Number of Useful Components in Gaussian Mixture Models for Patch-Based Image Denoising

  • Dai-Viet TranEmail author
  • Sébastien Li-Thiao-Té
  • Marie Luong
  • Thuong Le-Tien
  • Françoise Dibos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10884)


When using Gaussian mixture models (GMMs) as a prior for image denoising under the Bayesian maximum a posteriori (MAP) perspective, only a single prominent Gaussian component is usually selected to recover a noisy image patch, which leads to computationally efficient implementations. We attempt to justify this on several image datasets by evaluating the number of Gaussian components required for recovering patches. We show that even patches without a prominent component in the prior can be recovered with little loss of performance. Comparisons between two dictionary choices and between small and large models suggest that large gains are attainable, but only one component is required for reconstruction.


Gaussian mixture model Image denoising Image priors 


  1. 1.
    Buades, A., Coll, B., Morel, J.M.: A non-local algorithm for image denoising. In: CVPR, pp. 60–65 (2005)Google Scholar
  2. 2.
    Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 2080–2095 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Sig. Process. 4311–4322 (2006)Google Scholar
  4. 4.
    Trinh, D.H., Luong, M., Dibos, F., Rocchisani, J.M., Pham, C.D., Nguyen, T.Q.: Novel example-based method for super-resolution and denoising of medical images. IEEE Trans. Image Process. 1882–1895 (2014)Google Scholar
  5. 5.
    Jain, V., Seung, S.: Natural image denoising with convolutional networks. Adv. Neural Inf. Process. Syst. 21, 769–776 (2009)Google Scholar
  6. 6.
    Zhang, K., Zuo, W., Chen, Y., Meng, D., Zhang, L.: Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. IEEE Trans. Image Process. 3142–3155 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Zoran, D., Weiss, Y.: From learning models of natural image patches to whole image restoration. In: IEEE International Conference on Computer Vision, pp. 479–486 (2011)Google Scholar
  8. 8.
    Xu, J., Zhang, L., Zuo, W., Zhang, D., Feng, X.: Patch group based nonlocal self-similarity prior learning for image denoising. In: IEEE ICCV, pp. 244–252 (2015)Google Scholar
  9. 9.
    Niknejad, M., Rabbani, H., Babaie-Zadeh, M.: Image restoration using Gaussian mixture models with spatially constrained patch clustering. IEEE TIP 3624–3636 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Khan, F.S., Anwer, R.M., van de Weijer, J., Bagdanov, A.D., Vanrell, M., Lopez, A.M.: Color attributes for object detection. In: CVPR, pp. 3306–3313 (2012)Google Scholar
  11. 11.
    Huang, J.B., Singh, A., Ahuja, N.: Single image super-resolution from transformed self-exemplars. In: CVPR, pp. 5197–5206 (2015)Google Scholar
  12. 12.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 898–916 (2011)CrossRefGoogle Scholar
  13. 13.
    Brodatz, P.: Textures: A Photographic Album for Artists and Designers. Dover, New York (1966)Google Scholar
  14. 14.
    Cimpoi, M., Maji, S., Kokkinos, I., Mohamed, S., Vedaldi, A.: Describing textures in the wild. In: CVPR (2014)Google Scholar
  15. 15.
    Clark, K., et al.: The cancer imaging archive (TCIA): maintaining and operating a public information repository. J. Digit. Imaging 1045–1057 (2013)CrossRefGoogle Scholar
  16. 16.
    Martino, A.D., et al.: The autism brain imaging data exchange: towards a large-scale evaluation of the intrinsic brain architecture in autism. Mol. Psychiatry 659–667 (2013)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Dai-Viet Tran
    • 1
    • 2
    Email author
  • Sébastien Li-Thiao-Té
    • 1
  • Marie Luong
    • 2
  • Thuong Le-Tien
    • 3
  • Françoise Dibos
    • 1
  1. 1.Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539VilletaneuseFrance
  2. 2.Université Paris 13, Sorbonne Paris Cité, L2TI, EA 3043VilletaneuseFrance
  3. 3.Ho Chi Minh City University of TechnologyHo Chi Minh CityVietnam

Personalised recommendations