Skip to main content
SpringerLink
Log in

Super-resolution image reconstruction using fractional-order total variation and adaptive regularization parameters

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Single-image super-resolution (SR) reconstruction aims to obtain a high-resolution (HR) image from a low-resolution (LR) image. In this paper, a hybrid single-image SR model integrated total variation (TV) and fractional-order TV (FOTV) is proposed to pursuit the adaptive reconstruction of the HR image. Specifically, fractional order in the proposed SR model is adaptively set according to the textural feature of the LR image firstly; then, the SR model is separated into two sub-models with each of them containing exactly one regularization parameter. These two sub-models are solved by using alternating direction multiplier method, and two regularization parameters are concurrently updated by using discrepancy principle. Finally, the solutions of two sub-models are interactively averaged to reconstruct HR image. The results of experiments indicated that the proposed hybrid SR model with adaptive regularization parameters has a comparative performance compared with state-of-the-art methods. Moreover, it would be potentially more adaptive for the condition of varied blurred kernels.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Maeland, E.: On the comparison of interpolation methods. IEEE Trans. Med. Imaging 7(3), 213–217 (1988)

    Article  Google Scholar 

  2. Dong, C., Loy, C.C., He, K., Tang, X.: Learning a deep convolutional network for image super-resolution. In: European Conference on Computer Vision (ECCV) 2014: Computer Vision, pp. 184–199 (2014)

    Chapter  Google Scholar 

  3. 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. 26(7), 3142–3155 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, K., Zuo, W., Zhang, L.: Learning a single convolutional super-resolution network for multiple degradations (2017). arXiv:1712.06116

  5. Kim, J., Lee, J.K., Lee, K.M.: Accurate image super-resolution using very deep convolutional networks. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1646–1654, June 2016

  6. Kim, J., Lee, J.K., Lee, K.M.: Deeply-recursive convolutional network for image super-resolution. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, Nevada, pp. 1637–1645, June 2016

  7. Ren, Z., He, C., Zhang, Q.: Fractional order total variation regularization for image super-resolution. Sig. Process. 93(9), 1408–2421 (2013)

    Article  Google Scholar 

  8. Chuanbo Chen, H., Liang, S.Z., Lyu, Z., Sarem, M.: A novel multi-image super-resolution reconstruction method using anisotropic fractional order adaptive norm. Vis. Comput. 31(9), 1217–1231 (2015)

    Article  Google Scholar 

  9. Dong, W., Zhang, L., Shi, G., Li, X.: Nonlocally centralized sparse representation for image restoration. IEEE Trans. Image Process. 22(4), 1620–1630 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang, K, Zuo, W., Shuhang, Z., Gu, L.: Learning deep CNN denoiser prior for image restoration. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, Hawaii, pp. 2808–2817 (2017)

  11. Marquina, A., Osher, S.J.: Image super-resolution by TV-regularization and Bregman iteration. J. Sci. Comput. 37(3), 367–382 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang, J., Wei, Z., Xiao, L.: A fast adaptive reweighted residual-feedback iterative algorithm for fractional-order total variation regularized multiplicative noise removal of partly-textured images. Sig. Process. 98(5), 381–395 (2014)

    Article  Google Scholar 

  13. Zhang, J., Wei, Z., Xiao, L.: Adaptive fractional-order multi-scale method for image denoising. J. Math. Imaging Vis. 43(1), 39–49 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mathieu, B., Melchior, P., Oustaliup, A., Ceyral, C.: Fractional differentiation for edge detection. Signal Process. 11(83), 2421–2432 (2003)

    Article  MATH  Google Scholar 

  15. Pu, Y.F., Zhou, J.L., Yuan, X.: Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement. IEEE Trans. Image Process. 19(2), 2491–2511 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Zhang, J., Chen, G., Li, D.: Fractional-order total variation combined with sparsifying transforms for compressive sensing sparse image reconstruction. J. Vis. Commun. Image Represent. 38, 407–422 (2016)

    Article  Google Scholar 

  17. Jun, Z., Zhihui, W.: A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising. Appl. Math. Model. 35(5), 2516–2528 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tian, D., Xue, D., Wang, D.: A fractional-order adaptive regularization primal-dual algorithm for image denoising. Inf. Sci. 296(7), 147–159 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Vainikko, G.M.: The discrepancy principle for a class of regularization methods. USSR Comput. Math. Math. Phys. 22(3), 1–19 (1982)

    Article  MATH  Google Scholar 

  20. Wen, Y.W., Chan, R.H.: Parameter selection for total variation-based image restoration using discrepancy principle. IEEE Trans. Image Process. 21(4), 1770–1781 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. He, C., Changhua, H., Zhang, W., Shi, B.: A fast adaptive parameter estimation for total variation image restoration. IEEE Trans. Image Process. 23(12), 4954–4967 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Chen, K., Piccolomini, E.L., Zama, F.: An automatic regularization parameter selection algorithm in the total variation model for image deblurring. Numer. Algorithms 67(1), 73–92 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Srivastava, R., Srivastava, S.: Restoration of poisson noise corrupted digital images with nonlinear PDE based filters along with the choice of regularization parameter estimation. Pattern Recogn. Lett. 34(10), 1175–1185 (2013)

    Article  Google Scholar 

  24. Santosa, E.T.F., Bassreib, A.: L- and \(\theta \)-curve approaches for the selection of regularization parameter in geophysical diffraction tomography. Comput. Geosci. 33(5), 618–629 (2007)

    Article  Google Scholar 

  25. Lin, Y., Wohlberg, B., Guo, H.: UPRE method for total variation parameter selection. Sig. Process. 90(8), 2546–2551 (2010)

    Article  MATH  Google Scholar 

  26. Oliveira, J.P., Bioucas-Dias, J.M., Figueiredo, M.A.T.: Adaptive total variation image deblurring: a majorization minimization approach. Signal Process. 89(9), 1683–1693 (2009)

    Article  MATH  Google Scholar 

  27. Babacan, S.D., Molina, R., Katsaggelos, A.K.: Variational Bayesian blind deconvolution using a total variation prior. IEEE Trans. Image Process. 18(1), 12–26 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Li, F., Shen, C., Shen, C., Zhang, G.: Variational denoising of partly textured images. J. Vis. Commun. Image Represent. 20, 293–300 (2009)

    Article  Google Scholar 

  29. Huang, J., Zhang, S., Metaxas, D.: Efficient MR image reconstruction for compressed MR imaging. Med. Image Anal. 15, 670–679 (2011)

    Article  Google Scholar 

  30. Ng, M.K., Weiss, P., Yuan, X.: Solving constrained total-variation image restoration and reconstruction problems via alternating direction methods. SIAM J. Sci. Comput. 32(5), 2710–2736 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

    Article  MATH  Google Scholar 

  32. Wahlberg, B., Boyd, S., Annergren, M., Wang, Y.: An ADMM algorithm for a class of total variation regularized estimation problems. In: Proceedings of the 16th IFAC Symposium on System Identification, Brussels, Belgium, pp. 83–88 July 2010

  33. Zhang, X., Burger, M., Bresson, X.: Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM J. Imaging Sci. 3(3), 253–276 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  34. Donoho, D.L., Johnstone, I.M.: Ideal spatial adaption by wavelet shrinkage. Biometrika 81, 425–455 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  35. Bevilacqua, M., Roumy, A., Guillemot, C., Alberi-Morel, M.L.: Low-complexity single-image super-resolution based on nonnegative neighbor embedding. In: Proceedings of the 23rd British Machine Vision Conference (BMVC) (2012)

  36. 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, pp. 711–730. Springer, Berlin (2012)

    Chapter  Google Scholar 

  37. Huang, J.B. Singh, A., Ahuja, N.: Single image superresolution using transformed self-exemplars. In: CVPR (2015)

  38. 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 (2001)

  39. Hui, T.-W., Loy, C.C., Tang, X.: Depth map super-resolution by deep multi-scale guidance. In: 2016 European Conference on Computer Vision (ECCV), Amsterdam, pp. 353–369, October 2016

  40. Wang, Z., Sheikh, H.R., Bovik, A.C., Simoncelli, E.P.: Imag equality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Article  Google Scholar 

  41. Dong, W., Zhang, L., Shi, G., Xiaolin, W.: Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans. Image Process. 20(7), 1838–1857 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  42. Yilun, J., Yin, W., Wotao, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sci. 1(3), 248–272 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electrical Engineering and Information Technology, Sichuan University, Chengdu, China

    Xiaomei Yang, Jiawei Zhang, Yanan Liu, Xiujuan Zheng & Kai Liu

Authors
  1. Xiaomei Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiawei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiujuan Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kai Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiujuan Zheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Zhang, J., Liu, Y. et al. Super-resolution image reconstruction using fractional-order total variation and adaptive regularization parameters. Vis Comput 35, 1755–1768 (2019). https://doi.org/10.1007/s00371-018-1570-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-018-1570-2

Keywords

Search

Navigation