메뉴 건너뛰기




Volumn 24, Issue 5, 2008, Pages

An iterative regularization method for the solution of the split feasibility problem in Banach spaces

Author keywords

[No Author keywords available]

Indexed keywords


EID: 54749125796     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/24/5/055008     Document Type: Article
Times cited : (144)

References (55)
  • 1
    • 0031537910 scopus 로고    scopus 로고
    • Convergence of Bregman projection methods for solving consistent convex feasibility problems in reflexive Banach spaces
    • Alber Y and Butnariu D 1997 Convergence of Bregman projection methods for solving consistent convex feasibility problems in reflexive Banach spaces J. Optim. Theory Appl. 92 33-61
    • (1997) J. Optim. Theory Appl. , vol.92 , Issue.1 , pp. 33-61
    • Alber, Y.1    Butnariu, D.2
  • 2
    • 31844434480 scopus 로고
    • Iterative regularization in Banach spaces
    • Alber Y I 1986 Iterative regularization in Banach spaces Sov. Math. (Iz. VUZ) 30 1-8
    • (1986) Sov. Math. (Iz. VUZ) , vol.30 , pp. 1-8
    • Alber, Y.I.1
  • 3
    • 0001769375 scopus 로고
    • On some estimates for projection operators in Banach spaces
    • Alber Y I and Notik A I 1995 On some estimates for projection operators in Banach spaces Commun. Appl. Nonlinear Anal. 2 47-55
    • (1995) Commun. Appl. Nonlinear Anal. , vol.2 , pp. 47-55
    • Alber, Y.I.1    Notik, A.I.2
  • 4
    • 0002780670 scopus 로고    scopus 로고
    • Iterative solution of unstable variational inequalities on approximately given sets
    • Alber Y I, Kartsatos A G and Litsyn E 1996 Iterative solution of unstable variational inequalities on approximately given sets Abstr. Appl. Anal. 1 45-64
    • (1996) Abstr. Appl. Anal. , vol.1 , Issue.1 , pp. 45-64
    • Alber, Y.I.1    Kartsatos, A.G.2    Litsyn, E.3
  • 5
    • 21744459385 scopus 로고    scopus 로고
    • Legendre functions and the method of random Bregman projections
    • Bauschke H H and Borwein J M 1997 Legendre functions and the method of random Bregman projections J. Convex Anal. 4 27-67
    • (1997) J. Convex Anal. , vol.4 , pp. 27-67
    • Bauschke, H.H.1    Borwein, J.M.2
  • 6
    • 0345138997 scopus 로고    scopus 로고
    • Construction of best Bregman approximations in reflexive Banach spaces
    • Bauschke H H and Combettes P L 2003 Construction of best Bregman approximations in reflexive Banach spaces Proc. Am. Math. Soc. 131 3757-66
    • (2003) Proc. Am. Math. Soc. , vol.131 , Issue.12 , pp. 3757-3766
    • Bauschke, H.H.1    Combettes, P.L.2
  • 7
    • 0042391294 scopus 로고    scopus 로고
    • Dykstra's algorithm with Bregman projections: A convergence proof
    • Bauschke H H and Lewis A S 2000 Dykstra's algorithm with Bregman projections: a convergence proof Optimization 48 409-27
    • (2000) Optimization , vol.48 , Issue.4 , pp. 409-427
    • Bauschke, H.H.1    Lewis, A.S.2
  • 8
    • 23044531274 scopus 로고    scopus 로고
    • Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces
    • Bauschke H H, Borwein J M and Combettes P L 2001 Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces Commun. Contemp. Math. 3 615-47
    • (2001) Commun. Contemp. Math. , vol.3 , Issue.4 , pp. 615-647
    • Bauschke, H.H.1    Borwein, J.M.2    Combettes, P.L.3
  • 11
    • 41449101407 scopus 로고    scopus 로고
    • A generalized conditional gradient method for non-linear operator equations with sparsity constraints
    • Bredies K, Bonesky T, Lorenz D A and Maass P 2007 A generalized conditional gradient method for non-linear operator equations with sparsity constraints Inverse Problems 23 2041-58
    • (2007) Inverse Problems , vol.23 , Issue.5 , pp. 2041-2058
    • Bredies, K.1    Bonesky, T.2    Lorenz, D.A.3    Maass, P.4
  • 12
    • 49949144765 scopus 로고
    • The relaxation method for finding common points of convex sets and its application to the solution of problems in convex programming
    • Bregman L M 1967 The relaxation method for finding common points of convex sets and its application to the solution of problems in convex programming USSR Comput. Math. Math. Phys. 7 200-17
    • (1967) USSR Comput. Math. Math. Phys. , vol.7 , Issue.3 , pp. 200-217
    • Bregman, L.M.1
  • 13
    • 0034769650 scopus 로고    scopus 로고
    • A proximal point method for the variational inequality problem in Banach spaces
    • Burachik R S and Scheimberg S 2001 A proximal point method for the variational inequality problem in Banach spaces SIAM J. Control Optim. 39 1633-49
    • (2001) SIAM J. Control Optim. , vol.39 , Issue.5 , pp. 1633-1649
    • Burachik, R.S.1    Scheimberg, S.2
  • 14
    • 36549078210 scopus 로고    scopus 로고
    • Error estimation for Bregman iterations and inverse scale space methods in image restoration
    • Burger M, Resmerita E and He L 2007 Error estimation for Bregman iterations and inverse scale space methods in image restoration Computing 81 109-35 (Special Issue on Industrial Geometry) Guest ed B Jüttler, H Pottmann, O Scherzer
    • (2007) Computing , vol.81 , Issue.2-3 , pp. 109-135
    • Burger, M.1    Resmerita, E.2    He, L.3
  • 16
    • 31844434904 scopus 로고    scopus 로고
    • Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces
    • pp
    • Butnariu D and Resmerita E 2006 Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces Abstr. Appl. Anal. 39 pp Article ID 84919
    • (2006) Abstr. Appl. Anal. , pp. 39
    • Butnariu, D.1    Resmerita, E.2
  • 17
    • 85174220880 scopus 로고    scopus 로고
    • Total convexity for powers of the norm in uniformly convex Banach spaces
    • Butnariu D, Iusem A N and Resmerita E 2000 Total convexity for powers of the norm in uniformly convex Banach spaces J. Convex Anal. 7 319-34
    • (2000) J. Convex Anal. , vol.7 , pp. 319-334
    • Butnariu, D.1    Iusem, A.N.2    Resmerita, E.3
  • 18
    • 0042972614 scopus 로고    scopus 로고
    • On uniform convexity, total convexity and convergence of the proximal point and outer Bregman projection algorithms in Banach spaces
    • Butnariu D, Iusem A N and Zlinescu C 2003 On uniform convexity, total convexity and convergence of the proximal point and outer Bregman projection algorithms in Banach spaces J. Convex Anal. 10 35-61
    • (2003) J. Convex Anal. , vol.10 , pp. 35-61
    • Butnariu, D.1    Iusem, A.N.2    Zlinescu, C.3
  • 19
    • 0036538286 scopus 로고    scopus 로고
    • Iterative oblique projection onto convex sets and the split feasibility problem
    • Byrne C 2002 Iterative oblique projection onto convex sets and the split feasibility problem Inverse Problems 18 441-53
    • (2002) Inverse Problems , vol.18 , Issue.2 , pp. 441-453
    • Byrne, C.1
  • 20
    • 1342265919 scopus 로고    scopus 로고
    • A unified treatment of some iterative algorithms in signal processing and image reconstruction
    • Byrne C 2004 A unified treatment of some iterative algorithms in signal processing and image reconstruction Inverse Problems 20 103-20
    • (2004) Inverse Problems , vol.20 , Issue.1 , pp. 103-120
    • Byrne, C.1
  • 21
    • 0035565698 scopus 로고    scopus 로고
    • Proximity function minimization using multiple Bregman projections, with applications to split feasibility and Kullback-leibler distance minimization
    • Byrne C and Censor Y 2001 Proximity function minimization using multiple Bregman projections, with applications to split feasibility and Kullback-leibler distance minimization Ann. Oper. Res. 105 77-98
    • (2001) Ann. Oper. Res. , vol.105 , pp. 77-98
    • Byrne, C.1    Censor, Y.2
  • 22
    • 0037289090 scopus 로고    scopus 로고
    • Block-iterative algorithms with underrelaxed Bregman projections
    • Censor Y and Herman G T 2002 Block-iterative algorithms with underrelaxed Bregman projections SIAM J. Optim. 13 283-97
    • (2002) SIAM J. Optim. , vol.13 , Issue.1 , pp. 283-297
    • Censor, Y.1    Herman, G.T.2
  • 24
    • 28544451131 scopus 로고    scopus 로고
    • The multiple-sets split feasibility problem and its applications for inverse problems
    • Censor Y, Elfving T, Kopf N and Bortfeld T 2005 The multiple-sets split feasibility problem and its applications for inverse problems Inverse Problems 21 2071-84
    • (2005) Inverse Problems , vol.21 , Issue.6 , pp. 2071-2084
    • Censor, Y.1    Elfving, T.2    Kopf, N.3    Bortfeld, T.4
  • 25
    • 33751021369 scopus 로고    scopus 로고
    • Perturbed projections and subgradient projections for the multiple-sets split feasibility problem
    • Censor Y, Motova A and Segal A 2007 Perturbed projections and subgradient projections for the multiple-sets split feasibility problem J. Math. Anal. Appl. 327 1244-56
    • (2007) J. Math. Anal. Appl. , vol.327 , Issue.2 , pp. 1244-1256
    • Censor, Y.1    Motova, A.2    Segal, A.3
  • 27
    • 0027541192 scopus 로고
    • The foundations of set-theoretic estimation
    • Combettes P L 1993 The foundations of set-theoretic estimation Proc. IEEE 81 182-208
    • (1993) Proc. IEEE , vol.81 , Issue.2 , pp. 182-208
    • Combettes, P.L.1
  • 28
    • 77954607855 scopus 로고    scopus 로고
    • The convex feasibility problem in image recovery
    • Combettes P L 1996 The convex feasibility problem in image recovery Adv. Imaging Electron Phys. 95 155-270
    • (1996) Adv. Imaging Electron Phys. , vol.95 , pp. 155-270
    • Combettes, P.L.1
  • 29
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • Daubechies I, Defrise M and De Mol C 2004 An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Commun. Pure Appl. Math. 57 1413-57
    • (2004) Commun. Pure Appl. Math. , vol.57 , Issue.11 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 31
    • 33646365077 scopus 로고    scopus 로고
    • For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution
    • Donoho D L 2006 For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution Commun. Pure Appl. Math. 59 797-829
    • (2006) Commun. Pure Appl. Math. , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.L.1
  • 32
    • 0001702688 scopus 로고
    • Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
    • Eckstein J 1993 Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming Math. Oper. Res. 18 202-26
    • (1993) Math. Oper. Res. , vol.18 , Issue.1 , pp. 202-226
    • Eckstein, J.1
  • 33
    • 84880683689 scopus 로고
    • Iteration methods for convexly constrained ill-posed problems in Hilbert space
    • Eicke B 1992 Iteration methods for convexly constrained ill-posed problems in Hilbert space Numer. Funct. Anal. Optim. 13 413-29
    • (1992) Numer. Funct. Anal. Optim. , vol.13 , Issue.5 , pp. 413-429
    • Eicke, B.1
  • 34
    • 0002811034 scopus 로고
    • On the moduli of convexity and smoothness
    • Figiel T 1976 On the moduli of convexity and smoothness Stud. Math. 56 121-55
    • (1976) Stud. Math. , vol.56 , pp. 121-155
    • Figiel, T.1
  • 35
    • 0040893030 scopus 로고
    • A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
    • Hanke M, Neubauer A and Scherzer O 1995 A convergence analysis of the Landweber iteration for nonlinear ill-posed problems Numer. Math. 72 21-37
    • (1995) Numer. Math. , vol.72 , Issue.1 , pp. 21-37
    • Hanke, M.1    Neubauer, A.2    Scherzer, O.3
  • 36
    • 34249721452 scopus 로고    scopus 로고
    • A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
    • Hofmann B, Kaltenbacher B, Pöschl C and Scherzer O 2007 A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators Inverse Problems 23 987-1010
    • (2007) Inverse Problems , vol.23 , Issue.3 , pp. 987-1010
    • Hofmann, B.1    Kaltenbacher, B.2    Pöschl, C.3    Scherzer, O.4
  • 37
    • 0031190440 scopus 로고    scopus 로고
    • Proximal minimization methods with generalized Bregman functions
    • Kiwiel K C 1997 Proximal minimization methods with generalized Bregman functions SIAM J. Control Optim. 35 1142-68
    • (1997) SIAM J. Control Optim. , vol.35 , Issue.4 , pp. 1142-1168
    • Kiwiel, K.C.1
  • 40
    • 0000324993 scopus 로고
    • Approximation of the solutions of some variational inequalities
    • Mosco U 1967 Approximation of the solutions of some variational inequalities Ann. Sc. Norm. Sup. Pisa 21 373-94
    • (1967) Ann. Sc. Norm. Sup. Pisa , vol.21 , pp. 373-394
    • Mosco, U.1
  • 41
    • 19844370110 scopus 로고    scopus 로고
    • An iterative regularization method for total variation based image restoration
    • Osher S, Burger M, Goldfarb D, Xu J and Yin W 2005 An iterative regularization method for total variation based image restoration Multiscale Modelling Simul. 4 460-89
    • (2005) Multiscale Modelling Simul. , vol.4 , Issue.2 , pp. 460-489
    • Osher, S.1    Burger, M.2    Goldfarb, D.3    Xu, J.4    Yin, W.5
  • 42
    • 33746908577 scopus 로고    scopus 로고
    • Continuity properties of projection operators
    • Penot J P 2003 Continuity properties of projection operators J. Inequalities Appl. 5 509-21
    • (2003) J. Inequalities Appl. , vol.5 , pp. 509-521
    • Penot, J.P.1
  • 43
    • 7544247966 scopus 로고    scopus 로고
    • Characterizations of metric projections in Banach spaces and applications
    • Penot J P and Ratsimahalo R 1998 Characterizations of metric projections in Banach spaces and applications Abstr. Appl. Anal. 3 85-103
    • (1998) Abstr. Appl. Anal. , vol.3 , Issue.1-2 , pp. 85-103
    • Penot, J.P.1    Ratsimahalo, R.2
  • 44
    • 25444477311 scopus 로고    scopus 로고
    • A note on the CQ algorithm for the split feasibility problem
    • Qu B and Xiu N 2005 A note on the CQ algorithm for the split feasibility problem Inverse Problems 21 1655-65
    • (2005) Inverse Problems , vol.21 , Issue.5 , pp. 1655-1665
    • Qu, B.1    Xiu, N.2
  • 45
    • 7544227520 scopus 로고    scopus 로고
    • On total convexity, Bregman projections and stability in Banach spaces
    • Resmerita E 2004 On total convexity, Bregman projections and stability in Banach spaces J. Convex Anal. 11 1-16
    • (2004) J. Convex Anal. , vol.11 , pp. 1-16
    • Resmerita, E.1
  • 46
    • 23244453192 scopus 로고    scopus 로고
    • Regularization of ill-posed problems in Banach spaces: Convergence rates
    • Resmerita E 2005 Regularization of ill-posed problems in Banach spaces: convergence rates Inverse Problems 21 1303-14
    • (2005) Inverse Problems , vol.21 , Issue.4 , pp. 1303-1314
    • Resmerita, E.1
  • 48
    • 31844445760 scopus 로고    scopus 로고
    • Nonlinear iterative methods for linear ill-posed problems in Banach spaces
    • Schöpfer F, Louis A K and Schuster T 2006 Nonlinear iterative methods for linear ill-posed problems in Banach spaces Inverse Problems 22 311-29
    • (2006) Inverse Problems , vol.22 , Issue.1 , pp. 311-329
    • Schöpfer, F.1    Louis, A.K.2    Schuster, T.3
  • 49
    • 51749085642 scopus 로고    scopus 로고
    • Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods
    • Schöpfer F, Schuster T and Louis A K 2008 Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods J. Inverse Ill-posed Problem at press
    • (2008) J. Inverse Ill-posed Problem
    • Schöpfer, F.1    Schuster, T.2    Louis, A.K.3
  • 50
    • 34548228266 scopus 로고    scopus 로고
    • An iterative algorithm for nonlinear inverse problems with joint sparsity constraints in vector-valued regimes and an application to color image inpainting
    • Teschke G and Ramlau R 2007 An iterative algorithm for nonlinear inverse problems with joint sparsity constraints in vector-valued regimes and an application to color image inpainting Inverse Problems 5 1851-70
    • (2007) Inverse Problems , vol.5 , pp. 1851-1870
    • Teschke, G.1    Ramlau, R.2
  • 51
    • 50749132985 scopus 로고
    • Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
    • Xu Z-B and Roach G F 1991 Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces J. Math. Anal. Appl. 157 189-210
    • (1991) J. Math. Anal. Appl. , vol.157 , Issue.1 , pp. 189-210
    • Xu, Z.-B.1    Roach, G.F.2
  • 52
    • 4043102605 scopus 로고    scopus 로고
    • The relaxed CQ algorithm solving the split feasibility problem
    • Yang Q 2004 The relaxed CQ algorithm solving the split feasibility problem Inverse Problems 20 1261-6
    • (2004) Inverse Problems , vol.20 , Issue.4 , pp. 1261-1266
    • Yang, Q.1
  • 53
    • 10844252460 scopus 로고    scopus 로고
    • On variable-step relaxed projection algorithm for variational inequalities
    • Yang Q 2005 On variable-step relaxed projection algorithm for variational inequalities J. Math. Anal. Appl. 302 166-79
    • (2005) J. Math. Anal. Appl. , vol.302 , Issue.1 , pp. 166-179
    • Yang, Q.1
  • 55
    • 25444479430 scopus 로고    scopus 로고
    • Several solution methods for the split feasibility problem
    • Zhao J and Yang Q 2005 Several solution methods for the split feasibility problem Inverse Problems 21 1791-9
    • (2005) Inverse Problems , vol.21 , Issue.5 , pp. 1791-1799
    • Zhao, J.1    Yang, Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.