메뉴 건너뛰기




Volumn 25, Issue 11, 2009, Pages

Nonlinear regularization methods for ill-posed problems with piecewise constant or strongly varying solutions

Author keywords

[No Author keywords available]

Indexed keywords

AUXILIARY FUNCTIONS; BENCH-MARK PROBLEMS; CAUCHY PROBLEMS; ILL POSED; ILL POSED PROBLEM; LEVEL SETS; NON-LINEAR TRANSFORMATIONS; NONLINEAR ILL-POSED PROBLEMS; NUMERICAL EXAMPLE; PIECEWISE CONSTANT; REGULARIZATION METHODS; REGULARIZATION THEORY; REGULARIZED APPROXIMATION; SMOOTH APPROXIMATION; SMOOTH FUNCTIONS; SOLUTION SPACE;

EID: 70450191696     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/11/115014     Document Type: Article
Times cited : (30)

References (31)
  • 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
    • 33748750897 scopus 로고    scopus 로고
    • Solving elliptic Cauchy problems and the identification of nonlinear corrosion
    • Alessandrini G and Sincich E 2007 Solving elliptic Cauchy problems and the identification of nonlinear corrosion J. Comput. Appl. Math. 198 307-20
    • (2007) J. Comput. Appl. Math. , vol.198 , pp. 307-320
    • Alessandrini, G.1    Sincich, E.2
  • 5
    • 0000834834 scopus 로고
    • The problem of the convergence of the iteratively regularized Gau-Newton method
    • Bakushinskii A B 1992 The problem of the convergence of the iteratively regularized Gau-Newton method Comput. Math. Math. Phys. 32 1353-9
    • (1992) Comput. Math. Math. Phys. , vol.32 , pp. 1353-1359
    • Bakushinskii, A.B.1
  • 6
    • 33947371334 scopus 로고    scopus 로고
    • Why is the Cauchy problem severely ill-posed?
    • Ben Belgacem F 2007 Why is the Cauchy problem severely ill-posed? Inverse Problems 23 823-36
    • (2007) Inverse Problems , vol.23 , pp. 823-836
    • Ben Belgacem, F.1
  • 7
    • 0035473388 scopus 로고    scopus 로고
    • A level set method for inverse problems
    • Burger M 2001 A level set method for inverse problems Inverse Problems 17 1327-55
    • (2001) Inverse Problems , vol.17 , pp. 1327-1355
    • Burger, M.1
  • 8
    • 84923072065 scopus 로고    scopus 로고
    • Integral equations for inverse problems in corrosion detection from partial Cauchy data
    • Cakoni F and Kress R 2007 Integral equations for inverse problems in corrosion detection from partial Cauchy data Inverse Problems Imaging 1 229-45
    • (2007) Inverse Problems Imaging , vol.1 , pp. 229-245
    • Cakoni, F.1    Kress, R.2
  • 9
    • 0029328073 scopus 로고
    • Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations
    • Chambolle A 1995 Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations SIAM J. Appl. Math. 55 827-63
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 827-863
    • Chambolle, A.1
  • 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 R67-131
    • (2006) Inverse Problems , vol.22
    • Dorn, O.1    Lesselier, D.2
  • 12
    • 34047158696 scopus 로고    scopus 로고
    • Preconditioning CGNE-iterations for inverse problems
    • Egger H 2007 Preconditioning CGNE-iterations for inverse problems Numer. Line Algebra Appl. 14 183-96
    • (2007) Numer. Line Algebra Appl. , vol.14 , pp. 183-196
    • Egger, H.1
  • 13
    • 26644456996 scopus 로고    scopus 로고
    • Preconditioning Landweber iteration in Hilbert scales
    • Egger H and Neubauer A 2005 Preconditioning Landweber iteration in Hilbert scales Numer. Math. 101 643-62
    • (2005) Numer. Math. , vol.101 , pp. 643-662
    • Egger, H.1    Neubauer, A.2
  • 15
    • 0035518988 scopus 로고    scopus 로고
    • A Mann iterative regularization method for elliptic Cauchy problems
    • Engl H and Leitão A 2001 A Mann iterative regularization method for elliptic Cauchy problems Numer. Funct. Anal. Optim. 22 861-4
    • (2001) Numer. Funct. Anal. Optim. , vol.22 , pp. 861-864
    • Engl, H.1    Leitão, A.2
  • 16
    • 0023288851 scopus 로고
    • Detection of mines by electric measurements
    • Friedman A 1987 Detection of mines by electric measurements SIAM J. Appl. Math. 47 201-12
    • (1987) SIAM J. Appl. Math. , vol.47 , pp. 201-212
    • Friedman, A.1
  • 17
    • 27744433287 scopus 로고    scopus 로고
    • Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators
    • Frühauf F, Scherzer O and Leitão 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    Leitão, A.3
  • 19
    • 0031212101 scopus 로고    scopus 로고
    • An inverse problem in corrosion detection
    • Inglese G 1997 An inverse problem in corrosion detection Inverse Problems 13 977-94
    • (1997) Inverse Problems , vol.13 , pp. 977-994
    • Inglese, G.1
  • 20
    • 0030088214 scopus 로고    scopus 로고
    • A review of reconstruction techniques for capacitance tomography
    • Isaksen O 1996 A review of reconstruction techniques for capacitance tomography Meas. Sci. Technol. 7 325-37 (Pubitemid 126574905)
    • (1996) Measurement Science and Technology , vol.7 , Issue.3 , pp. 325-337
    • Isaksen, O.1
  • 21
    • 0032393455 scopus 로고    scopus 로고
    • A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems
    • Kaltenbacher B 1998 A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems Numer. Math. 79 501-28
    • (1998) Numer. Math. , vol.79 , pp. 501-528
    • Kaltenbacher, B.1
  • 22
    • 0034250874 scopus 로고    scopus 로고
    • An iterative method for solving elliptic Cauchy problems
    • Leitão A 2000 An iterative method for solving elliptic Cauchy problems Numer. Funct. Anal. Optim. 21 715-42
    • (2000) Numer. Funct. Anal. Optim. , vol.21 , pp. 715-742
    • Leitão, A.1
  • 23
    • 33744522439 scopus 로고    scopus 로고
    • On inverse doping profile problems for the stationary voltage-current map
    • Leitão A, Markowich P A and Zubelli J P 2006 On inverse doping profile problems for the stationary voltage-current map Inverse Problems 22 1071-88
    • (2006) Inverse Problems , vol.22 , pp. 1071-1088
    • Leitão, A.1    Markowich, P.A.2    Zubelli, J.P.3
  • 24
    • 0037275743 scopus 로고    scopus 로고
    • On the relation between constraint regularization, level sets, and shape optimization
    • Leitão A and Scherzer O 2003 On the relation between constraint regularization, level sets, and shape optimization Inverse Problems 19 L1-11
    • (2003) Inverse Problems , vol.19
    • Leitão, A.1    Scherzer, O.2
  • 25
    • 84990602490 scopus 로고
    • Optimal approximation by piecewise smooth functions and associated variational problems
    • Mumford D and Shah J 1989 Optimal approximation by piecewise smooth functions and associated variational problems Commun. Pure Appl. Math 42 577-685
    • (1989) Commun. Pure Appl. Math , vol.42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 26
    • 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
  • 27
    • 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
  • 28
    • 84996143735 scopus 로고    scopus 로고
    • A level set approach for inverse problems involving obstacles
    • Santosa F 1996 A level set approach for inverse problems involving obstacles ESAIM: Control optim. Calc. Var. 1 17-33
    • (1996) ESAIM: Control Optim. Calc. Var. , vol.1 , pp. 17-33
    • Santosa, F.1
  • 30
    • 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
  • 31
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.