Minimization of an Edge-Preserving Regularization Functional by Conjugate Gradient Type Methods

  • Jian-Feng Cai
  • Raymond Chan
  • Benedetta Morini
Part of the Mathematics and Visualization book series (MATHVISUAL)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. P. Bertsekas. Nonlinear Programming. Athena Scientific, 1999.Google Scholar
  2. 2.
    A. Bovik. Handbook of Image and Video Processing. Academic Press, 2000.Google Scholar
  3. 3.
    R. H. Chan, C.-W. Ho, and M. Nikolova. Convergence of Newton’s method for a minimization problem in impulse noise removal. J. Comput. Math., 22(2):168–177,2004.MathSciNetGoogle Scholar
  4. 4.
    R. H. Chan, C.-W. Ho, and M. Nikolova. Salt-and-pepper noise removal by median-type noise detector and edge-preserving regularization. IEEE Trans. Image Process., 14(10):1479–1485, 2005.CrossRefGoogle Scholar
  5. 5.
    R. H. Chan, C. Hu, and M. Nikolova. An iterative procedure for removing random-valued impulse noise. IEEE Signal Proc. Letters, 11(12):921–924, 2004.CrossRefGoogle Scholar
  6. 6.
    P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud. Deterministic edge-preserving regularization in computed imaging. IEEE Trans. Image Process., 6(2):298–311, 1997.CrossRefGoogle Scholar
  7. 7.
    T. Chen and H. R. Wu. Adaptive impulse detection using center-weighted median filters. IEEE Signal Proc. Letters, 8(1):1–3, 2001.CrossRefGoogle Scholar
  8. 8.
    Y. H. Dai and Y. Yuan. A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim., 10(1):177–182, 1999.CrossRefMathSciNetGoogle Scholar
  9. 9.
    R. Fletcher. Practical methods of optimization. A Wiley-Interscience Publication. John Wiley & Sons Ltd., Chichester, second edition, 1987.Google Scholar
  10. 10.
    R. Fletcher and C. M. Reeves. Function minimization by conjugate gradients. Comput. J., 7:149–154, 1964.CrossRefMathSciNetGoogle Scholar
  11. 11.
    P. J. Green. Bayesian reconstructions from emission tomography data using a modified EM algorithm. IEEE Trans. Medical Imaging, 9(1):84–93, 1990.CrossRefGoogle Scholar
  12. 12.
    M. R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems. J. Research Nat. Bur. Standards, 49:409-436 (1953), 1952.MathSciNetGoogle Scholar
  13. 13.
    H. Hwang and R. A. Haddad. Adaptive median filters: new algorithms and results. IEEE Trans. Image Process., 4(4):499–502, 1995.CrossRefGoogle Scholar
  14. 14.
    M. Nikolova. A variational approach to remove outliers and impulse noise. J. Math. Imaging Vision, 20(1-2):99–120, 2004. Special issue on mathematics and image analysis.CrossRefMathSciNetGoogle Scholar
  15. 15.
    E. Polak and G. Ribière. Note sur la convergence de méthodes de directions conjuguées. Rev. Française Informat. Recherche Opérationnelle, 3(16):35–43, 1969.Google Scholar
  16. 16.
    W. Rudin. Principles of mathematical analysis. McGraw-Hill Book Co., New York, third edition, 1976. International Series in Pure and Applied Mathematics.Google Scholar
  17. 17.
    G. W. Stewart and Ji Guang Sun. Matrix perturbation theory. Computer Science and Scientific Computing. Academic Press Inc., Boston, MA, 1990.Google Scholar
  18. 18.
    J. Sun and J. Zhang. Global convergence of conjugate gradient methods without line search. Ann. Oper. Res., 103:161–173, 2001.CrossRefMathSciNetGoogle Scholar
  19. 19.
    R. S. Varga. Matrix iterative analysis, volume 27 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, expanded edition, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jian-Feng Cai
    • 1
  • Raymond Chan
    • 2
  • Benedetta Morini
    • 3
  1. 1.Department of MathematicsThe Chinese University of Hong KongShatinHong Kong
  2. 2.Department of MathematicsThe Chinese University of Hong KongShatinHong Kong
  3. 3.Dipartimento di Energetica “S. Steccco”Università di FirenzeFirenzeItalia

Personalised recommendations