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Volumn , Issue , 2008, Pages 1-196

Iterative Regularization Methods for Nonlinear Ill-Posed Problems

Author keywords

discrepancy principle; Landweber iteration; level set methods; multi level methods; Newton type methods; Nonlinear ill posed problems; parameter estimation problems; Radon transform; regularization

Indexed keywords


EID: 85144395410     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1515/9783110208276     Document Type: Book
Times cited : (638)

References (161)
  • 2
    • 5244289648 scopus 로고
    • On the stability of iterative methods for the solution of linear ill-posed problems
    • O. M. Alifanov and S. V. Rumyantsev, On the stability of iterative methods for the solution of linear ill-posed problems, Soviet Math. Dokl. 20 (1979), pp. 1133–1136.
    • (1979) Soviet Math. Dokl. , vol.20 , pp. 1133-1136
    • Alifanov, O.M.1    Rumyantsev, S.V.2
  • 3
    • 0000834834 scopus 로고
    • The problem of the convergence of the iteratively regularized Gauss-Newton method
    • A. B. Bakushinsky, The problem of the convergence of the iteratively regularized Gauss-Newton method, Comput. Math. Math. Phys. 32 (1992), pp. 1353–1359.
    • (1992) Comput. Math. Math. Phys. , vol.32 , pp. 1353-1359
    • Bakushinsky, A.B.1
  • 5
    • 28544444551 scopus 로고    scopus 로고
    • Iterative Methods for Approximate Solution of Inverse Problems
    • Springer, Dordrecht
    • A. B. Bakushinsky and M. Y. Kokurin, Iterative Methods for Approximate Solution of Inverse Problems, Mathematics and Its Applications 577. Springer, Dordrecht, 2004.
    • (2004) Mathematics and Its Applications , vol.577
    • Bakushinsky, A.B.1    Kokurin, M.Y.2
  • 6
    • 84966225538 scopus 로고
    • Analysis of a multilevel iterative method for nonlinear finite element equations
    • R. E. Bank and D. J. Rose, Analysis of a multilevel iterative method for nonlinear finite element equations, Math. Comput. 39 (1982), pp. 453–465.
    • (1982) Math. Comput. , vol.39 , pp. 453-465
    • Bank, R.E.1    Rose, D.J.2
  • 8
    • 28544447290 scopus 로고    scopus 로고
    • A Lepskij-type stopping rule for regularized Newton methods
    • F. Bauer and T. Hohage, A Lepskij-type stopping rule for regularized Newton methods, Inverse Problems 21 (2005), pp. 1975–1991.
    • (2005) Inverse Problems , vol.21 , pp. 1975-1991
    • Bauer, F.1    Hohage, T.2
  • 10
    • 0004870127 scopus 로고    scopus 로고
    • On the Landweber iteration for nonlinear ill-posed problems
    • A. Binder, M. Hanke, and O. Scherzer, On the Landweber iteration for nonlinear ill-posed problems, J. Inv. Ill-Posed Problems 4 (1996), pp. 381–389.
    • (1996) J. Inv. Ill-Posed Problems , vol.4 , pp. 381-389
    • Binder, A.1    Hanke, M.2    Scherzer, O.3
  • 11
    • 0031532935 scopus 로고    scopus 로고
    • On convergence rates for the iteratively regularized Gauss-Newton method
    • B. Blaschke, A. Neubauer, and O. Scherzer, On convergence rates for the iteratively regularized Gauss-Newton method, IMA Journal of Numer. Anal. 17 (1997), pp. 421–436.
    • (1997) IMA Journal of Numer. Anal. , vol.17 , pp. 421-436
    • Blaschke, B.1    Neubauer, A.2    Scherzer, O.3
  • 12
    • 0036904346 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • L. Borcea, Electrical impedance tomography, Inverse Problems 18 (2002), pp. R99–R136.
    • (2002) Inverse Problems , vol.18 , pp. R99-R136
    • Borcea, L.1
  • 14
    • 84966233568 scopus 로고
    • Multilevel adaptive solutions to boundary value problems
    • A. Brandt, Multilevel adaptive solutions to boundary value problems, Math. Comp. 31 (1977), pp. 333–390.
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 16
    • 0000827660 scopus 로고
    • Construction of fixed poins of nonlinear mappings in Hilbert space
    • F. Browder and W. V. Petryshyn, Construction of fixed poins of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), pp. 197–228.
    • (1967) J. Math. Anal. Appl. , vol.20 , pp. 197-228
    • Browder, F.1    Petryshyn, W.V.2
  • 17
    • 84968510937 scopus 로고
    • A class of methods for solving nonlinear simultaneous equations
    • C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comp. 19 (1965), pp. 577–593.
    • (1965) Math. Comp. , vol.19 , pp. 577-593
    • Broyden, C.G.1
  • 18
    • 85025244653 scopus 로고    scopus 로고
    • Error bounds of discretization methods for boundary integral equations with noisy data
    • G. Bruckner, S. Prößdorf, and G. Vainikko, Error bounds of discretization methods for boundary integral equations with noisy data, Appl. Anal. 63 (1996), pp. 25–37.
    • (1996) Appl. Anal. , vol.63 , pp. 25-37
    • Bruckner, G.1    Prößdorf, S.2    Vainikko, G.3
  • 20
    • 1342329760 scopus 로고    scopus 로고
    • Levenberg-Marquardt level set methods for inverse obstacle problems
    • M. Burger, Levenberg-Marquardt level set methods for inverse obstacle problems, Inverse Problems 20 (2004), pp. 259–282.
    • (2004) Inverse Problems , vol.20 , pp. 259-282
    • Burger, M.1
  • 22
    • 33847617979 scopus 로고    scopus 로고
    • Regularizing Newton-Kaczmarz methods for nonlinear ill-posed problems
    • M. Burger and B. Kaltenbacher, Regularizing Newton-Kaczmarz methods for nonlinear ill-posed problems, SIAM J. Numer. Anal. 44 (2006), pp. 153–182.
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 153-182
    • Burger, M.1    Kaltenbacher, B.2
  • 23
    • 0036683969 scopus 로고    scopus 로고
    • Iterative regularization of parameter identification problems by sequential quadratic programming methods
    • M. Burger and W. Mühlhuber, Iterative regularization of parameter identification problems by sequential quadratic programming methods, Inverse Problems 18 (2002), pp. 943–969.
    • (2002) Inverse Problems , vol.18 , pp. 943-969
    • Burger, M.1    Mühlhuber, W.2
  • 24
    • 0010048713 scopus 로고    scopus 로고
    • Numerical approximation of an SQP-type method for parameter identification
    • M. Burger, Numerical approximation of an SQP-type method for parameter identification, SIAM J. Numer. Anal. 40 (2002), pp. 1775–1797.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1775-1797
    • Burger, M.1
  • 25
    • 23844524180 scopus 로고    scopus 로고
    • A survey on level set methods for inverse problems and optimal design
    • M. Burger and S. Osher, A survey on level set methods for inverse problems and optimal design, Eur. J. Appl. Math. 16 (2005), pp. 263–301.
    • (2005) Eur. J. Appl. Math. , vol.16 , pp. 263-301
    • Burger, M.1    Osher, S.2
  • 26
    • 47249148730 scopus 로고
    • Quantitative 2D and 3D Schlieren imaging for acoustic power and intensity measurements
    • T. Charlebois and R. Pelton, Quantitative 2D and 3D Schlieren imaging for acoustic power and intensity measurements, Medical Electronics (1995), pp. 789–792.
    • (1995) Medical Electronics , pp. 789-792
    • Charlebois, T.1    Pelton, R.2
  • 27
    • 0026254310 scopus 로고
    • New size × curvature conditions for strict quasiconvexity of sets
    • G. Chavent, New size × curvature conditions for strict quasiconvexity of sets, SIAM J. Control Optim. 29 (1991), pp. 1348–1372.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 1348-1372
    • Chavent, G.1
  • 28
    • 0039852371 scopus 로고
    • Quasi-convex sets and size × curvature condition, applications to nonlinear inversion
    • G. Chavent, Quasi-convex sets and size × curvature condition, applications to nonlinear inversion, Appl. Math. Optim. 24 (1991), pp. 129–169.
    • (1991) Appl. Math. Optim. , vol.24 , pp. 129-169
    • Chavent, G.1
  • 29
    • 0032074977 scopus 로고    scopus 로고
    • State space regularization: Geometric theory
    • G. Chavent and K. Kunisch, State space regularization: geometric theory, Appl. Math. Optim. 37 (1998), pp. 243–267.
    • (1998) Appl. Math. Optim. , vol.37 , pp. 243-267
    • Chavent, G.1    Kunisch, K.2
  • 31
    • 0003603616 scopus 로고
    • Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems
    • Kluwer, Dordrecht
    • I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Mathematics and its Applications 62. Kluwer, Dordrecht, 1990.
    • (1990) Mathematics and Its Applications , vol.62
    • Cioranescu, I.1
  • 32
    • 84942964039 scopus 로고
    • Stability for parameter estimation in two point boundary value problems
    • F. Colonius and K. Kunisch, Stability for parameter estimation in two point boundary value problems, J. Reine Angew. Math. 370 (1986), pp. 1–29.
    • (1986) J. Reine Angew. Math. , vol.370 , pp. 1-29
    • Colonius, F.1    Kunisch, K.2
  • 33
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • I. Daubechies, M. Defrise, and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. 57 (2004), pp. 1413–1457.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    de Mol, C.3
  • 34
    • 0345179899 scopus 로고
    • A note on stopping rules for iterative regularization methods and filtered SVD
    • (P. C. Sabatier, ed.), pp., Academic Press, London, Orlando, San Diego, New York
    • M. Defrise and C. De Mol, A note on stopping rules for iterative regularization methods and filtered SVD. Inverse Problems: An Interdisciplinary Study (P. C. Sabatier, ed.), pp. 261–268. Academic Press, London, Orlando, San Diego, New York, 1987.
    • (1987) Inverse Problems: An Interdisciplinary Study , vol.261-268
    • Defrise, M.1    de Mol, C.2
  • 35
    • 43949161376 scopus 로고
    • Shape analysis via oriented distance functions
    • M. C. Delfour and J.-P. Zolésio, Shape analysis via oriented distance functions, J. Funct. Anal. 123 (1994), pp. 129–201.
    • (1994) J. Funct. Anal. , vol.123 , pp. 129-201
    • Delfour, M.C.1    Zolésio, J.-P.2
  • 36
    • 0002663672 scopus 로고
    • Quasi-Newton methods, motivation and theory
    • J. E. Dennis and J. J. Moré, Quasi-Newton methods, motivation and theory, SIAM Review 19 (1977), pp. 46–89.
    • (1977) SIAM Review , vol.19 , pp. 46-89
    • Dennis, J.E.1    Moré, J.J.2
  • 37
    • 0345875999 scopus 로고    scopus 로고
    • A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
    • P. Deuflhard, H. W. Engl, and O. Scherzer, A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions, Inverse Problems 14 (1998), pp. 1081–1106.
    • (1998) Inverse Problems , vol.14 , pp. 1081-1106
    • Deuflhard, P.1    Engl, H.W.2    Scherzer, O.3
  • 38
    • 0001820687 scopus 로고
    • Affine invariant convergence theorems for Newton’s method and extensions to related methods
    • P. Deuflhard and G. Heindl, Affine invariant convergence theorems for Newton’s method and extensions to related methods, SIAM J. Numer. Anal. 16 (1979), pp. 1– 10.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 1-10
    • Deuflhard, P.1    Heindl, G.2
  • 39
    • 0026940480 scopus 로고
    • Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem
    • P. Deuflhard and F. Potra, Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem, SIAM J. Numer. Anal. 29 (1992), pp. 1395– 1412.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1395-1412
    • Deuflhard, P.1    Potra, F.2
  • 40
    • 34547263528 scopus 로고    scopus 로고
    • Fast fully iterative Newton-type methods for inverse problems
    • H. Egger, Fast fully iterative Newton-type methods for inverse problems, J. Inv. Ill-Posed Problems 15 (2007), pp. 257–275.
    • (2007) J. Inv. Ill-Posed Problems , vol.15 , pp. 257-275
    • Egger, H.1
  • 41
    • 55549123024 scopus 로고    scopus 로고
    • Y-Scale regularization
    • H. Egger, Y-Scale regularization, SIAM J. Numer. Anal. 46 (2008), pp. 419–436.
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 419-436
    • Egger, H.1
  • 42
    • 26644456996 scopus 로고    scopus 로고
    • Preconditioning Landweber iteration in Hilbert scales
    • H. Egger and A. Neubauer, Preconditioning Landweber iteration in Hilbert scales, Numer. Math. 101 (2005), pp. 643–662.
    • (2005) Numer. Math. , vol.101 , pp. 643-662
    • Egger, H.1    Neubauer, A.2
  • 43
    • 84880683689 scopus 로고
    • Iteration methods for convexly constrained ill-posed problems in Hilbert space
    • B. Eicke, Iteration methods for convexly constrained ill-posed problems in Hilbert space, Numer. Funct. Anal. Optim. 13 (1992), pp. 413–429.
    • (1992) Numer. Funct. Anal. Optim. , vol.13 , pp. 413-429
    • Eicke, B.1
  • 44
    • 0039911550 scopus 로고
    • The instability of some gradient methods for ill-posed problems
    • B. Eicke, A. K. Louis, and R. Plato, The instability of some gradient methods for ill-posed problems, Numer. Math. 58 (1990), pp. 129–134.
    • (1990) Numer. Math. , vol.58 , pp. 129-134
    • Eicke, B.1    Louis, A.K.2    Plato, R.3
  • 46
    • 0013013557 scopus 로고
    • On projection methods for solving linear ill-posed problems
    • (A. Vogel, ed.), pp., Vieweg, Braunschweig
    • H. W. Engl and A. Neubauer, On projection methods for solving linear ill-posed problems. Model Optimization in Exploration Geophysics (A. Vogel, ed.), pp. 73– 92. Vieweg, Braunschweig, 1987.
    • (1987) Model Optimization in Exploration Geophysics , pp. 73-92
    • Engl, H.W.1    Neubauer, A.2
  • 47
    • 0034499545 scopus 로고    scopus 로고
    • A new approach to convergence rate analysis of Tiknonov regularization for parameter identification in heat conduction
    • H. W. Engl and J. Zou, A new approach to convergence rate analysis of Tiknonov regularization for parameter identification in heat conduction, Inverse Problems 16 (2000), pp. 1907–1923.
    • (2000) Inverse Problems , vol.16 , pp. 1907-1923
    • Engl, H.W.1    Zou, J.2
  • 48
    • 0003448545 scopus 로고    scopus 로고
    • Partial differential equations
    • AMS, Providence, RI
    • L. C. Evans, Partial differential equations, Graduate Studies in Mathematics 19. AMS, Providence, RI, 1998.
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 50
    • 84935920131 scopus 로고
    • Iterative solution methods for inconsistent linear equations with non self-adjoint operators
    • S. F. Gilyazov, Iterative solution methods for inconsistent linear equations with non self-adjoint operators, Moscow Univ. Comput. Math. Cybernet 78 (1977), pp. 8–13.
    • (1977) Moscow Univ. Comput. Math. Cybernet , vol.78 , pp. 8-13
    • Gilyazov, S.F.1
  • 51
    • 0042663981 scopus 로고    scopus 로고
    • The rise and rise of medical imaging
    • P. Gould, The rise and rise of medical imaging, Medical Physics (2003), pp. 29–31.
    • (2003) Medical Physics , pp. 29-31
    • Gould, P.1
  • 54
    • 85072900806 scopus 로고    scopus 로고
    • Stable approximate evaluation of unbounded operators
    • 1894. Springer, Berlin
    • C. W. Groetsch, Stable approximate evaluation of unbounded operators, Lecture Notes in Mathematics 1894. Springer, Berlin, 2007.
    • (2007) Lecture Notes in Mathematics
    • Groetsch, C.W.1
  • 55
    • 0013018579 scopus 로고
    • Convergence of a general projection method for an operator equation of the first kind
    • C. W. Groetsch and A. Neubauer, Convergence of a general projection method for an operator equation of the first kind, Houston J. Math. 14 (1988), pp. 201–208.
    • (1988) Houston J. Math. , vol.14 , pp. 201-208
    • Groetsch, C.W.1    Neubauer, A.2
  • 56
    • 0028728043 scopus 로고
    • Hierarchical extension operators and local multigrid methods in domain decomposition preconditioners
    • G. Haase, U. Langer, A. Meyer, and S.V. Nepomnyashikh, Hierarchical extension operators and local multigrid methods in domain decomposition preconditioners, East-West J. Numer. Math. 2 (1994), pp. 179–193.
    • (1994) East-West J. Numer. Math. , vol.2 , pp. 179-193
    • Haase, G.1    Langer, U.2    Meyer, A.3    Nepomnyashikh, S.V.4
  • 57
    • 13744252043 scopus 로고    scopus 로고
    • Quasi-Newton methods for large-scale electromagnetic inverse problems
    • E. Haber, Quasi-Newton methods for large-scale electromagnetic inverse problems, Inverse Problems 21 (2005), pp. 305–323.
    • (2005) Inverse Problems , vol.21 , pp. 305-323
    • Haber, E.1
  • 58
    • 0035665003 scopus 로고    scopus 로고
    • A multigrid method for distributed parameter estimation problems
    • E. Haber and U. Ascher, A multigrid method for distributed parameter estimation problems, Inverse Problems 17 (2001), pp. 1847–1864.
    • (2001) Inverse Problems , vol.17 , pp. 1847-1864
    • Haber, E.1    Ascher, U.2
  • 60
    • 84894234564 scopus 로고
    • Fixed points of nonexpanding maps
    • B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc. 73 (1967), pp. 957–961.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 957-961
    • Halpern, B.1
  • 61
    • 48049104901 scopus 로고    scopus 로고
    • Kaczmarz methods for regularizing nonlinear ill-posed equations II: Applications
    • M. Haltmeier, R. Kowar, A. Leitao, and O. Scherzer, Kaczmarz methods for regularizing nonlinear ill-posed equations II: Applications, Inverse Problems and Imaging 1 (2007), pp. 507–523.
    • (2007) Inverse Problems and Imaging , vol.1 , pp. 507-523
    • Haltmeier, M.1    Kowar, R.2    Leitao, A.3    Scherzer, O.4
  • 62
    • 85044958349 scopus 로고    scopus 로고
    • Kaczmarz methods for regularizing nonlinear ill-posed equations I: Convergence analysis
    • M. Haltmeier, A. Leitao, and O. Scherzer, Kaczmarz methods for regularizing nonlinear ill-posed equations I: convergence analysis, Inverse Problems and Imaging 1 (2007), pp. 289–298.
    • (2007) Inverse Problems and Imaging , vol.1 , pp. 289-298
    • Haltmeier, M.1    Leitao, A.2    Scherzer, O.3
  • 63
    • 0003062572 scopus 로고    scopus 로고
    • A regularization Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems
    • M. Hanke, A regularization Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems, Inverse Problems 13 (1997), pp. 79–95.
    • (1997) Inverse Problems , vol.13 , pp. 79-95
    • Hanke, M.1
  • 64
    • 0031275314 scopus 로고    scopus 로고
    • Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problems
    • M. Hanke, Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problems, Numer. Funct. Anal. Optim. 18 (1997), pp. 971–993.
    • (1997) Numer. Funct. Anal. Optim. , vol.18 , pp. 971-993
    • Hanke, M.1
  • 65
    • 0032400284 scopus 로고    scopus 로고
    • Nonstationary iterated Tikhonov regularization
    • M. Hanke and C. W. Groetsch, Nonstationary iterated Tikhonov regularization, J. Optim. Theory Appl. 98 (1998), pp. 37–53.
    • (1998) J. Optim. Theory Appl. , vol.98 , pp. 37-53
    • Hanke, M.1    Groetsch, C.W.2
  • 67
    • 0040893030 scopus 로고
    • A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
    • M. Hanke, A. Neubauer, and O. Scherzer, A convergence analysis of the Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995), pp. 21–37.
    • (1995) Numer. Math. , vol.72 , pp. 21-37
    • Hanke, M.1    Neubauer, A.2    Scherzer, O.3
  • 68
    • 0033406590 scopus 로고    scopus 로고
    • Two-level preconditioners for regularized inverse problems I: Theory
    • M. Hanke and C. R. Vogel, Two-level preconditioners for regularized inverse problems I: Theory, Numer. Math. 83 (1999), pp. 385–402.
    • (1999) Numer. Math. , vol.83 , pp. 385-402
    • Hanke, M.1    Vogel, C.R.2
  • 71
    • 33749470937 scopus 로고    scopus 로고
    • An iterative method for the inverse scattering problem from sound-hard obstacles
    • F. Hettlich, An iterative method for the inverse scattering problem from sound-hard obstacles, ZAMM 76 (1996), pp. 165–168.
    • (1996) ZAMM , vol.76 , pp. 165-168
    • Hettlich, F.1
  • 72
    • 3042609180 scopus 로고    scopus 로고
    • The Landweber iteration applied to inverse conductive scattering problems
    • F. Hettlich, The Landweber iteration applied to inverse conductive scattering problems, Inverse Problems 14 (1998), pp. 931–947.
    • (1998) Inverse Problems , vol.14 , pp. 931-947
    • Hettlich, F.1
  • 73
    • 0000298487 scopus 로고    scopus 로고
    • Iterative methods for the reconstruction of an inverse potential problem
    • F. Hettlich and W. Rundell, Iterative methods for the reconstruction of an inverse potential problem, Inverse Problems 12 (1996), pp. 251–266.
    • (1996) Inverse Problems , vol.12 , pp. 251-266
    • Hettlich, F.1    Rundell, W.2
  • 74
    • 0011052133 scopus 로고    scopus 로고
    • Recovery of the support of a source term in an elliptic differential equation
    • F. Hettlich, Recovery of the support of a source term in an elliptic differential equation, Inverse Problems 13 (1997), pp. 959–976.
    • (1997) Inverse Problems , vol.13 , pp. 959-976
    • Hettlich, F.1
  • 75
    • 0002215984 scopus 로고    scopus 로고
    • The determination of a discontinuity in a conductivity from a single boundary measurement
    • F. Hettlich, The determination of a discontinuity in a conductivity from a single boundary measurement, Inverse Problems 14 (1998), pp. 67–82.
    • (1998) Inverse Problems , vol.14 , pp. 67-82
    • Hettlich, F.1
  • 76
    • 0009616058 scopus 로고    scopus 로고
    • A second degree method for nonlinear inverse problems
    • F. Hettlich, A second degree method for nonlinear inverse problems, SIAM J. Numer. Anal. 37 (2000), pp. 587–620.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 587-620
    • Hettlich, F.1
  • 77
    • 0000670255 scopus 로고    scopus 로고
    • Logarithmic convergence rates of the iteratively regularized Gauß-Newton method for an inverse potential and an inverse scattering problem
    • T. Hohage, Logarithmic convergence rates of the iteratively regularized Gauß-Newton method for an inverse potential and an inverse scattering problem, Inverse Problems 13 (1997), pp. 1279–1299.
    • (1997) Inverse Problems , vol.13 , pp. 1279-1299
    • Hohage, T.1
  • 78
    • 0004893513 scopus 로고    scopus 로고
    • Convergence rates of a regularized Newton method in sound-hard inverse scattering
    • T. Hohage, Convergence rates of a regularized Newton method in sound-hard inverse scattering, SIAM J. Numer. Anal. 36 (1999), pp. 125–142.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 125-142
    • Hohage, T.1
  • 80
    • 0034187252 scopus 로고    scopus 로고
    • Regularization of exponentially ill-posed problems
    • T. Hohage, Regularization of exponentially ill-posed problems, Numer. Funct. Anal. Optim. 21 (2000), pp. 439–464.
    • (2000) Numer. Funct. Anal. Optim. , vol.21 , pp. 439-464
    • Hohage, T.1
  • 81
    • 0000726131 scopus 로고    scopus 로고
    • A Newton-type method for a transmission problem in inverse scattering
    • T. Hohage and C. Schormann, A Newton-type method for a transmission problem in inverse scattering, Inverse Problems 14 (1998), pp. 1207–1228.
    • (1998) Inverse Problems , vol.14 , pp. 1207-1228
    • Hohage, T.1    Schormann, C.2
  • 82
    • 84860523889 scopus 로고    scopus 로고
    • Statistical and Computational Inverse Problems
    • Springer, New York
    • J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Applied Mathematical Sciences 160. Springer, New York, 2005.
    • (2005) Applied Mathematical Sciences , vol.160
    • Kaipio, J.1    Somersalo, E.2
  • 83
    • 0000130782 scopus 로고    scopus 로고
    • Some Newton type methods for the regularization of nonlinear ill-posed problems
    • B. Kaltenbacher, Some Newton type methods for the regularization of nonlinear ill-posed problems, Inverse Problems 13 (1997), pp. 729–753.
    • (1997) Inverse Problems , vol.13 , pp. 729-753
    • Kaltenbacher, B.1
  • 84
    • 0032164679 scopus 로고    scopus 로고
    • On Broyden’s method for ill-posed problems
    • B. Kaltenbacher, On Broyden’s method for ill-posed problems, Numer. Funct. Anal. Optim. 19 (1998), pp. 807–833.
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , pp. 807-833
    • Kaltenbacher, B.1
  • 85
    • 0032393455 scopus 로고    scopus 로고
    • A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems
    • B. Kaltenbacher, A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems, Numer. Math. 79 (1998), pp. 501–528.
    • (1998) Numer. Math. , vol.79 , pp. 501-528
    • Kaltenbacher, B.1
  • 86
    • 0012966823 scopus 로고    scopus 로고
    • A projection-regularized Newton method for nonlinear ill-posed problems and its application to parameter identification problems with finite element discretization
    • B. Kaltenbacher, A projection-regularized Newton method for nonlinear ill-posed problems and its application to parameter identification problems with finite element discretization, SIAM J. Numer. Anal. 37 (2000), pp. 1885–1908.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 1885-1908
    • Kaltenbacher, B.1
  • 87
    • 0041734177 scopus 로고    scopus 로고
    • Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems
    • B. Kaltenbacher, Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems, Inverse Problems 16 (2000), pp. 1523– 1539.
    • (2000) Inverse Problems , vol.16 , pp. 1523-1539
    • Kaltenbacher, B.1
  • 88
    • 0035419872 scopus 로고    scopus 로고
    • On the regularizing properties of a full multigrid method for ill-posed problems
    • B. Kaltenbacher, On the regularizing properties of a full multigrid method for ill-posed problems, Inverse Problems 17 (2001), pp. 767–788.
    • (2001) Inverse Problems , vol.17 , pp. 767-788
    • Kaltenbacher, B.1
  • 89
    • 0141976336 scopus 로고    scopus 로고
    • V-cycle convergence of some multigrid methods for ill-posed problems
    • B. Kaltenbacher, V-cycle convergence of some multigrid methods for ill-posed problems, Math. Comp. 72 (2003), pp. 1711–1730.
    • (2003) Math. Comp. , vol.72 , pp. 1711-1730
    • Kaltenbacher, B.1
  • 90
    • 0037308881 scopus 로고    scopus 로고
    • Identification of nonlinear B-H curves based on magnetic field computations and multigrid methods for ill-posed problems
    • B. Kaltenbacher, M. Kaltenbacher, and S. Reitzinger, Identification of nonlinear B-H curves based on magnetic field computations and multigrid methods for ill-posed problems, Eur. J. Appl. Math. 14 (2003), pp. 15–38.
    • (2003) Eur. J. Appl. Math. , vol.14 , pp. 15-38
    • Kaltenbacher, B.1    Kaltenbacher, M.2    Reitzinger, S.3
  • 91
    • 33744516421 scopus 로고    scopus 로고
    • Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions
    • B. Kaltenbacher and A. Neubauer, Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions, Inverse Problems 22 (2006), pp. 1105–1119.
    • (2006) Inverse Problems , vol.22 , pp. 1105-1119
    • Kaltenbacher, B.1    Neubauer, A.2
  • 92
    • 0036395618 scopus 로고    scopus 로고
    • Convergence rates of the continuous regularized Gauss-Newton method
    • B. Kaltenbacher, A. Neubauer, and A. G. Ramm, Convergence rates of the continuous regularized Gauss-Newton method, J. Inv. Ill-Posed Problems 10 (2002), pp. 261–280.
    • (2002) J. Inv. Ill-Posed Problems , vol.10 , pp. 261-280
    • Kaltenbacher, B.1    Neubauer, A.2    Ramm, A.G.3
  • 93
    • 0036432049 scopus 로고    scopus 로고
    • A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems
    • B. Kaltenbacher and J. Schicho, A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems, Numer. Math. 93 (2002), pp. 77–107.
    • (2002) Numer. Math. , vol.93 , pp. 77-107
    • Kaltenbacher, B.1    Schicho, J.2
  • 94
    • 0001224287 scopus 로고
    • Multilevel algorithms for ill-posed problems
    • J. T. King, Multilevel algorithms for ill-posed problems, Numer. Math. 61 (1992), pp. 311–334.
    • (1992) Numer. Math. , vol.61 , pp. 311-334
    • King, J.T.1
  • 95
    • 36149033735 scopus 로고
    • The domain derivative and two applications in inverse scattering theory
    • A. Kirsch, The domain derivative and two applications in inverse scattering theory, Inverse Problems 9 (1993), pp. 81–96.
    • (1993) Inverse Problems , vol.9 , pp. 81-96
    • Kirsch, A.1
  • 97
    • 84990623154 scopus 로고
    • Optimal design and relaxation of variational problems. I
    • R. Kohn and G. Strang, Optimal design and relaxation of variational problems. I, Comm. Pure Appl. Math. 39 (1986), pp. 113–137.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 113-137
    • Kohn, R.1    Strang, G.2
  • 98
    • 84990602642 scopus 로고
    • Optimal design and relaxation of variational problems. II
    • R. Kohn, Optimal design and relaxation of variational problems. II, Comm. Pure Appl. Math. 39 (1986), pp. 139–182.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 139-182
    • Kohn, R.1
  • 99
    • 84990617033 scopus 로고
    • Optimal design and relaxation of variational problems. III
    • R. Kohn, Optimal design and relaxation of variational problems. III, Comm. Pure Appl. Math. 39 (1986), pp. 353–377.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 353-377
    • Kohn, R.1
  • 100
    • 10044264317 scopus 로고    scopus 로고
    • Saving lives, one land mine at a time, IEEE
    • K. Kowalenko, Saving lives, one land mine at a time, IEEE, The Institute 28 (2004), pp. 1, 10–11.
    • (2004) The Institute , vol.28-11 , pp. 1
    • Kowalenko, K.1
  • 101
    • 33744541048 scopus 로고    scopus 로고
    • Convergence analysis of a Landweber-Kaczmarz method for solving nonlinear ill-posed problems
    • (V. G. Romanov, S. I. Kabanikhin, Yu. E. Anikonov, and A. L. Bukhgeim, eds.), pp., VSP, Zeist
    • R. Kowar and O. Scherzer, Convergence analysis of a Landweber-Kaczmarz method for solving nonlinear ill-posed problems. Ill-Posed and Inverse Problems (V. G. Romanov, S. I. Kabanikhin, Yu. E. Anikonov, and A. L. Bukhgeim, eds.), pp. 69– 90. VSP, Zeist, 2002.
    • (2002) Ill-Posed and Inverse Problems , pp. 69-90
    • Kowar, R.1    Scherzer, O.2
  • 103
    • 0000865204 scopus 로고
    • A quasi-Newton method in inverse obstacle scattering
    • R. Kress and W. Rundell, A quasi-Newton method in inverse obstacle scattering, Inverse Problems 10 (1994), pp. 1145–1157.
    • (1994) Inverse Problems , vol.10 , pp. 1145-1157
    • Kress, R.1    Rundell, W.2
  • 105
    • 0032860847 scopus 로고    scopus 로고
    • Thermoacoustic computed tomography – technical considerations
    • R. A. Kruger, D. R. Reinecke, and G. A. Kruger, Thermoacoustic computed tomography – technical considerations, Medical Physics 26 (1999), pp. 1832–1837.
    • (1999) Medical Physics , vol.26 , pp. 1832-1837
    • Kruger, R.A.1    Reinecke, D.R.2    Kruger, G.A.3
  • 106
    • 0036033582 scopus 로고    scopus 로고
    • Thermoacoustic CT of the Breast, Proc
    • R. A. Kruger, K. M. Stantz, and W. L. Kiser, Thermoacoustic CT of the Breast, Proc. SPIE 4682 (2002), pp. 521–525.
    • (2002) SPIE , vol.4682 , pp. 521-525
    • Kruger, R.A.1    Stantz, K.M.2    Kiser, W.L.3
  • 107
    • 0348207563 scopus 로고    scopus 로고
    • A derivative free Landweber iteration for parameter identification in certain elliptic PDEs
    • P. Kügler, A derivative free Landweber iteration for parameter identification in certain elliptic PDEs, Inverse Problems 19 (2003), pp. 1407–1426.
    • (2003) Inverse Problems , vol.19 , pp. 1407-1426
    • Kügler, P.1
  • 109
    • 4544220701 scopus 로고    scopus 로고
    • Identification of a temperature dependent heat conductivity from single boundary measurements
    • P. Kügler, Identification of a temperature dependent heat conductivity from single boundary measurements, SIAM J. Numer. Anal. 41 (2003), pp. 1543–1563.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1543-1563
    • Kügler, P.1
  • 110
    • 0000518587 scopus 로고
    • An iteration formula for Fredholm integral equations of the first kind
    • L. Landweber, An iteration formula for Fredholm integral equations of the first kind, Amer. J. Math. 73 (1951), pp. 615–624.
    • (1951) Amer. J. Math. , vol.73 , pp. 615-624
    • Landweber, L.1
  • 111
    • 0003796632 scopus 로고
    • Springer, Berlin, Heidelberg, New York
    • V. G. Maz’ya, Sobolev Spaces. Springer, Berlin, Heidelberg, New York, 1985.
    • (1985) Sobolev Spaces
    • Maz’Ya, V.G.1
  • 112
    • 34250413705 scopus 로고
    • An iterative procedure for the solution of constrained nonlinear equations with applications to optimization problems
    • S. F. McCormick, An iterative procedure for the solution of constrained nonlinear equations with applications to optimization problems, Numer. Math. 23 (1975), pp. 371–385.
    • (1975) Numer. Math. , vol.23 , pp. 371-385
    • McCormick, S.F.1
  • 113
    • 5644249938 scopus 로고
    • The methods of Kaczmarz and row orthogonalization for solving linear equations and least squares problems in Hilbert space
    • S. F. McCormick, The methods of Kaczmarz and row orthogonalization for solving linear equations and least squares problems in Hilbert space, Indiana Univ. Math. J. 26 (1977), pp. 1137–1150.
    • (1977) Indiana Univ. Math. J. , vol.26 , pp. 1137-1150
    • McCormick, S.F.1
  • 114
    • 0016470075 scopus 로고
    • A uniform approach to gradient methods for linear operator equations
    • S. F. McCormick and G. H. Rodrigue, A uniform approach to gradient methods for linear operator equations, J. Math. Anal. Appl. 49 (1975), pp. 275–285.
    • (1975) J. Math. Anal. Appl. , vol.49 , pp. 275-285
    • McCormick, S.F.1    Rodrigue, G.H.2
  • 115
    • 34250147449 scopus 로고
    • Solution of underdetermined nonlinear equations by stationary iteration methods
    • K. H. Meyn, Solution of underdetermined nonlinear equations by stationary iteration methods, Numer. Math. 42 (1983), pp. 161–172.
    • (1983) Numer. Math. , vol.42 , pp. 161-172
    • Meyn, K.H.1
  • 116
    • 0000739264 scopus 로고
    • On the solution of functional equations by the method of regularization
    • V. A. Morozov, On the solution of functional equations by the method of regularization, Soviet Math. Dokl. 7 (1966), pp. 414–417.
    • (1966) Soviet Math. Dokl. , vol.7 , pp. 414-417
    • Morozov, V.A.1
  • 118
    • 21344485372 scopus 로고
    • Convergence of Newton-like methods for singular operator equations using outer inverses
    • M. Z. Nashed and X. Chen, Convergence of Newton-like methods for singular operator equations using outer inverses, Numer. Math. 66 (1993), pp. 235–257.
    • (1993) Numer. Math. , vol.66 , pp. 235-257
    • Nashed, M.Z.1    Chen, X.2
  • 119
    • 0000363718 scopus 로고
    • Regularisierung schlecht gestellter Probleme durch Projektionsver-fahren
    • F. Natterer, Regularisierung schlecht gestellter Probleme durch Projektionsver-fahren, Numer. Math. 28 (1977), pp. 329–341.
    • (1977) Numer. Math. , vol.28 , pp. 329-341
    • Natterer, F.1
  • 120
    • 84951418001 scopus 로고
    • Error bounds for Tikhonov regularization in Hilbert scales
    • F. Natterer, Error bounds for Tikhonov regularization in Hilbert scales, Appl. Anal. 18 (1984), pp. 29–37.
    • (1984) Appl. Anal. , vol.18 , pp. 29-37
    • Natterer, F.1
  • 123
    • 84948247213 scopus 로고
    • Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales
    • A. Neubauer, Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales, Appl. Anal. 46 (1992), pp. 59–72.
    • (1992) Appl. Anal. , vol.46 , pp. 59-72
    • Neubauer, A.1
  • 124
    • 0034381932 scopus 로고    scopus 로고
    • On Landweber iteration for nonlinear ill-posed problems in Hilbert scales
    • A. Neubauer, On Landweber iteration for nonlinear ill-posed problems in Hilbert scales, Numer. Math. 85 (2000), pp. 309–328.
    • (2000) Numer. Math. , vol.85 , pp. 309-328
    • Neubauer, A.1
  • 125
    • 0010013232 scopus 로고
    • A convergent rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems
    • A. Neubauer and O. Scherzer, A convergent rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems, ZAA 14 (1995), pp. 369–377.
    • (1995) ZAA , vol.14 , pp. 369-377
    • Neubauer, A.1    Scherzer, O.2
  • 126
    • 0003754684 scopus 로고    scopus 로고
    • Level set methods and dynamic implicit surfaces
    • Springer, New York
    • S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces, Applied Mathematical Sciences 153. Springer, New York, 2003.
    • (2003) Applied Mathematical Sciences , vol.153
    • Osher, S.1    Fedkiw, R.2
  • 127
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988), pp. 12–49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 128
    • 33745677836 scopus 로고    scopus 로고
    • Monotonicity-preserving interproximation for BH curves
    • C. Pechstein and B. Jüttler, Monotonicity-preserving interproximation for BH curves, J. Comp. Appl. Math. 196 (2006), pp. 45–57.
    • (2006) J. Comp. Appl. Math. , vol.196 , pp. 45-57
    • Pechstein, C.1    Jüttler, B.2
  • 129
    • 0013235011 scopus 로고    scopus 로고
    • On the characterization of self-regularization properties of a fully discrete projection method for Symm’s integral equation
    • S. V. Pereverzev and S. Prößdorf, On the characterization of self-regularization properties of a fully discrete projection method for Symm’s integral equation, J. Integral Equations Appl. 12 (2000), pp. 113–130.
    • (2000) J. Integral Equations Appl. , vol.12 , pp. 113-130
    • Pereverzev, S.V.1    Prößdorf, S.2
  • 130
    • 0000824964 scopus 로고
    • Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings
    • W. V. Petryshyn and T. E. Williamson, Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl. 43 (1973), pp. 459–497.
    • (1973) J. Math. Anal. Appl. , vol.43 , pp. 459-497
    • Petryshyn, W.V.1    Williamson, T.E.2
  • 132
    • 0003056816 scopus 로고
    • On the regularization of projection methods for solving ill-posed problems
    • R. Plato and G. Vainikko, On the regularization of projection methods for solving ill-posed problems, Numer. Math. 57 (1990), pp. 63–79.
    • (1990) Numer. Math. , vol.57 , pp. 63-79
    • Plato, R.1    Vainikko, G.2
  • 133
    • 85144383170 scopus 로고
    • J. Radon, Gesammelte Abhandlungen – Collected Works, Band 2 (P. M. Gruber, E. Hlawka, W. Nöbauer, and L. Schmetterer, eds.). Verlag d. Österr. Akad. d. Wiss., Birkhäuser, Basel
    • J. Radon, Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten (reprinted). J. Radon, Gesammelte Abhandlungen – Collected Works, Band 2 (P. M. Gruber, E. Hlawka, W. Nöbauer, and L. Schmetterer, eds.). Verlag d. Österr. Akad. d. Wiss., Birkhäuser, Basel, 1987.
    • (1987) Über Die Bestimmung Von Funktionen Durch Ihre Integralwerte längs Gewisser Mannigfaltigkeiten (Reprinted)
    • Radon, J.1
  • 134
    • 0032687625 scopus 로고    scopus 로고
    • A modified Landweber-method for inverse problems
    • R. Ramlau, A modified Landweber-method for inverse problems, Numer. Funct. Anal. Optim. 20 (1999), pp. 79–98.
    • (1999) Numer. Funct. Anal. Optim. , vol.20 , pp. 79-98
    • Ramlau, R.1
  • 135
    • 0032642260 scopus 로고    scopus 로고
    • A numerical method for solving nonlinear ill-posed problems
    • A. G. Ramm and A. B. Smirnova, A numerical method for solving nonlinear ill-posed problems, Numer. Funct. Anal. Optim. 20 (1999), pp. 317–332.
    • (1999) Numer. Funct. Anal. Optim. , vol.20 , pp. 317-332
    • Ramm, A.G.1    Smirnova, A.B.2
  • 136
    • 0031542819 scopus 로고    scopus 로고
    • A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization
    • A. Rieder, A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization, Numer. Math. 75 (1997), pp. 501–522.
    • (1997) Numer. Math. , vol.75 , pp. 501-522
    • Rieder, A.1
  • 137
    • 0035590701 scopus 로고    scopus 로고
    • On convergence rates of inexact Newton regularizations
    • A. Rieder, On convergence rates of inexact Newton regularizations, Numer. Math. 88 (2001), pp. 347–365.
    • (2001) Numer. Math. , vol.88 , pp. 347-365
    • Rieder, A.1
  • 138
    • 33646472477 scopus 로고    scopus 로고
    • Inexact Newton regularization using conjugate gradients as inner iteration
    • A. Rieder, Inexact Newton regularization using conjugate gradients as inner iteration, SIAM J. Numer. Anal. 43 (2005), pp. 604–622.
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 604-622
    • Rieder, A.1
  • 139
    • 0022718875 scopus 로고
    • Broyden’s method in Hilbert space
    • E. W. Sachs, Broyden’s method in Hilbert space, Mathematical Programming 35 (1986), pp. 71–82.
    • (1986) Mathematical Programming , vol.35 , pp. 71-82
    • Sachs, E.W.1
  • 140
    • 84996143735 scopus 로고
    • A level-set approach for inverse problems involving obstacles
    • pp
    • F. Santosa, A level-set approach for inverse problems involving obstacles, ESAIM Contrôle Optim. Calc. Var. 1 (1995/96), pp. 17–33.
    • (1995) ESAIM Contrôle Optim. Calc. Var. , vol.1 , pp. 17-33
    • Santosa, F.1
  • 141
    • 0010014032 scopus 로고
    • Convergence criteria of iterative methods based on Landweber iteration for nonlinear problems
    • O. Scherzer, Convergence criteria of iterative methods based on Landweber iteration for nonlinear problems, J. Math. Anal. Appl. 194 (1995), pp. 911–933.
    • (1995) J. Math. Anal. Appl. , vol.194 , pp. 911-933
    • Scherzer, O.1
  • 142
    • 0041098562 scopus 로고    scopus 로고
    • A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems
    • O. Scherzer, A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems, Numer. Funct. Anal. Optim. 17 (1996), pp. 197–214.
    • (1996) Numer. Funct. Anal. Optim. , vol.17 , pp. 197-214
    • Scherzer, O.1
  • 143
    • 0032335142 scopus 로고    scopus 로고
    • An iterative multi level algorithm for solving nonlinear ill-posed problems
    • O. Scherzer, An iterative multi level algorithm for solving nonlinear ill-posed problems, Numer. Math. 80 (1998), pp. 570–600.
    • (1998) Numer. Math. , vol.80 , pp. 570-600
    • Scherzer, O.1
  • 144
    • 0032122772 scopus 로고    scopus 로고
    • A modified Landweber iteration for solving parameter estimation problems
    • O. Scherzer, A modified Landweber iteration for solving parameter estimation problems, Appl. Math. Optim. 38 (1998), pp. 45–68.
    • (1998) Appl. Math. Optim. , vol.38 , pp. 45-68
    • Scherzer, O.1
  • 146
    • 31844445760 scopus 로고    scopus 로고
    • Nonlinear iterative methods for linear ill-posed problems in Banach spaces
    • F. Schöpfer, A. K. Louis, and T. Schuster, Nonlinear iterative methods for linear ill-posed problems in Banach spaces, Inverse Problems 22 (2006), pp. 311–329.
    • (2006) Inverse Problems , vol.22 , pp. 311-329
    • Schöpfer, F.1    Louis, A.K.2    Schuster, T.3
  • 147
    • 0008522406 scopus 로고
    • Nonconvergence results for the application of least-squares estimation to ill-posed problems
    • T. I. Seidman, Nonconvergence results for the application of least-squares estimation to ill-posed problems, J. Optim. Theory Appl. 30 (1980), pp. 535–547.
    • (1980) J. Optim. Theory Appl. , vol.30 , pp. 535-547
    • Seidman, T.I.1
  • 150
    • 0013243263 scopus 로고
    • On the asymptotical regularization of nonlinear ill-posed problems
    • U. Tautenhahn, On the asymptotical regularization of nonlinear ill-posed problems, Inverse Problems 10 (1994), pp. 1405–1418.
    • (1994) Inverse Problems , vol.10 , pp. 1405-1418
    • Tautenhahn, U.1
  • 151
    • 0013286501 scopus 로고
    • Projection methods and self-regularization in ill-posed problems
    • G. Vainikko and U. Hämarik, Projection methods and self-regularization in ill-posed problems, Sov. Math. 29 (1985), pp. 1–20.
    • (1985) Sov. Math. , vol.29 , pp. 1-20
    • Vainikko, G.1    Hämarik, U.2
  • 152
    • 0039599972 scopus 로고
    • Error estimates of the successive approximation method for ill-posed problems
    • G. M. Vainikko, Error estimates of the successive approximation method for ill-posed problems, Automat. Remote Control 40 (1980), pp. 356–363.
    • (1980) Automat. Remote Control , vol.40 , pp. 356-363
    • Vainikko, G.M.1
  • 154
    • 38249030933 scopus 로고
    • Iterative methods for solving ill-posed problems with a priori information in Hilbert spaces
    • V. V. Vasin, Iterative methods for solving ill-posed problems with a priori information in Hilbert spaces, USSR Comput. Math. Math. Phys. 28 (1988), pp. 6–13.
    • (1988) USSR Comput. Math. Math. Phys. , vol.28 , pp. 6-13
    • Vasin, V.V.1
  • 156
    • 33845879408 scopus 로고    scopus 로고
    • Seeing the invisible, IEEE
    • E. Vonderheid, Seeing the invisible, IEEE, The Institute 27 (2003), pp. 1, 13.
    • (2003) The Institute 27 , vol.13 , pp. 1
    • Vonderheid, E.1
  • 157
    • 85144454706 scopus 로고
    • Proceedings of the 1995 Design Engineering Technical Conferences, Vibration Control, Analysis, and Identification
    • (eds.)
    • K.-W. Wang et al. (eds.), Proceedings of the 1995 Design Engineering Technical Conferences, Vibration Control, Analysis, and Identification, Vol. 3, Part C. The American Society of Mechanical Engineers, New York, 1995.
    • (1995) Part C. the American Society of Mechanical Engineers, New York , vol.3
    • Wang, K.-W.1
  • 158
    • 0004018866 scopus 로고    scopus 로고
    • Institute of Physics Publishing, Bristol, Philadelphia,, reprint of the 1988 edition
    • S. Webb (ed.), The Physics of Medical Imaging. Institute of Physics Publishing, Bristol, Philadelphia, 2000, reprint of the 1988 edition.
    • (2000) The Physics of Medical Imaging
    • Webb, S.1
  • 159
    • 0038509905 scopus 로고    scopus 로고
    • In industry, seeing is believing
    • R. West, In industry, seeing is believing, Physics World (2003), pp. 27–30.
    • (2003) Physics World , pp. 27-30
    • West, R.1
  • 160
    • 28844438544 scopus 로고    scopus 로고
    • Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction
    • M. Xu and L.-H. V. Wang, Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction, Physical Review E 67 (2003), pp. 1–15.
    • (2003) Physical Review E , vol.67 , pp. 1-15
    • Xu, M.1    Wang, L.-H.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.