Robust Noisy Image Super-Resolution Using \(\ell _1\)-norm Regularization and Non-local Constraint

  • Bo Yue
  • Shuang WangEmail author
  • Xuefeng LiangEmail author
  • Licheng Jiao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10116)


Conventional coupled dictionary learning approaches are designed for noiseless image super-resolution (SR), but quite sensitive to noisy images. We find the cause is the commonly used \(\ell _2\)-norm coefficients transition term. In this paper, we propose a robust \(\ell _1\)-norm solution by introducing two sub-terms: LR coefficient sparsity constraint term and HR coefficient conversion term, which are able to prevent the noise transmission from noisy input to output. By incorporating our simple yet effective non-linear model inspired by auto-encoder, the proposed \(\ell _1\)-norm dictionary learning achieves a more accurate coefficients conversion. Moreover, we bring the non-local similarity constraint from pixel domain to the sparse coefficients optimization. The improved sparse representation further enhances SR inference on both noisy and noiseless images. Using standard metrics, we show that results are significantly clearer than state-of-the-arts on noisy images and sharper on denoised images.


Sparse Representation High Resolution Image Dictionary Learning Sparse Coefficient Beta Process 
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.



This work is supported by the National Basic Research Program (973 Program) of China (No. 2013CB329402), the Fund for Foreign Scholars in University Research and Teaching Programs (the 111 Project) (No. B07048), the Program for Cheung Kong Scholars and Innovative Research Team in University (No. IRT 15R53), and JSPS Grants-in-Aid for Scientific Research C (No. 15K00236) for funding.

Supplementary material

426013_1_En_3_MOESM1_ESM.pdf (4.6 mb)
Supplementary material 1 (pdf 4747 KB)


  1. 1.
    Yang, J., Wright, J., Huang, T.S., Ma, Y.: Image super-resolution via sparse representation. IEEE. Trans. Image Process. 19, 2861–2873 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Yang, J., Wang, Z., Lin, Z., Cohen, S., Huang, T.: Coupled dictionary training for image super-resolution. IEEE. Trans. Image Process. 21, 3467–3478 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Zeyde, R., Elad, M., Protter, M.: On single image scale-up using sparse-representations. In: Boissonnat, J.-D., Chenin, P., Cohen, A., Gout, C., Lyche, T., Mazure, M.-L., Schumaker, L. (eds.) Curves and Surfaces 2010. LNCS, vol. 6920, pp. 711–730. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-27413-8_47 CrossRefGoogle Scholar
  4. 4.
    Wang, S., Zhang, L., Liang, Y., Pan, Q.: Semi-coupled dictionary learning with applications to image super-resolution and photo-sketch synthesis. In: CVPR, pp. 2216–2223. IEEE (2012)Google Scholar
  5. 5.
    Huang, D.A., Wang, Y.C.F.: Coupled dictionary and feature space learning with applications to cross-domain image synthesis and recognition. In: ICCV, pp. 2496–2503. IEEE (2013)Google Scholar
  6. 6.
    He, L., Qi, H., Zaretzki, R.: Beta process joint dictionary learning for coupled feature spaces with application to single image super-resolution. In: CVPR, pp. 345–352. IEEE (2013)Google Scholar
  7. 7.
    Timofte, R., De, V., Van Gool, L.: Anchored neighborhood regression for fast example-based super-resolution. In: ICCV, pp. 1920–1927. IEEE (2013)Google Scholar
  8. 8.
    Timofte, R., De Smet, V., Van Gool, L.: A+: adjusted anchored neighborhood regression for fast super-resolution. In: Cremers, D., Reid, I., Saito, H., Yang, M.-H. (eds.) ACCV 2014. LNCS, vol. 9006, pp. 111–126. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-16817-3_8 Google Scholar
  9. 9.
    Peleg, T., Elad, M.: A statistical prediction model based on sparse representations for single image super-resolution. IEEE. Trans. Image Process. 23, 2569–2582 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Schulter, S., Leistner, C., Bischof, H.: Fast and accurate image upscaling with super-resolution forests. In: CVPR, pp. 3791–3799. IEEE (2015)Google Scholar
  11. 11.
    Timofte, R., Rothe, R., Van Gool, L.: Seven ways to improve example-based single image super resolution. arXiv preprint arxiv:1511.02228 (2015)
  12. 12.
    Kim, J., Lee, J.K., Lee, K.M.: Accurate image super-resolution using very deep convolutional networks (2015). arXiv preprint arxiv:1511.04587
  13. 13.
    Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Dong, C., Loy, C.C., He, K., Tang, X.: Image super-resolution using deep convolutional networks. IEEE. Trans. Pattern Anal. Mach. Intell. 38, 295–307 (2015)CrossRefGoogle Scholar
  15. 15.
    Dai, D., Timofte, R., Van Gool, L.: Jointly optimized regressors for image super-resolution. In: Computer Graphics Forum, Wiley Online Library, pp. 95–104 (2015)Google Scholar
  16. 16.
    Singh, A., Porikli, F., Ahuja, N.: Super-resolving noisy images. In: CVPR, pp. 2846–2853. IEEE (2014)Google Scholar
  17. 17.
    Buades, A., Coll, B., Morel, J.M.: A non-local algorithm for image denoising. In: CVPR, pp. 60–65. IEEE (2005)Google Scholar
  18. 18.
    Zhang, K., Tao, D., Gao, X., Li, X., Xiong, Z.: Learning multiple linear mappings for efficient single image super-resolution. IEEE. Trans. Image Process. 24, 846–861 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Protter, M., Elad, M., Takeda, H., Milanfar, P.: Generalizing the nonlocal-means to super-resolution reconstruction. IEEE. Trans. Image Process. 18, 36–51 (2009)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Chen, X., Lin, Q., Kim, S., Carbonell, J.G., Xing, E.P., et al.: Smoothing proximal gradient method for general structured sparse regression. Ann. Appl. Stat. 6, 719–752 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Chalasani, R., Principe, J.C.: Deep predictive coding networks. arXiv preprint arxiv:1301.3541 (2013)
  22. 22.
    Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans. Image Process. 16, 2080–2095 (2007)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Dong, C., Loy, C.C., He, K., Tang, X.: Learning a deep convolutional network for image super-resolution. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8692, pp. 184–199. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-10593-2_13 Google Scholar
  24. 24.
    Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: ICCV, pp. 416–423. IEEE (2001)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and ComputationXidian UniversityXi’anChina
  2. 2.IST, Graduate School of InformaticsKyoto UniversityKyotoJapan

Personalised recommendations