On Single Image Scale-Up Using Sparse-Representations

  • Roman Zeyde
  • Michael Elad
  • Matan Protter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6920)


This paper deals with the single image scale-up problem using sparse-representation modeling. The goal is to recover an original image from its blurred and down-scaled noisy version. Since this problem is highly ill-posed, a prior is needed in order to regularize it. The literature offers various ways to address this problem, ranging from simple linear space-invariant interpolation schemes (e.g., bicubic interpolation), to spatially-adaptive and non-linear filters of various sorts. We embark from a recently-proposed successful algorithm by Yang et. al. [1,2], and similarly assume a local Sparse-Land model on image patches, serving as regularization. Several important modifications to the above-mentioned solution are introduced, and are shown to lead to improved results. These modifications include a major simplification of the overall process both in terms of the computational complexity and the algorithm architecture, using a different training approach for the dictionary-pair, and introducing the ability to operate without a training-set by boot-strapping the scale-up task from the given low-resolution image. We demonstrate the results on true images, showing both visual and PSNR improvements.


Image Patch Sparse Code Reconstruction Phase Visual Artifact Bicubic Interpolation 
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.


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  1. 1.
    Yang, J., Wright, J., Huang, T., Ma, Y.: Image super-resolution as sparse representation of raw image patches. In: IEEE Computer Vision and Pattern Recognition (CVPR) (June 2008)Google Scholar
  2. 2.
    Yang, J., Wright, J., Huang, T., Ma, Y.: Image super-resolution via sparse representation. IEEE Trans. on Image Processing (to appear)Google Scholar
  3. 3.
    Farsiu, S., Robinson, D., Elad, M., Milanfar, P.: Advances and Challenges in Super-Resolution. International Journal of Imaging Systems and Technology 14(2), 47–57 (2004); special issue on high-resolution image reconstructionCrossRefGoogle Scholar
  4. 4.
    Hou, H.S., Andrews, H.C.: Cubic spline for image interpolation and digital filtering. IEEE Transactions on Signal Processing 26, 508–517 (1978)CrossRefzbMATHGoogle Scholar
  5. 5.
    Irani, M., Peleg, S.: Improving Resolution by Image Registration. CVGIP: Graphical Models and Image Processing 53, 231–239 (1991)Google Scholar
  6. 6.
    Schultz, R.R., Stevenson, R.L.: A Bayesian Approach to Image Expansion for Improved Definition. IEEE Transactions on Image Processing 3(3), 233–242 (1994)CrossRefGoogle Scholar
  7. 7.
    Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning Low-Level Vision. International Journal of Computer Vision 40(1), 25–47 (2000)CrossRefzbMATHGoogle Scholar
  8. 8.
    Li, X., Orchard, M.: New Edge-Directed Interpolation. IEEE Transactions on Image Processing 10, 1521–1527 (2001)CrossRefGoogle Scholar
  9. 9.
    Chang, H., Yeung, D.-Y., Xiong, Y.: Super-resolution through neighbor embedding. In: IEEE Conference on Computer Vision and Pattern Classification (CVPR), vol. 1, pp. 275–282 (2004)Google Scholar
  10. 10.
    Elad, M., Datsenko, D.: Example-Based Regularization Deployed to Super-Resolution Reconstruction of a Single Image. The Computer Journal 50(4), 1–16 (2007)zbMATHGoogle Scholar
  11. 11.
    Sun, J., Xu, Z., Shum, H.: Image super-resolution using gradient profile prior. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1–8 (2008)Google Scholar
  12. 12.
    Elad, M., Aharon, M.: Image denoising via learned dictionaries and sparse representation. In: International Conference on Computer Vision and Pattern Recognition, New York, June 17-22 (2006)Google Scholar
  13. 13.
    Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. on Image Processing 15(12), 3736–3745 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Bruckstein, A.M., Donoho, D.L., Elad, M.: From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images. SIAM Review 51(1), 34–81 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Elad, M.: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  16. 16.
    Wang, J., Zhu, S., Gong, Y.: Resolution enhancement based on learning the sparse association of image patches. Pattern Recognition Letters 31(1) (January 2010)Google Scholar
  17. 17.
    Lou, Y., Bertozzi, A., Soatto, S.: Direct sparse deblurring. J. Math. Imag. Vis. (August 13, 2010)Google Scholar
  18. 18.
    Zhang, X., Wu, X.: Image interpolation by adaptive 2-d autoregressive modeling and soft-decision estimation. IEEE Trans. Image Process. 17(6), 887–896 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Mallat, S., Yu, G.: Super-Resolution with Sparse Mixing Estimators. IEEE Trans. on Image Processing 19(11), 2889–2900 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Aharon, M., Elad, M., Bruckstein, A.M.: The K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Trans. on Signal Processing 54(11), 4311–4322 (2006)CrossRefGoogle Scholar
  21. 21.
    Rubinstein, R., Zibulevsky, M., Elad, M.: Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit, Technical Report - CS Technion (April 2008)Google Scholar
  22. 22.
    Glasner, D., Bagon, S., Irani, M.: Super-Resolution from a Single Image. In: International Conference on Computer Vision, ICCV (October 2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Roman Zeyde
    • 1
  • Michael Elad
    • 1
  • Matan Protter
    • 1
  1. 1.The Computer Science DepartmentTechnion, Israel Institute of TechnologyHaifaIsrael

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