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Volumn 16, Issue 8, 2006, Pages 1347-1373

Reconstruction of singular surfaces by shape sensitivity analysis and level set method

Author keywords

Clear layers; Diffusion equations; Interface conditions; Inverse problems; Level set method; Optical tomography; Shape sensitivity analysis; Tangential diffusion process

Indexed keywords


EID: 33747147745     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021820250600156X     Document Type: Article
Times cited : (10)

References (40)
  • 2
    • 0842290715 scopus 로고    scopus 로고
    • Structural optimization using sensitivity analysis and a level set method
    • G. Allaire, F. Jouve and A. M. Toader, Structural optimization using sensitivity analysis and a level set method, J. Comput. Phys. 194 (2004) 363-393.
    • (2004) J. Comput. Phys. , vol.194 , pp. 363-393
    • Allaire, G.1    Jouve, F.2    Toader, A.M.3
  • 3
    • 0002309872 scopus 로고
    • An optimal design problem with perimeter penalization
    • L. Ambrosio and G. Buttazzo, An optimal design problem with perimeter penalization, Calc. Var. 1 (1993) 55-69.
    • (1993) Calc. Var. , vol.1 , pp. 55-69
    • Ambrosio, L.1    Buttazzo, G.2
  • 4
    • 0032638277 scopus 로고    scopus 로고
    • Optical tomography in medical imaging
    • S. R. Arridge, Optical tomography in medical imaging, Inverse Problems 15 (1999) R41-R93.
    • (1999) Inverse Problems , vol.15
    • Arridge, S.R.1
  • 5
    • 0033965769 scopus 로고    scopus 로고
    • The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions
    • S. R. Arridge, H. Dehghani, M. Schweiger and E. Okada, The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions, Med. Phys. 27 (2000) 252-264.
    • (2000) Med. Phys. , vol.27 , pp. 252-264
    • Arridge, S.R.1    Dehghani, H.2    Schweiger, M.3    Okada, E.4
  • 6
    • 0036588725 scopus 로고    scopus 로고
    • Transport through diffusive and non-diffusive regions, embedded objects, and clear layers
    • G. Bal, Transport through diffusive and non-diffusive regions, embedded objects, and clear layers, SIAM J. Appl. Math. 62 (2002) 1677-1697.
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 1677-1697
    • Bal, G.1
  • 7
    • 13744259841 scopus 로고    scopus 로고
    • Reconstructions in impedance and optical tomography with singular interfaces
    • G. Bal, Reconstructions in impedance and optical tomography with singular interfaces, Inverse Problems 21 (2005) 113-131.
    • (2005) Inverse Problems , vol.21 , pp. 113-131
    • Bal, G.1
  • 8
    • 0347024809 scopus 로고    scopus 로고
    • Generalized diffusion model in optical tomography with clear layers
    • G. Bal and K. Ren, Generalized diffusion model in optical tomography with clear layers, J. Opt. Soc. Am. A 20 (2003) 2355-2364.
    • (2003) J. Opt. Soc. Am. A , vol.20 , pp. 2355-2364
    • Bal, G.1    Ren, K.2
  • 9
    • 3042677691 scopus 로고    scopus 로고
    • Level set methods for geometric inverse problem in linear elasticity
    • H. Ben Ameur, M. Burger and B. Hackl, Level set methods for geometric inverse problem in linear elasticity, Inverse Problems 20 (2004) 673-696.
    • (2004) Inverse Problems , vol.20 , pp. 673-696
    • Ben Ameur, H.1    Burger, M.2    Hackl, B.3
  • 11
    • 23844524180 scopus 로고    scopus 로고
    • A survey on level set methods for inverse problems and optimal design
    • M. Burger and S. J. Osher, A survey on level set methods for inverse problems and optimal design, Euro. J. Appl. Math. 16 (2005) 263-301.
    • (2005) Euro. J. Appl. Math. , vol.16 , pp. 263-301
    • Burger, M.1    Osher, S.J.2
  • 12
    • 0344550387 scopus 로고    scopus 로고
    • Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients
    • T. F. Chan and X.-C. Tai, Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients, J. Comput. Phys. 193 (2003) 40-66.
    • (2003) J. Comput. Phys. , vol.193 , pp. 40-66
    • Chan, T.F.1    Tai, X.-C.2
  • 13
    • 0002631224 scopus 로고    scopus 로고
    • A simple level set method for solving Stefan problems
    • S. Chen, B. Merriman, S. Osher and P. Smereka, A simple level set method for solving Stefan problems, J. Comput. Phys. 135 (1997) 8-29.
    • (1997) J. Comput. Phys. , vol.135 , pp. 8-29
    • Chen, S.1    Merriman, B.2    Osher, S.3    Smereka, P.4
  • 15
    • 0036557535 scopus 로고    scopus 로고
    • A model for the quasi-static growth of brittle fractures: Existence and approximation results
    • G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures: Existence and approximation results, Arch. Rationonal Mech. Anal. 162 (2002) 101-135.
    • (2002) Arch. Rationonal Mech. Anal. , vol.162 , pp. 101-135
    • Dal Maso, G.1    Toader, R.2
  • 18
    • 4043149294 scopus 로고    scopus 로고
    • Shape reconstruction in scattering media with void using a transport model and level sets
    • O. Dorn, Shape reconstruction in scattering media with void using a transport model and level sets, Canad. Appl. Math. Quart. 10 (2001) 239-275.
    • (2001) Canad. Appl. Math. Quart. , vol.10 , pp. 239-275
    • Dorn, O.1
  • 20
    • 0141750666 scopus 로고    scopus 로고
    • Identification of contact regions in semiconductor transistors by level-set methods
    • W. Fang and K. Ito, Identification of contact regions in semiconductor transistors by level-set methods, J. Comput. Appl. Math. 159 (2003) 399-410.
    • (2003) J. Comput. Appl. Math. , vol.159 , pp. 399-410
    • Fang, W.1    Ito, K.2
  • 21
    • 0742269371 scopus 로고    scopus 로고
    • Shape sensitivity for the Laplace-Beltrami operator with singularities
    • J. Ferchichi and J.-P. Zolésio, Shape sensitivity for the Laplace-Beltrami operator with singularities, J. Diff. Eqns. 196 (2004) 340-384.
    • (2004) J. Diff. Eqns. , vol.196 , pp. 340-384
    • Ferchichi, J.1    Zolésio, J.-P.2
  • 22
    • 0029987994 scopus 로고    scopus 로고
    • An investigation of light transport through scattering bodies with non-scattering regions
    • M. Firbank, S. R. Arridge, M. Schweiger and D. T. Delpy, An investigation of light transport through scattering bodies with non-scattering regions, Phys. Med. Biol. 41 (1996) 767-783.
    • (1996) Phys. Med. Biol. , vol.41 , pp. 767-783
    • Firbank, M.1    Arridge, S.R.2    Schweiger, M.3    Delpy, D.T.4
  • 25
    • 0016091219 scopus 로고
    • Phénomènes de transmission à travers des couches minces de conductivité élevée
    • P. H. Hung and E. Sánchez-Palencia, Phénomènes de transmission à travers des couches minces de conductivité élevée, J. Math. Anal. Appl. 47 (1974) 284-309.
    • (1974) J. Math. Anal. Appl. , vol.47 , pp. 284-309
    • Hung, P.H.1    Sánchez-Palencia, E.2
  • 27
    • 0035473295 scopus 로고    scopus 로고
    • Level set function approach to an inverse interface problem
    • K. Ito, K. Kunisch and Z. Li, Level set function approach to an inverse interface problem, Inverse Problems 17 (2001) 1225-1242.
    • (2001) Inverse Problems , vol.17 , pp. 1225-1242
    • Ito, K.1    Kunisch, K.2    Li, Z.3
  • 28
    • 0000386587 scopus 로고    scopus 로고
    • Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set
    • A. Litman, D. Lesselier and F. Santosa, Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set, Inverse Problems 14 (1998) 685-704.
    • (1998) Inverse Problems , vol.14 , pp. 685-704
    • Litman, A.1    Lesselier, D.2    Santosa, F.3
  • 31
    • 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 and F. Santosa, 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.
    • (2001) J. Comput. Phys. , vol.171 , pp. 272-288
    • Osher, S.J.1    Santosa, F.2
  • 32
    • 44749084234 scopus 로고
    • Front propagation with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. J. Osher and J. A. Sethian, Front propagation 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.J.1    Sethian, J.A.2
  • 34
    • 0000311941 scopus 로고    scopus 로고
    • Boundary conditions for light propagation in diffusive media with nonscattering regions
    • J. Ripoll, M. Nieto-Vesperinas, S. R. Arridge and H. Dehghani, Boundary conditions for light propagation in diffusive media with nonscattering regions, J. Opt. Soc. Am. A 17 (2000) 1671-1682.
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 1671-1682
    • Ripoll, J.1    Nieto-Vesperinas, M.2    Arridge, S.R.3    Dehghani, H.4
  • 35
    • 84996143735 scopus 로고    scopus 로고
    • A level-set approach for inverse problems involving obstacles
    • F. Santosa, A level-set approach for inverse problems involving obstacles, ESAIM: Control, Optim. Calculus Variations 1 (1996) 17-33.
    • (1996) ESAIM: Control, Optim. Calculus Variations , vol.1 , pp. 17-33
    • Santosa, F.1
  • 38
    • 0001351887 scopus 로고
    • Differentiation with respect to the domain in boundary value problems
    • J. Simon, Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. Optim. 2 (1980) 649-687.
    • (1980) Numer. Funct. Anal. Optim. , vol.2 , pp. 649-687
    • Simon, J.1
  • 40
    • 28144444111 scopus 로고
    • A levelset approach for computing solutions to incompressible two-phase flow
    • M. Sussman, P. Smereka and S. Osher, A levelset approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146-159.
    • (1994) J. Comput. Phys. , vol.114 , pp. 146-159
    • Sussman, M.1    Smereka, P.2    Osher, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.