Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Computer Vision – ACCV 2016 Workshops (ACCV 2016)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10116))

Included in the following conference series:

  • 1831 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The matrix \(\mathbf {L}\) (non-local constraint) is applied to regularize \(\alpha _h\) as the function (4).

References

  1. Yang, J., Wright, J., Huang, T.S., Ma, Y.: Image super-resolution via sparse representation. IEEE. Trans. Image Process. 19, 2861–2873 (2010)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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

    Chapter  Google Scholar 

  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. 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. 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. 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. 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. 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)

    Article  MathSciNet  Google Scholar 

  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. Timofte, R., Rothe, R., Van Gool, L.: Seven ways to improve example-based single image super resolution. arXiv preprint arxiv:1511.02228 (2015)

  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. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. Singh, A., Porikli, F., Ahuja, N.: Super-resolving noisy images. In: CVPR, pp. 2846–2853. IEEE (2014)

    Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chalasani, R., Principe, J.C.: Deep predictive coding networks. arXiv preprint arxiv:1301.3541 (2013)

  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)

    Article  MathSciNet  Google Scholar 

  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. 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 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Xidian University, Xi’an, China

    Bo Yue, Shuang Wang & Licheng Jiao

  2. IST, Graduate School of Informatics, Kyoto University, Kyoto, Japan

    Xuefeng Liang

Authors
  1. Bo Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xuefeng Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Licheng Jiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Shuang Wang or Xuefeng Liang .

Editor information

Editors and Affiliations

  1. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Chu-Song Chen

  2. Tsinghua University , Beijing, China

    Jiwen Lu

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Kai-Kuang Ma

1 Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 4747 KB)

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Yue, B., Wang, S., Liang, X., Jiao, L. (2017). Robust Noisy Image Super-Resolution Using \(\ell _1\)-norm Regularization and Non-local Constraint. In: Chen, CS., Lu, J., Ma, KK. (eds) Computer Vision – ACCV 2016 Workshops. ACCV 2016. Lecture Notes in Computer Science(), vol 10116. Springer, Cham. https://doi.org/10.1007/978-3-319-54407-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-54407-6_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54406-9

  • Online ISBN: 978-3-319-54407-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation