Simultaneous Denoising and Illumination Correction via Local Data-Fidelity and Nonlocal Regularization

  • Jun Liu
  • Xue-cheng Tai
  • Haiyang Huang
  • Zhongdan Huan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)

Abstract

In this paper, we provide a new model for simultaneous denoising and illumination correction. A variational framework based on local maximum likelihood estimation (MLE) and a nonlocal regularization is proposed and studied. The proposed minimization problem can be efficiently solved by the augmented Lagrangian method coupled with a maximum expectation step. Experimental results show that our model can provide more homogeneous denoisng results compared to some earlier variational method. In addition, the new method also produces good results under both Gaussian and non-Gaussian noise such as Gaussian mixture, impulse noise and their mixtures.

Keywords

Noisy Image Impulse Noise Augmented Lagrangian Method Bias Function Split Bregman Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Nikolova, M.: A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision 20, 99–120 (2004)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Bar, L., Sochen, N., Kiryati, N.: Image deblurring in the presence of impulsive noise. International Journal of Computer Vision 70, 279–298 (2006)CrossRefMATHGoogle Scholar
  4. 4.
    Cai, J., Chan, R., Nikolova, M.: Two-phase approach for deblurring images corrupted by impulse plus Gaussian noise. Inverse Problems and Imaging 2, 187–204 (2008)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Liu, J., Huang, H., Huan, Z., Zhang, H.: Adaptive variational method for restoring color images with high density impulse noise. International Journal of Computer Vision 90, 131–149 (2010)CrossRefGoogle Scholar
  6. 6.
    Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Modeling & Simulation 4(2), 490–530 (2005)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Modeling & Simulation 7(3), 1005–1028 (2008)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Jung, M., Vese, L.A.: Image restoration via nonlocal Mumford-Shah regularizers. UCLA C.A.M. Report 08-35 (2008)Google Scholar
  9. 9.
    Wells, W.M., Grimson, E.L., Kikinis, R., Jolesz, F.A.: Adaptive segmentation of MRI data. IEEE Transactions on Medical Imaging 15, 429–442 (1996)CrossRefGoogle Scholar
  10. 10.
    Ahmed, M.N., Yamany, S.M., Mohamed, N., Farag, A.A., Moriarty, T.: A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Transactions on Medical Imaging 21, 193–198 (2002)CrossRefGoogle Scholar
  11. 11.
    Ashburner, J., Friston, K.J.: Unified segmentation. Neuroimage 26(3), 839–851 (2005)CrossRefGoogle Scholar
  12. 12.
    Li, C., Huang, R., Ding, Z., Gatenby, C., Metaxas, D.N., Gore, J.C.: A variational level set approach to segmentation and bias correction of images with intensity inhomogeneity. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 1083–1091. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Tai, X.C., Wu, C.L.: Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. UCLA C.A.M. Report 09-05 (2009)Google Scholar
  14. 14.
    Wu, C.L., Tai, X.C.: Augmented Lagrangian method, dual methods, and split bregman iteration for ROF, vectorial TV, and high order models. UCLA C.A.M. Report 09-76 (2009)Google Scholar
  15. 15.
    Rockafellar, R.T.: Convex analysis. Princeton University Press, Princeton (1970)CrossRefMATHGoogle Scholar
  16. 16.
    Bae, E., Yuan, J., Tai, X.C.: Global minimization for continuous multiphase partitioning problems using a dual approach. UCLA C.A.M. Report 09-75 (2009)Google Scholar
  17. 17.
    Goldstein, T., Osher, S.: The split Bregman method for L1 regularized problems. UCLA C.A.M. Report 08-29 (2008)Google Scholar
  18. 18.
    Setzer, M.: Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 464–476. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Zhang, X., Burgery, M., Bresson, X., Osher, S.: Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. UCLA C.A.M. Report 09-03 (2009)Google Scholar
  20. 20.
    Wang, H.H., Haddad, R.A.: Adaptive median filters: new algorithms and results. IEEE Transactions on Image Processing 4, 499–502 (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jun Liu
    • 1
  • Xue-cheng Tai
    • 2
    • 3
  • Haiyang Huang
    • 1
  • Zhongdan Huan
    • 1
  1. 1.School of Mathematical Sciences, Laboratory of Mathematics and Complex SystemsBeijing Normal UniversityBeijingP.R. China
  2. 2.School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore
  3. 3.Department of MathematicsUniversity of BergenNorway

Personalised recommendations