메뉴 건너뛰기




Volumn 76, Issue 1-2, 2006, Pages 135-148

A note on the dual treatment of higher-order regularization functionals

Author keywords

Convex optimization; Dual optimization methods; G norm; Higher order regularization; Rudin Osher Fatemi model; Support vector regression

Indexed keywords

CONVEX OPTIMIZATION; DUAL OPTIMIZATION METHODS; G-NORM; HIGHER ORDER REGULARIZATION; SUPPORT VECTOR REGRESSIONS;

EID: 27644449659     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-005-0129-z     Document Type: Article
Times cited : (79)

References (29)
  • 2
    • 35248822315 scopus 로고    scopus 로고
    • Image decomposition application to SAR images. In: Scale-space and PDE methods in computer vision
    • (Griffin, L. D., Lillholm, M., eds.). Berlin: Springer
    • Aujol, J.-F., Aubert, G., Blanc-Féraud, L., Chambolle A.: Image decomposition application to SAR images. In: Scale-space and PDE methods in computer vision (Griffin, L. D., Lillholm, M., eds.). Lecture Notes in Computer Science, vol. 2695. Berlin: Springer 2003, pp. 297-312.
    • (2003) Lecture Notes in Computer Science , vol.2695 , pp. 297-312
    • Aujol, J.-F.1    Aubert, G.2    Blanc-Féraud, L.3    Chambolle, A.4
  • 3
    • 1242352408 scopus 로고    scopus 로고
    • An algorithm for total variation minimization and applications
    • Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vision 20, 89-97 (2004).
    • (2004) J. Math. Imaging Vision , vol.20 , pp. 89-97
    • Chambolle, A.1
  • 4
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • Chambolle, A, Lions, P.-L.: Image recovery via total variation minimization and related problems. Numer. Math. 76, 167-188 (1997).
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 5
    • 0033295350 scopus 로고    scopus 로고
    • A nonlinear primal-dual method for total-variation based image restoration
    • Chan, T. F., Golub, G. H., Mulet, P.: A nonlinear primal-dual method for total-variation based image restoration. SIAM J. Sci. Comput. 20(6), 1964-1977 (1999).
    • (1999) SIAM J. Sci. Comput. , vol.20 , Issue.6 , pp. 1964-1977
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 6
    • 0035074671 scopus 로고    scopus 로고
    • High-order total variation-based image restoration
    • Chan T. F., Marquina, A., Mulet, P.: High-order total variation-based image restoration. SIAM J. Sci. Comput. 22(2), 503-516 (2000).
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.2 , pp. 503-516
    • Chan, T.F.1    Marquina, A.2    Mulet, P.3
  • 8
    • 0035608644 scopus 로고    scopus 로고
    • Local extremes, runs, strings and multiresolution
    • Davies, P. L., Kovac, A.: Local extremes, runs, strings and multiresolution. Ann. Stat. 29, 1-65 (2001).
    • (2001) Ann. Stat. , vol.29 , pp. 1-65
    • Davies, P.L.1    Kovac, A.2
  • 10
    • 0000249788 scopus 로고    scopus 로고
    • An equivalence between sparse approximation and support vector machines
    • Girosi. F.: An equivalence between sparse approximation and support vector machines. Neural Comput. 10(6), 1455-1480 (1998).
    • (1998) Neural Comput. , vol.10 , Issue.6 , pp. 1455-1480
    • Girosi, F.1
  • 12
    • 27644494231 scopus 로고    scopus 로고
    • Variational methods on the space of functions of bounded Hessian for convexification and denoising
    • University of Innsbruck, Austria
    • Hinterberger, W., Scherzer, O.: Variational methods on the space of functions of bounded Hessian for convexification and denoising. Technical Report, University of Innsbruck, Austria, 2003.
    • (2003) Technical Report
    • Hinterberger, W.1    Scherzer, O.2
  • 13
    • 4544249333 scopus 로고    scopus 로고
    • Total bounded variation regularization as a bilaterally constrained optimization problem
    • Hintermüller, W., Kunisch, K.: Total bounded variation regularization as a bilaterally constrained optimization problem. SIAM J. Appl. Math. 64(4), 1311-1333 (2004).
    • (2004) SIAM J. Appl. Math. , vol.64 , Issue.4 , pp. 1311-1333
    • Hintermüller, W.1    Kunisch, K.2
  • 14
    • 24644473686 scopus 로고    scopus 로고
    • Noise removal using fourth-order partial differential equations with applications to medical magnetic resonance images in space and time
    • Department of Mathematics, University of California at Los Angeles
    • Lysaker, M., Lundervold, A., Tai, X.-C.: Noise removal using fourth-order partial differential equations with applications to medical magnetic resonance images in space and time. Technical report CAM-02-44, Department of Mathematics, University of California at Los Angeles, 2002.
    • (2002) Technical Report , vol.CAM-02-44
    • Lysaker, M.1    Lundervold, A.2    Tai, X.-C.3
  • 15
    • 0031514745 scopus 로고    scopus 로고
    • Locally adaptive regression splines
    • Mammen, E., van de Geer, S.: Locally adaptive regression splines. Ann. Stat. 25(1), 387-413 (1997).
    • (1997) Ann. Stat. , vol.25 , Issue.1 , pp. 387-413
    • Mammen, E.1    Van De Geer, S.2
  • 16
    • 0042090130 scopus 로고
    • Best summation formulae and discrete splines via mathematical programming
    • Mangasarian, O. L., Schumaker, L. L.: Best summation formulae and discrete splines via mathematical programming. SIAM J. Numer. Anal. 70(3), 448-459 (1973).
    • (1973) SIAM J. Numer. Anal. , vol.70 , Issue.3 , pp. 448-459
    • Mangasarian, O.L.1    Schumaker, L.L.2
  • 17
    • 0000561116 scopus 로고
    • On the implementation of a primal-dual interior point method
    • Mehrotra, S.: On the implementation of a primal-dual interior point method. SIAM J. Optim. 2(4), 575-601 (1992).
    • (1992) SIAM J. Optim. , vol.2 , Issue.4 , pp. 575-601
    • Mehrotra, S.1
  • 18
    • 0038508524 scopus 로고    scopus 로고
    • Oscillating patterns in image processing and nonlinear evolution equations
    • Providence: AMS
    • Meyer, Y.: Oscillating patterns in image processing and nonlinear evolution equations. University Lecture Series, vol. 22. Providence: AMS 2001.
    • (2001) University Lecture Series , vol.22
    • Meyer, Y.1
  • 19
    • 0031250126 scopus 로고    scopus 로고
    • Regularization, scale-space and edge detection filters
    • Nielsen, M., Florack, L., Deriche, R.: Regularization, scale-space and edge detection filters. J. Math. Imaging Vision 7, 291-307 (1997).
    • (1997) J. Math. Imaging Vision , vol.7 , pp. 291-307
    • Nielsen, M.1    Florack, L.2    Deriche, R.3
  • 20
    • 24644436949 scopus 로고    scopus 로고
    • On the use of dual norms in bounded variation type regularization
    • Department of Computer Science, University of Innsbruck, Austria
    • Obereder, A., Osher, S., Scherzer, O.: On the use of dual norms in bounded variation type regularization. Technical report, Department of Computer Science, University of Innsbruck, Austria, 2004.
    • (2004) Technical Report
    • Obereder, A.1    Osher, S.2    Scherzer, O.3
  • 21
    • 0025465145 scopus 로고
    • Scale space and edge detection using anisotropic diffusion
    • Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12, 629-639 (1990).
    • (1990) IEEE Trans. Pattern Anal. Machine Intell. , vol.12 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 22
    • 0004267646 scopus 로고
    • Princeton: Princeton University Press
    • Rockafellar, R. T.: Convex analysis. Princeton: Princeton University Press 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 23
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Rudin, L. I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992).
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 24
    • 0031653225 scopus 로고    scopus 로고
    • Denoising with higher-order derivatives of bounded variation and an application to parameter estimation
    • Scherzer, O.: Denoising with higher-order derivatives of bounded variation and an application to parameter estimation. Computing 60, 1-27 (1998).
    • (1998) Computing , vol.60 , pp. 1-27
    • Scherzer, O.1
  • 25
    • 24644476589 scopus 로고    scopus 로고
    • Relations between higher-order TV regularization and support vector regression
    • Scale-space and PDE methods in computer vision (Kimmel, R., Sochen, N., Weickert, J., eds.). Berlin: Springer
    • Steidl, G., Didas, S., Neumann, J.: Relations between higher-order TV regularization and support vector regression. In: Scale-space and PDE methods in computer vision (Kimmel, R., Sochen, N., Weickert, J., eds.). Lecture Notes in Computer Science, vol. 3459. Berlin: Springer 2005, pp. 515-527.
    • (2005) Lecture Notes in Computer Science , vol.3459 , pp. 515-527
    • Steidl, G.1    Didas, S.2    Neumann, J.3
  • 28
    • 24644509839 scopus 로고    scopus 로고
    • A four-pixel scheme for singular differential equations
    • Scale-space and PDE methods in computer vision (Kimmel, R., Sochen, N., Weickert, J., eds.). Berlin: Springer
    • Welk, M., Weickert, J., Steidl, G.: A four-pixel scheme for singular differential equations. In: Scale-space and PDE methods in computer vision (Kimmel, R., Sochen, N., Weickert, J., eds.). Lecture Notes in Computer Science, vol. 3459. Berlin: Springer 2005, pp. 610-621.
    • (2005) Lecture Notes in Computer Science , vol.3459 , pp. 610-621
    • Welk, M.1    Weickert, J.2    Steidl, G.3
  • 29
    • 0034298888 scopus 로고    scopus 로고
    • Fourth-order partial differential equations for noise removal
    • You, Y.-L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Processing 9(10), 1723-1730 (2000).
    • (2000) IEEE Trans. Image Processing , vol.9 , Issue.10 , pp. 1723-1730
    • You, Y.-L.1    Kaveh, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.