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A novel super-resolution image and video reconstruction approach based on Newton-Thiele’s rational kernel in sparse principal component analysis

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Abstract

In this paper, we propose a new image and video sequences reconstruction approach, where the Newton-Thiele’s vector valued rational interpolation is combined with the sparse principal component analysis. Through observation of the degraded model, the reconstruction scheme is performed by two steps. Firstly, the sparse principal component analysis and the linear minimum mean square-error estimation method are used to remove the noise from the degraded image. And then, the Newton-Thiele’s vector valued rational interpolation is used to magnify the denoising result, by which the details and texture regions of image can be well preserved. By using this novel reconstruction model by Newton-Thiele’s rational kernel in sparse principal component analysis, the final reconstructed results not only have good visual effect, but also have rich texture details. In order to show the effectiveness and robustness of the proposed method, we have done plenty of experiments on images and video sequences, and the experimental results show that the proposed method can produce better high-quality resolution results, as compared with the state-of-the-art methods.

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References

  1. Bai T, Tan JQ, Hu M, Wang Y (2014) A novel algorithm for removal of salt and pepper noise using continued fractions interpolation. Signal Process 102:247–255

    Article  Google Scholar 

  2. Bertero M, Boccacci P (1998) Introduction to inverse problems in imaging. IOP, Bristol

    Book  MATH  Google Scholar 

  3. Dong WS, Zhang L, Shi GM, Wu XL (2011) Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans Imag Process 20(7):1838–1857

    Article  MathSciNet  Google Scholar 

  4. Dong WS, Zhang L, Shi GM (2011) Centralized sparse representation for image restoration. IEEE Int Conf Comput Vision (ICCV) 1259–1266. doi:10.1109/ICCV.2011.6126377

  5. Graves-Morris PR (1983) Vector valued rational interpolants I. Numer Math 42(3):331–348

    Article  MathSciNet  MATH  Google Scholar 

  6. He L, Qi HR, Zaretzki R (2013) Beta process joint dictionary learning for coupled feature spaces with application to single image super-resolution. 26th IEEE Conf Comput Vis Pattern Recognit 345–352

  7. He L, Tan JQ, Su Z, Luo XN, Xie CJ (2015) Super-resolution by polar Newton-Thiele’s rational kernel in centralized sparsity paradigm. Sign Process Image Commun 31:86–99

    Article  Google Scholar 

  8. Hu M, Tan JQ (2006) Adaptive osculatory rational interpolation for image processing. J Comput Appl Math 195:46–53

    Article  MathSciNet  MATH  Google Scholar 

  9. Huo X, Tan JQ, He L, Hu M (2014) An automatic video scratch removal based on Thiele type continued fraction. Multimed Tools Appl 71(2):451–467

    Article  Google Scholar 

  10. Jiang JJ, Hu RM, Han Z, Lu T (2014) Efficient single image super-resolution via graph-constrained least squares regression. Multimed Tools Appl 72(3):2573–2596

    Article  Google Scholar 

  11. Liu P, Eom KB (2013) Restoration of multispectral images by total variation with auxiliary image. Opt Lasers Eng 51(7):873–882

    Article  Google Scholar 

  12. Liu C, Shum H, Freeman W (2007) Face hallucination: theory and practice. Int J Comput Vis 75(1):115–134

    Article  Google Scholar 

  13. Meng DY, Zhao Q, Xu ZB (2012) Improve robustness of sparse PCA by L 1-norm maximization. Pattern Recogn 45(1):487–497

    Article  MATH  Google Scholar 

  14. Sajjad M, Ejaz N, Baik SW (2014) Multi-kernel based adaptive interpolation for image super-resolution. Multimed Tools Appl 72(3):2063–2085

    Article  Google Scholar 

  15. Shahar O, Faktor A, Irani M (2011) Space-time super-resolution from a single video. IEEE Conf Comput Vis Pattern Recognit 3353–3360. doi:10.1109/CVPR.2011.5995360

  16. Sun J, Xu ZZ, Shum H (2008) Image super-resolution using gradient profile prior. IEEE Conf Comput Vis Pattern Recognit (CVPR) 1–8. doi:10.1109/CVPR.2008.4587659

  17. Sun J, Zheng NN, Tao H, Shum H (2003) Image hallucination with primal sketch priors. IEEE Comput Soc Conf Comput Vis Pattern Recognit (CVPR) 2:729–736. doi:10.1109/CVPR.2003.1211539

    Google Scholar 

  18. Sun J, Zheng NN, Tao H, Shum HY (2003) Image hallucination with primal sketch prior. IEEE Comput Soc Conf Comput Vis Pattern Recognit (CVPR) 2:II-729–II-736. doi:10.1109/CVPR.2003.1211539

    Google Scholar 

  19. Tan JQ (2003) Computation of vector valued blending rational interpolants. J Chin Univ 12(1):91–98

    MathSciNet  MATH  Google Scholar 

  20. Tan JQ, Tang S (2000) Bivariate composite vector valued rational interpolation. Math Comput 69:1521–1532

    Article  MathSciNet  MATH  Google Scholar 

  21. Tan JQ, Zhu GQ (1998) General framework for vector valued interpolants. proceedings of third china-Japan seminar on numerical math. Science Press, Beijing/New York, pp 273–278

    Google Scholar 

  22. Tang Y, Yuan Y, Yan PK, Li XL (2013) Greedy regression in sparse coding space for single-image super-resolution. J Vis Commun Imag Represent 24(2):148–159

    Article  Google Scholar 

  23. Wan BK, Meng L, Ming D, Qi HZ (2009) Video image super-resolution restoration based on iterative back-projection algorithm. IEEE Int Conf Comput Intell Meas Syst Appl 46–49. doi:10.1109/CIMSA.2009.5069916

  24. Wang Q, Tang X, Shum HY (2005) Patch based blind image super resolution. Proc Tenth IEEE Int Conf Comput Vis (ICCV) 1:709–716. doi:10.1109/ICCV.2005.186

    Article  Google Scholar 

  25. Xu J, Zhang L, Zuo WM, Zhang D, Feng XC (2015) Patch group based nonlocal self-similarity prior learning for image denoising. IEEE Int Conf Comput Vis 244–252

  26. Yahya AA, Tan JQ, Hu M (2014) A blending method based on partial differential equations for image denoising. Multimed Tools Appl 73(3):1843–1862

    Article  Google Scholar 

  27. Yang JC, Wright J, Huang T, Ma Y (2008) Image super-resolution as sparse representation of raw image patches. Comput Vis Pattern Recognit 1–8. doi:10.1109/CVPR.2008.4587647

  28. Yang JC, Wright J, Huang T, Ma Y (2010) Image super-resolution via sparse representation. IEEE Trans Image Process 19(11):2861–2873

    Article  MathSciNet  Google Scholar 

  29. Zass R, Shashua A (2006) Nonnegative sparse PCA. 20th Ann Conf Neural Inf Process Syst 1561–1568

  30. Zhang L, Dong WS, Zhang D, Shi GM (2010) Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recogn 43(4):1531–1549

    Article  MATH  Google Scholar 

  31. Zoran D, Weiss Y (2011) From learning models of natural image patches to whole image restoration. IEEE Int Conf Comput Vis 2011:479–486. doi:10.1109/ICCV.2011.6126278

    Google Scholar 

  32. Zou H, Hastie T, Tibshirani R (2004) Sparse principal component analysis. J Comput Graph Stat 15(2):265–286

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the referees for their valuable comments and constructive suggestions which greatly help improve the clarity of the paper. This work is supported by the National Natural Science Foundation of China under Grant Nos. 61472466, 61502141, and 61070227, the NSFC-Guangdong Joint Foundation (Key Project) under Grant No. U1135003, the Anhui Provincial Natural Science Foundation under Grant No. 1508085QF128, and the Fundamental Research Funds for the Central Universities under Grant No. JZ2015HGXJ0175.

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Authors and Affiliations

  1. School of Computer and Information, School of Mathematics, Hefei University of Technology, Hefei, 230009, China

    Lei He, Jieqing Tan & Xing Huo

  2. Institute of Intelligent Machines, Chinese Academy of Science, Hefei, China

    Chengjun Xie

Authors
  1. Lei He
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  2. Jieqing Tan
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  3. Xing Huo
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  4. Chengjun Xie
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Correspondence to Lei He.

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He, L., Tan, J., Huo, X. et al. A novel super-resolution image and video reconstruction approach based on Newton-Thiele’s rational kernel in sparse principal component analysis. Multimed Tools Appl 76, 9463–9483 (2017). https://doi.org/10.1007/s11042-016-3557-1

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  • DOI: https://doi.org/10.1007/s11042-016-3557-1

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