods with applications for identifying piecewise constant functions Int. J. Numer. Anal. Modelling 1 25-47
    • (2004) Int. J. Numer. Anal. Modelling , vol.1 , pp. 25-47
    • Tai, X.C.1    Chan, T.F.2
  • 46
    • 34147142049 scopus 로고    scopus 로고
    • A piecewise constant level set method for elliptic inverse problems
    • Tai X C and Li H 2007 A piecewise constant level set method for elliptic inverse problems Appl. Numer. Math. 57 686-96
    • (2007) Appl. Numer. Math. , vol.57 , pp. 686-696
    • Tai, X.C.1    Li, H.2
  • 47
    • 70350258691 scopus 로고    scopus 로고
    • A piecewise-constant binary model for electrical impedance tomography
    • Tanushev N M and Vese L A 2007 A piecewise-constant binary model for electrical impedance tomography Inverse Problems Imaging 1 423-35
    • (2007) Inverse Problems Imaging , vol.1 , pp. 423-435
    • Tanushev, N.M.1    Vese, L.A.2
  • 48
  • 49
    • 33646947060 scopus 로고    scopus 로고
    • On level set regularization for highly ill-posed distributed parameter estimation problems
    • van den Doel K and Ascher U M 2006 On level set regularization for highly ill-posed distributed parameter estimation problems J. Comput. Phys. 216 707-23
    • (2006) J. Comput. Phys. , vol.216 , pp. 707-723
    • Van Den Doel, K.1    Ascher, U.M.2
  • 50
    • 34249722624 scopus 로고    scopus 로고
    • Dynamic level set regularization for large distributed parameter estimation problems
    • van den Doel K and Ascher U M 2007 Dynamic level set regularization for large distributed parameter estimation problems Inverse Problems 23 1271-88
    • (2007) Inverse Problems , vol.23 , pp. 1271-1288
    • Van Den Doel, K.1    Ascher, U.M.2
  • 51
    • 0036891794 scopus 로고    scopus 로고
    • A multiphase level set framework for image segmentation using the mumford and shah model
    • Vese L A and Chan T F 2002 A multiphase level set framework for image segmentation using the mumford and shah model Int. J. Comput. Vis. 50 271-93
    • (2002) Int. J. Comput. Vis. , vol.50 , pp. 271-293
    • Vese, L.A.1    Chan, T.F.2
  • 52
    • 0033242223 scopus 로고    scopus 로고
    • Sparse matrix computations arising in distributed parameter identification
    • (Sparse and structured matrices and their applications (Coeur d'Alene, ID, 1996))
    • Vogel C R 1999 Sparse matrix computations arising in distributed parameter identification SIAM J. Matrix Anal. Appl. 20 1027-37 (Sparse and structured matrices and their applications (Coeur d'Alene, ID, 1996))
    • (1999) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 1027-1037
    • Vogel, C.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.