메뉴 건너뛰기




Volumn 27, Issue 1, 2007, Pages 59-66

The equivalence of the taut string algorithm and BV-regularization

Author keywords

Equivalence relations; Optimization; Regularization; Total variation; Variational derivatives; Variational methods

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; IMAGING SYSTEMS; OPTIMIZATION;

EID: 33846270363     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-006-9796-4     Document Type: Article
Times cited : (39)

References (20)
  • 1
    • 36149030663 scopus 로고
    • Analysis of bounded variation penalty methods for ill-posed problems
    • R. Acar and C.R. Vogel, "Analysis of bounded variation penalty methods for ill-posed problems," Inverse Probl., Vol. 10, pp. 1217-1229, 1994.
    • (1994) Inverse Probl , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.R.2
  • 3
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • A. Chambolle and P.L. Lions, "Image recovery via total variation minimization and related problems," Numer. Math., Vol. 76, pp. 167-188, 1997.
    • (1997) Numer. Math , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.L.2
  • 4
    • 0035608644 scopus 로고    scopus 로고
    • Local extremes, runs, strings and multiresolution
    • With discussion and rejoinder by the authors
    • P.L. Davies and A. Kovac, "Local extremes, runs, strings and multiresolution," Ann. Statist., Vol. 29, pp. 1-65, 2001. With discussion and rejoinder by the authors.
    • (2001) Ann. Statist , vol.29 , pp. 1-65
    • Davies, P.L.1    Kovac, A.2
  • 5
    • 0000427927 scopus 로고    scopus 로고
    • Convergence of an iterative method for total variation denoising
    • D.C. Dobson and C.R. Vogel, "Convergence of an iterative method for total variation denoising," SIAM J. Num. Anal., Vol. 34, pp. 1779-1791, 1997.
    • (1997) SIAM J. Num. Anal , vol.34 , pp. 1779-1791
    • Dobson, D.C.1    Vogel, C.R.2
  • 6
    • 0029341230 scopus 로고
    • Nonlinear image recovery with halfquadratic regularization
    • D. Geman and C. Yang, "Nonlinear image recovery with halfquadratic regularization," IEEE Transactions on Image Processing, Vol. 4, pp. 932-945, 1995.
    • (1995) IEEE Transactions on Image Processing , vol.4 , pp. 932-945
    • Geman, D.1    Yang, C.2
  • 10
    • 33846282586 scopus 로고    scopus 로고
    • K. Ito and K. Kunisch, Lagrangian formulation of nonsmooth convex optimization in Hubert spaces, in Control of partial differential equations and applications E. Casas (Ed.), Lect. Notes Pure Appl. Math., New York, 174, pp. 107-117, 1996. Proceedings of the IFIP TC7.
    • K. Ito and K. Kunisch, "Lagrangian formulation of nonsmooth convex optimization in Hubert spaces," in Control of partial differential equations and applications E. Casas (Ed.), Lect. Notes Pure Appl. Math., New York, Vol. 174, pp. 107-117, 1996. Proceedings of the IFIP TC7.
  • 11
    • 0033457563 scopus 로고    scopus 로고
    • An active set strategy based on the augmented Lagrangian formulation for image restoration
    • K. Ito and K. Kunisch, "An active set strategy based on the augmented Lagrangian formulation for image restoration," M2AN Math. Model. Numer. Anal., Vol. 33, pp. 1-21, 1999.
    • (1999) M2AN Math. Model. Numer. Anal , vol.33 , pp. 1-21
    • Ito, K.1    Kunisch, K.2
  • 12
    • 0242676280 scopus 로고    scopus 로고
    • Restoration of edge-fiat-grey scales
    • K. Ito and K. Kunisch, "Restoration of edge-fiat-grey scales," Inverse Problems, Vol. 65, pp. 273-298, 2000.
    • (2000) Inverse Problems , vol.65 , pp. 273-298
    • Ito, K.1    Kunisch, K.2
  • 13
    • 0031514745 scopus 로고    scopus 로고
    • Locally adaptive regression splines
    • E. Mammen and S. van de Geer, "Locally adaptive regression splines," Ann. Statist., Vol. 25, pp. 387-413, 1997.
    • (1997) Ann. Statist , vol.25 , pp. 387-413
    • Mammen, E.1    van de Geer, S.2
  • 14
    • 44949282550 scopus 로고    scopus 로고
    • M.Z. Nashed and E.P. Hamilton, Local and global bivariational gradients and singular variational derivatives of functionals on Cn[a, b], Nonlinear Anal., 17, No. 9, pp. 841-862, 1991.
    • M.Z. Nashed and E.P. Hamilton, "Local and global bivariational gradients and singular variational derivatives of functionals on Cn[a, b]," Nonlinear Anal., Vol. 17, No. 9, pp. 841-862, 1991.
  • 15
    • 0032165154 scopus 로고    scopus 로고
    • Least squares and bounded variation regularization with nondifferentiable functional
    • M.Z. Nashed and O. Scherzer, "Least squares and bounded variation regularization with nondifferentiable functional," Num. Funct. Anal, and Optimiz., Vol. 19, pp. 873-901, 1998.
    • (1998) Num. Funct. Anal, and Optimiz , vol.19 , pp. 873-901
    • Nashed, M.Z.1    Scherzer, O.2
  • 16
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L.I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms." Physica D, Vol. 60, pp. 259-268, 1992.
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 17
    • 33846325726 scopus 로고    scopus 로고
    • Taut-string algorithm and regularization programs with G-norm data fit
    • to appear
    • O. Scherzer, "Taut-string algorithm and regularization programs with G-norm data fit," J. Math. Imaging and Vision, 2004. to appear.
    • (2004) J. Math. Imaging and Vision
    • Scherzer, O.1
  • 18
    • 0034135395 scopus 로고    scopus 로고
    • Relations between regularization and diffusion filtering
    • O. Scherzer and J. Weickert, "Relations between regularization and diffusion filtering," J. Math. Imag. Vision, Vol. 12, pp. 43-63, 2000.
    • (2000) J. Math. Imag. Vision , vol.12 , pp. 43-63
    • Scherzer, O.1    Weickert, J.2
  • 19
    • 24644476589 scopus 로고    scopus 로고
    • Relations between higher order TV regularization and support vector regression
    • Scale-Space and PDE Methods in Computer Vision, R. Kimmel, N. Sochen, and J. Weickert Eds
    • G. Steidl, S. Didas, and J. Neumann, "Relations between higher order TV regularization and support vector regression," in Scale-Space and PDE Methods in Computer Vision, R. Kimmel, N. Sochen, and J. Weickert (Eds.), LNCS 3459, pp. 515-527, 2005.
    • (2005) LNCS , vol.3459 , pp. 515-527
    • Steidl, G.1    Didas, S.2    Neumann, J.3
  • 20
    • 0242676282 scopus 로고
    • A multigrid method for total variation-based image denoising
    • K. Bowers and J. Lund Eds, Birkhauser, Progess in Systems and Control Theory
    • C. Vogel, "A multigrid method for total variation-based image denoising," in Computation and Control IV, K. Bowers and J. Lund (Eds.), Birkhauser, Vol. 20, 1995, Progess in Systems and Control Theory.
    • (1995) Computation and Control IV , vol.20
    • Vogel, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.