Single Noisy Image Super Resolution by Minimizing Nuclear Norm in Virtual Sparse Domain

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 841)


Super-resolving a noisy image is a challenging problem, and needs special care as compared to the conventional super resolution approaches, when the power of noise is unknown. In this scenario, we propose an approach to super-resolve single noisy image by minimizing nuclear norm in a virtual sparse domain that tunes with the power of noise via parameter learning. The approach minimizes nuclear norm to explore the inherent low-rank structure of visual data, and is further augmented with coarse-to-fine information by adaptively re-aligning the data along the principal components of a dictionary in virtual sparse domain. The experimental results demonstrate the robustness of our approach across different powers of noise.


Super resolution Noise Nuclear norm Virtual sparsity Dictionary 


  1. 1.
    Park, S.C., Park, M.K., Kang, M.G.: Super-resolution image reconstruction: a technical overview. IEEE Sig. Process. Mag. 20(3), 21–36 (2003)CrossRefGoogle Scholar
  2. 2.
    Stark, H., Oskoui, P.: High-resolution image recovery from image-plane arrays, using convex projections. J. Opt. Soc. Am. A 6(11), 1715–1726 (1989)CrossRefGoogle Scholar
  3. 3.
    Freeman, W., Jones, T., Pasztor, E.: Example-based super-resolution. IEEE Comput. Graph. Appl. 22(2), 56–65 (2002)CrossRefGoogle Scholar
  4. 4.
    Dong, W., Zhang, L., Shi, G., Wu, X.: Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans. Image Process. 20(7), 1838–1857 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Yang, J., Wright, J., Huang, T., Ma, Y.: Image super-resolution as sparse representation of raw image patches. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8, June 2008Google Scholar
  6. 6.
    Mandal, S., Sao, A.K.: Employing structural and statistical information to learn dictionary(s) for single image super-resolution in sparse domain. Sig. Process. Image Commun. 48, 63–80 (2016)CrossRefGoogle Scholar
  7. 7.
    Glasner, D., Bagon, S., Irani, M.: Super-resolution from a single image. In: IEEE International Conference on Computer Vision (ICCV), pp. 349–356, September 2009Google Scholar
  8. 8.
    Yang, C.-Y., Huang, J.-B., Yang, M.-H.: Exploiting self-similarities for single frame super-resolution. In: Kimmel, R., Klette, R., Sugimoto, A. (eds.) ACCV 2010. LNCS, vol. 6494, pp. 497–510. Springer, Heidelberg (2011). Scholar
  9. 9.
    Vishnukumar, S., Nair, M.S., Wilscy, M.: Edge preserving single image super-resolution with improved visual quality. Sig. Process. 105, 283–297 (2014)CrossRefGoogle Scholar
  10. 10.
    Mandal, S., Bhavsar, A., Sao, A.: Super-resolving a single intensity/range image via non-local means and sparse representation. In: Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP), pp. 1–8, December 2014Google Scholar
  11. 11.
    Singh, A., Porikli, F., Ahuja, N.: Super-resolving noisy images. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2846–2853, June 2014Google Scholar
  12. 12.
    Mandal, S., Bhavsar, A., Sao, A.K.: Noise adaptive super-resolution from single image via non-local mean and sparse representation. Sig. Process. 132, 134–149 (2017)CrossRefGoogle Scholar
  13. 13.
    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). Scholar
  14. 14.
    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, Cham (2015). Scholar
  15. 15.
    Yang, J., Wright, J., Huang, T., Ma, Y.: Image super-resolution via sparse representation. IEEE Trans. Image Process. 19(11), 2861–2873 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Mandal, S., Bhavsar, A., Sao, A.K.: Depth map restoration from undersampled data. IEEE Trans. Image Process. 26(1), 119–134 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Mandal, S., Sao, A.: Edge preserving single image super resolution in sparse environment. In: 20th IEEE International Conference on Image Processing (ICIP), pp. 967–971, September 2013Google Scholar
  18. 18.
    Yang, S., Wang, M., Chen, Y., Sun, Y.: Single-image super-resolution reconstruction via learned geometric dictionaries and clustered sparse coding. IEEE Trans. Image Process. 21(9), 4016–4028 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    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(3), 846–861 (2015)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Huang, J.B., Singh, A., Ahuja, N.: Single image super-resolution from transformed self-exemplars. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5197–5206, June 2015Google Scholar
  21. 21.
    Wang, S., Zhang, L., Liang, Y.: Nonlocal spectral prior model for low-level vision. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds.) ACCV 2012. LNCS, vol. 7726, pp. 231–244. Springer, Heidelberg (2013). Scholar
  22. 22.
    Gu, S., Xie, Q., Meng, D., Zuo, W., Feng, X., Zhang, L.: Weighted nuclear norm minimization and its applications to low level vision. Int. J. Comput. Vis. 121(2), 183–208 (2017)CrossRefGoogle Scholar
  23. 23.
    Dong, W., Shi, G., Li, X., Ma, Y., Huang, F.: Compressive sensing via nonlocal low-rank regularization. IEEE Trans. Image Process. 23(8), 3618–3632 (2014)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Dong, W., Shi, G., Li, X.: Nonlocal image restoration with bilateral variance estimation: a low-rank approach. IEEE Trans. Image Process. 22(2), 700–711 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Cai, J.F., Cands, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Image Processing and Computer Vision Lab, Department of Electrical EngineeringIIT MadrasChennaiIndia

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