메뉴 건너뛰기




Volumn 5, Issue 3, 2003, Pages 301-329

A framework for the construction of level set methods for shape optimization and reconstruction

Author keywords

Crystal growth; Gradient flows; Hamilton Jacobi equations; Inverse problems; Level sets; Materials science; Shape optimization; Shape reconstruction

Indexed keywords


EID: 0842267881     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/81     Document Type: Article
Times cited : (179)

References (77)
  • 1
    • 0002108952 scopus 로고    scopus 로고
    • The fast construction of extension velocities in level set methods
    • Zbl 0919.65074 MR 99j: 65189
    • ADALSTEINSSON, B. & SETHIAN, J. A. The fast construction of extension velocities in level set methods. J. Comput. Phys. 148 (1999), 2-22. Zbl 0919.65074 MR 99j: 65189
    • (1999) J. Comput. Phys. , vol.148 , pp. 2-22
    • Adalsteinsson, B.1    Sethian, J.A.2
  • 2
    • 0003796630 scopus 로고
    • Academic Press, New YorkZbl 0314.46030 MR 56 #9247
    • ADAMS, R. A. Sobolev Spaces. Academic Press, New York (1975). Zbl 0314.46030 MR 56 #9247
    • (1975) Sobolev Spaces
    • Adams, R.A.1
  • 3
    • 85129703098 scopus 로고    scopus 로고
    • Optimal stability for inverse elliptic boundary value problems with unknown boundary
    • Zbl pre01884316 MR 2002b: 35196
    • ALESSANDRINI, G., BERETTA, E., ROSSET, E., & VESSELLA, S. Optimal stability for inverse elliptic boundary value problems with unknown boundary. Ann. Scuola Norm. Sup. Pisa 29 (2001), 755-806. Zbl pre01884316 MR 2002b: 35196
    • (2001) Ann. Scuola Norm. Sup. Pisa , vol.29 , pp. 755-806
    • Alessandrini, G.1    Beretta, E.2    Rosset, E.3    Vessella, S.4
  • 4
    • 0001638402 scopus 로고
    • Local uniqueness in the inverse conductivity problem with one measurement
    • Zbl 0864.35114 MR 95m: 35197
    • ALESSANDRINI, G., ISAKOV, V., & POWELL, J. Local uniqueness in the inverse conductivity problem with one measurement. Trans. Amer. Math. Soc. 347 (1995), 3031-3041. Zbl 0864.35114 MR 95m: 35197
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 3031-3041
    • Alessandrini, G.1    Isakov, V.2    Powell, J.3
  • 5
    • 0032139281 scopus 로고    scopus 로고
    • The inverse conductivity problem with one measurement: Bounds on the size of the unknown object
    • Zbl 0953.35141 MR 99j: 35227
    • ALESSANDRINI, G. & ROSSET, E. The inverse conductivity problem with one measurement: Bounds on the size of the unknown object. SIAM J. Appl. Math. 58 (1998), 1060-1071. Zbl 0953.35141 MR 99j: 35227
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1060-1071
    • Alessandrini, G.1    Rosset, E.2
  • 6
    • 22844456697 scopus 로고    scopus 로고
    • Optimal size estimates for the inverse conductivity problem with one measurement
    • Zbl 0944.35108 MR 2000j: 35267
    • ALESSANDRINI, G., ROSSET, E., & SEO, J. K. Optimal size estimates for the inverse conductivity problem with one measurement. Proc. Amer. Math. Soc. 128 (2000), 53-64. Zbl 0944.35108 MR 2000j: 35267
    • (2000) Proc. Amer. Math. Soc. , vol.128 , pp. 53-64
    • Alessandrini, G.1    Rosset, E.2    Seo, J.K.3
  • 7
    • 0038053170 scopus 로고    scopus 로고
    • A level-set method for shape optimization
    • Zbl pre01777429 MR 2003b: 49041
    • ALLAIRE, G., JOUVE, F., & TOADER, A. M. A level-set method for shape optimization. C. R. Acad. Sci. Paris Sér. I 334 (2002), 1125-1130. Zbl pre01777429 MR 2003b: 49041
    • (2002) C. R. Acad. Sci. Paris Sér. I , vol.334 , pp. 1125-1130
    • Allaire, G.1    Jouve, F.2    Toader, A.M.3
  • 8
    • 21344449262 scopus 로고
    • Optimal geometry in equilibrium and growth
    • Zbl 0885.58015 MR 97h: 58054
    • ALMGREN, F.& TAYLOR, J. E. Optimal geometry in equilibrium and growth. Fractals 3 (1995), 713-723. Zbl 0885.58015 MR 97h: 58054
    • (1995) Fractals , vol.3 , pp. 713-723
    • Almgren, F.1    Taylor, J.E.2
  • 9
    • 85032179767 scopus 로고    scopus 로고
    • Motion of a closed curve by minus the surface Laplacian of curvature
    • Zbl 0974.35053 MR 2002j: 35314
    • ALVAREZ, S. A. & LIU, C. Motion of a closed curve by minus the surface Laplacian of curvature. Differential Integral Equations 13 (2000), 1583-1594. Zbl 0974.35053 MR 2002j: 35314
    • (2000) Differential Integral Equations , vol.13 , pp. 1583-1594
    • Alvarez, S.A.1    Liu, C.2
  • 10
    • 0003338459 scopus 로고    scopus 로고
    • Curvature and distance function from a manifold
    • Zbl 0941.53009 MR 2001d: 49070
    • AMBROSIO, L. & MANTEGAZZA, C. Curvature and distance function from a manifold. J. Geom. Anal. 8 (1998), 723-748. Zbl 0941.53009 MR 2001d: 49070
    • (1998) J. Geom. Anal. , vol.8 , pp. 723-748
    • Ambrosio, L.1    Mantegazza, C.2
  • 13
    • 0032271479 scopus 로고    scopus 로고
    • Stable determination of boundaries from Cauchy data
    • Zbl 0928.35201 MR 99j: 35229
    • BERETTA, E. & VESSELLA, S. Stable determination of boundaries from Cauchy data. SIAM J. Math. Anal. 30 (1999), 220-232. Zbl 0928.35201 MR 99j: 35229
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 220-232
    • Beretta, E.1    Vessella, S.2
  • 14
    • 0004870127 scopus 로고    scopus 로고
    • On the Landweber iteration for nonlinear ill-posed problems
    • Zbl 0879.65037 MR 97j: 65096
    • BINDER, A., HANKE, M., & SCHERZER, O. On the Landweber iteration for nonlinear ill-posed problems. J. Inverse Ill-Posed Probl. 4 (1996), 381-389. Zbl 0879.65037 MR 97j: 65096
    • (1996) J. Inverse Ill-Posed Probl. , vol.4 , pp. 381-389
    • Binder, A.1    Hanke, M.2    Scherzer, O.3
  • 15
    • 0030164963 scopus 로고    scopus 로고
    • An inverse problem in thermal imaging
    • Zbl 0854.35125 MR 96m: 80002
    • BRYAN, K. & CAUDILL, L. F. An inverse problem in thermal imaging. SIAM J. Appl. Math. 56 (1996), 715-735. Zbl 0854.35125 MR 96m: 80002
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 715-735
    • Bryan, K.1    Caudill, L.F.2
  • 16
    • 0005205628 scopus 로고    scopus 로고
    • Uniqueness for a boundary identification problem in thermal imaging
    • Zbl 0911.35117 MR 2000g:35226
    • BRYAN, K. & CAUDILL, L. F. Uniqueness for a boundary identification problem in thermal imaging. Electron. J. Differ. Equ. Conf. 1 (1998), 23-39. Zbl 0911.35117 MR 2000g: 35226
    • (1998) Electron. J. Differ. Equ. Conf. , vol.1 , pp. 23-39
    • Bryan, K.1    Caudill, L.F.2
  • 17
    • 0001191809 scopus 로고    scopus 로고
    • Stability for an inverse boundary problem of determining a part of a boundary
    • Zbl 0934.35202 MR 2000e: 35235
    • BUKHGEIM, A. L., CHENG, J., & YAMAMOTO, M. Stability for an inverse boundary problem of determining a part of a boundary. Inverse Problems 15 (1999), 1021-1032. Zbl 0934.35202 MR 2000e: 35235
    • (1999) Inverse Problems , vol.15 , pp. 1021-1032
    • Bukhgeim, A.L.1    Cheng, J.2    Yamamoto, M.3
  • 18
    • 0035473388 scopus 로고    scopus 로고
    • A level set method for inverse problems
    • Zbl 0985.35106 MR 2002g: 35208
    • BURGER, M. A level set method for inverse problems, Inverse Problems 17 (2001), 1327-1355. Zbl 0985.35106 MR 2002g: 35208
    • (2001) Inverse Problems , vol.17 , pp. 1327-1355
    • Burger, M.1
  • 19
    • 1842561883 scopus 로고    scopus 로고
    • Inverse doping problems for semiconductor devices
    • T. F. Chan et al. (eds.), Kluwer Academic/Plenum Publishers
    • BURGER, M., ENGL, H. W., & MARKOWICH, P. Inverse doping problems for semiconductor devices. Recent Progress in Computational and Applied PDEs, T. F. Chan et al. (eds.), Kluwer Academic/Plenum Publishers (2002), 27-38.
    • (2002) Recent Progress in Computational and Applied PDEs , pp. 27-38
    • Burger, M.1    Engl, H.W.2    Markowich, P.3
  • 20
    • 0035665674 scopus 로고    scopus 로고
    • Identification of doping profiles in semiconductor devices
    • Zbl 0989.35139 MR 85g: 35121
    • BURGER, M., ENGL, H. W., MARKOWICH, P., & PIETRA, P. Identification of doping profiles in semiconductor devices. Inverse Problems 17 (2001), 1765-1795. Zbl 0989.35139 MR 85g: 35121
    • (2001) Inverse Problems , vol.17 , pp. 1765-1795
    • Burger, M.1    Engl, H.W.2    Markowich, P.3    Pietra, P.4
  • 23
    • 0005091671 scopus 로고    scopus 로고
    • Motion by intrinsic Laplacian of curvature
    • Zbl 0938.65144 MR 2002j: 65023
    • CHOPP, D. L. & SETHIAN, J. A. Motion by intrinsic Laplacian of curvature. Interfaces Free Bound. 1 (1999), 107-123. Zbl 0938.65144 MR 2002j: 65023
    • (1999) Interfaces Free Bound. , vol.1 , pp. 107-123
    • Chopp, D.L.1    Sethian, J.A.2
  • 26
    • 0026254180 scopus 로고
    • Velocity method and Lagrangian formulation for the computation of the shape Hessian
    • Zbl 0747.49007 MR 92j: 49042
    • DELFOUR, M. C. & ZOLéSIO, J.-P. Velocity method and Lagrangian formulation for the computation of the shape Hessian. SIAM J. Control Optim. 29 (1991), 1414-1442. Zbl 0747.49007 MR 92j: 49042
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 1414-1442
    • Delfour, M.C.1    Zolésio, J.-P.2
  • 27
    • 0034292566 scopus 로고    scopus 로고
    • A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets
    • Zbl 0983.35150 MR 2002a: 78025
    • DORN, O., MILLER, E. M., & RAPPAPORT, C. M. A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets. Inverse Problems 16 (2000), 1119-1156. Zbl 0983.35150 MR 2002a: 78025
    • (2000) Inverse Problems , vol.16 , pp. 1119-1156
    • Dorn, O.1    Miller, E.M.2    Rappaport, C.M.3
  • 28
    • 23844548466 scopus 로고    scopus 로고
    • Shape reconstruction in 2D from limitedview multifrequency electromagnetic data
    • Zbl 0988.78012 MR 2002f: 35219
    • DORN, O., MILLER, E. L., & RAPPAPORT, C. M. Shape reconstruction in 2D from limitedview multifrequency electromagnetic data. Contemp. Math. 278 (2001), 97-122. Zbl 0988.78012 MR 2002f: 35219
    • (2001) Contemp. Math. , vol.278 , pp. 97-122
    • Dorn, O.1    Miller, E.L.2    Rappaport, C.M.3
  • 30
    • 0032379074 scopus 로고    scopus 로고
    • The surface diffusion flow for immersed hypersurfaces
    • Zbl 0912.35161 MR 99f: 58042
    • ESCHER, J., MAYER, U., & SIMONETT, G. The surface diffusion flow for immersed hypersurfaces. SIAM J. Math. Anal. 29 (1998), 1419-1433. Zbl 0912.35161 MR 99f: 58042
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1419-1433
    • Escher, J.1    Mayer, U.2    Simonett, G.3
  • 31
    • 0003418232 scopus 로고
    • Springer, Berlin (Zbl 0176.00801 MR 41 #1976
    • FEDERER, H. Geometric Measure Theory. Springer, Berlin (1969). Zbl 0176.00801 MR 41 #1976
    • (1969) Geometric Measure Theory
    • Federer, H.1
  • 32
    • 0000020120 scopus 로고
    • On the uniqueness in the inverse conductivity problem with one measurement
    • Zbl 0703.35165 MR 91a: 35164
    • FRIEDMAN, A. & ISAKOV, V. On the uniqueness in the inverse conductivity problem with one measurement. Indiana Univ. Math. J. 38 (1989), 563-579. Zbl 0703.35165 MR 91a: 35164
    • (1989) Indiana Univ. Math. J. , vol.38 , pp. 563-579
    • Friedman, A.1    Isakov, V.2
  • 33
    • 0032400284 scopus 로고    scopus 로고
    • Nonstationary iterated Tikhonov regularization
    • Zbl 0910.47005 MR 99e: 65100
    • GROETSCH, C.W. & HANKE, M. Nonstationary iterated Tikhonov regularization. J. Optim. Theory Appl. 98 (1998), 37-53. Zbl 0910.47005 MR 99e: 65100
    • (1998) J. Optim. Theory Appl. , vol.98 , pp. 37-53
    • Groetsch, C.W.1    Hanke, M.2
  • 34
    • 0034298994 scopus 로고    scopus 로고
    • Nonstationary iterated Tikhonov-Morozov method and third order differential equations for the evaluation of unbounded operators
    • Zbl 0970.65059 MR 2001m: 65078
    • GROETSCH, C. W. & SCHERZER, O. Nonstationary iterated Tikhonov-Morozov method and third order differential equations for the evaluation of unbounded operators. Math. Methods Appl. Sci. 23 (2000), 1287-1300. Zbl 0970.65059 MR 2001m: 65078
    • (2000) Math. Methods Appl. Sci. , vol.23 , pp. 1287-1300
    • Groetsch, C.W.1    Scherzer, O.2
  • 35
    • 0040893030 scopus 로고
    • A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
    • Zbl 0840.65049 MR 96i: 65046
    • HANKE, M., NEUBAUER, A., & SCHERZER, O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math. 72 (1995), 21-37. Zbl 0840.65049 MR 96i: 65046
    • (1995) Numer. Math. , vol.72 , pp. 21-37
    • Hanke, M.1    Neubauer, A.2    Scherzer, O.3
  • 36
    • 0000298487 scopus 로고    scopus 로고
    • Iterative methods for the reconstruction of an inverse potential problem
    • Zbl 0621.35102 MR 97m: 65232
    • HETTLICH, F. & RUNDELL, W. Iterative methods for the reconstruction of an inverse potential problem. Inverse Problems 12 (1996), 251-266. Zbl 0621.35102 MR 97m: 65232
    • (1996) Inverse Problems , vol.12 , pp. 251-266
    • Hettlich, F.1    Rundell, W.2
  • 37
    • 0011052133 scopus 로고    scopus 로고
    • Recovery of the support of a source term in an elliptic differential equation
    • Zbl 0888.35135 MR 98g: 35213
    • HETTLICH, F. & RUNDELL, W. Recovery of the support of a source term in an elliptic differential equation. Inverse Problems 13 (1997), 959-976. Zbl 0888.35135 MR 98g: 35213
    • (1997) Inverse Problems , vol.13 , pp. 959-976
    • Hettlich, F.1    Rundell, W.2
  • 38
    • 0002215984 scopus 로고    scopus 로고
    • The determination of a discontinuity in a conductivity from a single boundary measurement
    • Zbl 0894.35126 MR 99b: 35210
    • HETTLICH, F. & RUNDELL, W. The determination of a discontinuity in a conductivity from a single boundary measurement. Inverse Problems 14 (1998), 67-82. Zbl 0894.35126 MR 99b: 35210
    • (1998) Inverse Problems , vol.14 , pp. 67-82
    • Hettlich, F.1    Rundell, W.2
  • 39
    • 0021624938 scopus 로고
    • On the identification of coefficients of elliptic problems by asymptotic regularization
    • Zbl 0576.65121 MR 86c: 35161
    • HOFFMANN, K. H. & SPREKELS, J. On the identification of coefficients of elliptic problems by asymptotic regularization. Numer. Funct. Anal. Optim. 7 (1984), 157-177. Zbl 0576.65121 MR 86c: 35161
    • (1984) Numer. Funct. Anal. Optim. , vol.7 , pp. 157-177
    • Hoffmann, K.H.1    Sprekels, J.2
  • 40
    • 3042941743 scopus 로고
    • On the identification of parameters in general variational inequalities by asymptotic regularization
    • Zbl 0652.35103 MR 87j: 35373
    • HOFFMANN, K. H. & SPREKELS, J. On the identification of parameters in general variational inequalities by asymptotic regularization. SIAM J. Math. Anal. 17 (1986), 1198-1217. Zbl 0652.35103 MR 87j: 35373
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 1198-1217
    • Hoffmann, K.H.1    Sprekels, J.2
  • 41
    • 84880630879 scopus 로고    scopus 로고
    • Special issue: Hele-Shaw flows and related problems
    • Zbl 0951.00024 MR 2001a: 76005
    • HOWISON, S. D. & OCKENDON, J. R. (eds.) Special issue: Hele-Shaw flows and related problems. Eur. J. Appl. Math. 10 (1999), 511-705. Zbl 0951.00024 MR 2001a: 76005
    • (1999) Eur. J. Appl. Math. , vol.10 , pp. 511-705
    • Howison, S.D.1    Ockendon, J.R.2
  • 42
    • 0000838061 scopus 로고
    • On the inverse conductivity problem with one measurement
    • Zbl 0724.35108 MR 91e: 35212a
    • ISAKOV, V. & POWELL, J. On the inverse conductivity problem with one measurement, Inverse Problems 6 (1990), 311-318. Zbl 0724.35108 MR 91e: 35212a
    • (1990) Inverse Problems , vol.6 , pp. 311-318
    • Isakov, V.1    Powell, J.2
  • 43
    • 0035473295 scopus 로고    scopus 로고
    • Level-set function approach to an inverse interface problem
    • Zbl 0986.35130 MR 2002h:35335
    • ITO, K., KUNISCH, K., & LI, Z. Level-set function approach to an inverse interface problem. Inverse Problems 17 (2001), 1225-1242. Zbl 0986.35130 MR 2002h: 35335
    • (2001) Inverse Problems , vol.17 , pp. 1225-1242
    • Ito, K.1    Kunisch, K.2
  • 44
    • 0034503787 scopus 로고    scopus 로고
    • Weighted ENO-schemes for Hamilton-Jacobi equations
    • Zbl 0957.35014 MR 2001e: 65124
    • JIANG, G. S. & PENG, D. Weighted ENO-schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21 (2000), 2126-2143. Zbl 0957.35014 MR 2001e: 65124
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 2126-2143
    • Jiang, G.S.1    Peng, D.2
  • 45
    • 0001495158 scopus 로고    scopus 로고
    • Numerical identification of discontinuous conductivity coefficients
    • Zbl 0934.35204 MR 98k: 78052
    • KANG, H., SEO, J. K., JIN, K., & SHEEN, D. Numerical identification of discontinuous conductivity coefficients. Inverse Problems 13 (1997), 113-123. Zbl 0934.35204 MR 98k: 78052
    • (1997) Inverse Problems , vol.13 , pp. 113-123
    • Kang, H.1    Seo, J.K.2    Jin, K.3    Sheen, D.4
  • 46
    • 0003003643 scopus 로고    scopus 로고
    • A method for imaging corrosion damage in thin plates from electrostatic data
    • Zbl 0851.35134
    • KAUP, P., SANTOSA, F., & VOGELIUS, M. A method for imaging corrosion damage in thin plates from electrostatic data. Inverse Problems 12 (1996), 279-293. Zbl 0851.35134
    • (1996) Inverse Problems , vol.12 , pp. 279-293
    • Kaup, P.1    Santosa, F.2    Vogelius, M.3
  • 47
    • 0028543322 scopus 로고
    • Estimation of interfaces from boundary measurements
    • Zbl 0807.35162 MR 95h: 35245
    • KUNISCH, K. & PAN, X. Estimation of interfaces from boundary measurements. SIAM J. Control Optim. 32 (1994), 1643-1674. Zbl 0807.35162 MR 95h: 35245
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 1643-1674
    • Kunisch, K.1    Pan, X.2
  • 48
    • 0000518587 scopus 로고
    • An iteration formula for Fredholm integral equations of the first kind
    • Zbl 0043.10602 MR 13,247c
    • LANDWEBER, L. An iteration formula for Fredholm integral equations of the first kind. Amer. J. Math. 73 (1951), 615-624. Zbl 0043.10602 MR 13,247c
    • (1951) Amer. J. Math. , vol.73 , pp. 615-624
    • Landweber, L.1
  • 50
    • 0000386587 scopus 로고    scopus 로고
    • Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set
    • Zbl 0912.35158 MR 99e: 78032
    • LITMAN, A., LESSELIER, D., & SANTOSA, F. Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set. Inverse Problems 14 (1998), 685-706. Zbl 0912.35158 MR 99e: 78032
    • (1998) Inverse Problems , vol.14 , pp. 685-706
    • Litman, A.1    Lesselier, D.2    Santosa, F.3
  • 51
    • 85032223198 scopus 로고
    • On the Mullins-Sekerka model for phase transitions in mixtures
    • Zbl 0742.35075 MR 92i: 80005
    • MILIC, N. On the Mullins-Sekerka model for phase transitions in mixtures, Quart. Appl. Math. 49 (1991), 437-445. Zbl 0742.35075 MR 92i: 80005
    • (1991) Quart. Appl. Math. , vol.49 , pp. 437-445
    • Milic, N.1
  • 54
    • 36849117884 scopus 로고
    • Morphological stability of a particle growing by diffusion or heat flow
    • MULLINS, W. W. & SEKERKA, R. F. Morphological stability of a particle growing by diffusion or heat flow. J. Appl. Phys. 34 (1963), 323-329.
    • (1963) J. Appl. Phys. , vol.34 , pp. 323-329
    • Mullins, W.W.1    Sekerka, R.F.2
  • 55
    • 0346367651 scopus 로고    scopus 로고
    • Structure of shape derivatives
    • MR 1 930 612
    • NOVRUZI, A. & PIERRE, M. Structure of shape derivatives. J. Evol. Equ. 2 (2002), 365-382. MR 1 930 612
    • (2002) J. Evol. Equ. , vol.2 , pp. 365-382
    • Novruzi, A.1    Pierre, M.2
  • 57
    • 0000653948 scopus 로고    scopus 로고
    • Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum
    • Zbl pre01655220 MR 2002f: 65088
    • OSHER, S. & SANTOSA, F. Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 171 (2001), 272-288. Zbl pre01655220 MR 2002f: 65088
    • (2001) J. Comput. Phys. , vol.171 , pp. 272-288
    • Osher, S.1    Santosa, F.2
  • 58
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • Zbl 0659.65132 MR 89h: 80012
    • OSHER, S. & A. SETHIAN, J. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988), 12-49. Zbl 0659.65132 MR 89h: 80012
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, A.2
  • 61
    • 0346488430 scopus 로고    scopus 로고
    • Scale-space properties of nonstationary iterative regularization methods
    • RADMOSER, E., SCHERZER, O., & WEICKERT, J. Scale-space properties of nonstationary iterative regularization methods. J. Vis. Commun. Image Repr. 8 (2000), 96-114.
    • (2000) J. Vis. Commun. Image Repr. , vol.8 , pp. 96-114
    • Radmoser, E.1    Scherzer, O.2    Weickert, J.3
  • 63
    • 0035665603 scopus 로고    scopus 로고
    • Shape inversion from TM and TE real data by controlled evolution of level sets
    • Zbl 0987.78500 MR 1 872 909
    • RAMANANJAONA, C., LAMBERT, M., & LESSELIER, D. Shape inversion from TM and TE real data by controlled evolution of level sets. Inverse Problems 17 (2001), 1585-1595. Zbl 0987.78500 MR 1 872 909
    • (2001) Inverse Problems , vol.17 , pp. 1585-1595
    • Ramananjaona, C.1    Lambert, M.2    Lesselier, D.3
  • 64
    • 0035419980 scopus 로고    scopus 로고
    • Shape reconstruction of buried obstacles by controlled evolution of a level set: From a min-max formulation to numerical experimentation
    • Zbl 0994.35121 MR 1 861 503
    • RAMANANJAONA, C., LAMBERT, M., LESSELIER, D., & ZOLéSIO, J.-P. Shape reconstruction of buried obstacles by controlled evolution of a level set: From a min-max formulation to numerical experimentation. Inverse Problems 17 (2001), 1087-1111. Zbl 0994.35121 MR 1 861 503
    • (2001) Inverse Problems , vol.17 , pp. 1087-1111
    • Ramananjaona, C.1    Lambert, M.2    Lesselier, D.3    Zolésio, J.-P.4
  • 66
    • 84996143735 scopus 로고    scopus 로고
    • A level-set approach for inverse problems involving obstacles
    • Zbl 0870.49016 MR 97f: 00011
    • SANTOSA, F. A level-set approach for inverse problems involving obstacles. ESAIM Controle Optim. Calc. Var. 1 (1996), 17-33. Zbl 0870.49016 MR 97f: 00011
    • (1996) ESAIM Controle Optim. Calc. Var. , vol.1 , pp. 17-33
    • Santosa, F.1
  • 67
    • 0010014032 scopus 로고
    • Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems
    • Zbl 0842.65036 MR 97d: 65033
    • SCHERZER, O. Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems. J. Math. Anal. Appl. 194 (1995), 911-933. Zbl 0842.65036 MR 97d: 65033
    • (1995) J. Math. Anal. Appl. , vol.194 , pp. 911-933
    • Scherzer, O.1
  • 68
    • 0034135395 scopus 로고    scopus 로고
    • Relations between regularization and diffusion filtering
    • Zbl 0945.68183 MR 2000k: 68167
    • SCHERZER, O. & WEICKERT, J. Relations between regularization and diffusion filtering. J. Math. Imaging Vision 12 (2000), 43-63. Zbl 0945.68183 MR 2000k: 68167
    • (2000) J. Math. Imaging Vision , vol.12 , pp. 43-63
    • Scherzer, O.1    Weickert, J.2
  • 69
    • 0003661003 scopus 로고    scopus 로고
    • 2nd ed., Cambridge Univ. Press, Cambridge ( Zbl 0973.76003 MR2000c: 65015
    • SETHIAN, J. A. Level Set Methods and Fast Marching Methods. 2nd ed., Cambridge Univ. Press, Cambridge (1999). Zbl 0973.76003 MR2000c: 65015
    • (1999) Level Set Methods and Fast Marching Methods
    • Sethian, J.A.1
  • 70
    • 0001176192 scopus 로고    scopus 로고
    • Structural boundary design via level set and immersed interface methods
    • Zbl 0994.74082 MR 2001h: 74074
    • SETHIAN, J. A. & WIEGMANN, A. Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163 (2000), 489-528. Zbl 0994.74082 MR 2001h: 74074
    • (2000) J. Comput. Phys. , vol.163 , pp. 489-528
    • Sethian, J.A.1    Wiegmann, A.2
  • 74
    • 0013243263 scopus 로고
    • On the asymptotical regularization of nonlinear ill-posed problems
    • Zbl 0828.65055 MR 95j: 65069
    • TAUTENHAHN, U. On the asymptotical regularization of nonlinear ill-posed problems. Inverse Problems 10 (1994), 1405-1418. Zbl 0828.65055 MR 95j: 65069
    • (1994) Inverse Problems , vol.10 , pp. 1405-1418
    • Tautenhahn, U.1
  • 75
  • 77
    • 0001461595 scopus 로고
    • The material derivative (or speed) method for shape optimization
    • NATO Adv. Study Inst. Ser. E, Appl. Sci. Nijhoff, The Hague ( Zbl 0517.73097 MR 84f: 49017
    • ZOLé SIO, J.-P. The material derivative (or speed) method for shape optimization. Optimization of Distributed Parameter Structures, Vol. II, NATO Adv. Study Inst. Ser. E, Appl. Sci. 50, Nijhoff, The Hague (1981), 1089-1151. Zbl 0517.73097 MR 84f: 49017
    • (1981) Optimization of Distributed Parameter Structures , vol.2 , Issue.50 , pp. 1089-1151
    • Zolésio, J.-P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.