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SCIENTIA SINICA Informationis
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SCIENTIA SINICA Informationis, Volume 50 , Issue 2 : 275-288(2020) https://doi.org/10.1360/N112018-00192

The algorithm of image super-resolution reconstruction via separable dictionaries

Fengzhen ZHANG 1,2,3, Yigang CEN 2,3,*, Ruizhen ZHAO 2,3, Yanhong WANG 2,3, Linna ZHANG 4, Shaohai HU 2,3
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  • ReceivedSep 14, 2018
  • AcceptedJan 17, 2019
  • PublishedFeb 12, 2020
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Abstract


Funded by

国家自然科学基金(61872034,61572067,61572063,61572461,11790305)

贵州省自然科学基金([2019]1064)

中央高校基本科研业务费(2017JBZ108)


References

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    Figure 1

    The flaw chart of K-SVD algorithm

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    Figure 2

    (Color online) The image super-resolution reconstruction based on sparse representation

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    Figure 3

    The flow chart of separable dictionary learning based on oblique manifold [14]

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    Figure 4

    (Color online) The graphics of (a) dictionary and (b) sparse represent coefficients

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    Figure 5

    The flow chart of separable dictionary learning based on 2D sparse coding and oblique manifold[15,16]

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    Figure 6

    (Color online) The super-resolution results of flower with magnification 4. (a) The original image; (b) Bicubic; (c) Zedye [8]; (d) ANR [20]; (e) SRCNN [21]; (f) SeDiLSR (ours); (g) ISeDiLSR (ours); (h) ASeDiLSR (ours)

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    Figure 7

    The super-resolution results of facial images with magnification 3

  • Table 1   Average PSNR, SSIM and time (s) on Set5, Set14 and B100
    Set5 Set14 B100
    2 3 4 2 3 4 2 3 4
    Bicubic
    PSNR 33.66 30.39 28.42 30.23 27.54 26 29.32 27.15 25.92
    SSIM 0.93 0.87 0.81 0.87 0.77 0.69 0.832 0.733 0.663
    Yang et al.
    PSNR – 31.41 – – 28.31 – – 27.72 –
    SSIM – 0.88 – – 0.79 – – 0.759 –
    Time – 42.14 – – 96.82 – – 30.04 –
    Zedye et al.
    PSNR 35.78 31.9 29.69 31.81 28.66 26.89 30.39 27.87 26.51
    SSIM 0.95 0.89 0.85 0.898 0.81 0.73 0.866 0.767 0.693
    Time 4.63 2.08 1.25 3.92 4.14 1.22 2.49 1.25 0.79
    ANR
    PSNR 35.79 31.9 26.69 31.76 28.64 26.86 30.42 27.88 26.51
    SSIM 0.949 0.898 0.844 0.899 0.808 0.734 0.869 0.77 0.696
    Time 0.78 0.45 0.34 0.97 0.9 0.46 0.59 0.4 0.31
    SRCNN
    PSNR 36.66 32.389 30.48 32.454 29 27.5 31.36 28.21 26.9
    SSIM 0.954 0.905 0.865 0.906 0.813 0.749 0.887 0.778 0.7
    Time 3.854 3.546 3.863 8.345 7.81 8.396 5.766 5.51 5.804
    SeDiLSR (ours)
    PSNR 35.52 31.945 29.66 32.028 28.93 27.05 31.32 28.46 26.95
    SSIM 0.95 0.9 0.85 0.917 0.831 0.76 0.9 0.8 0.73
    Time 3.135 0.8016 0.38 5.65 0.84 0.6 3.69 0.595 0.44
    ASeDiLSR (ours)
    PSNR 35.34 32.0 29.7 32.059 28.97 27.09 31.11 25.5 26.8
    SSIM 0.953 0.902 0.85 0.918 0.833 0.76 0.904 0.806 0.733
    Time 2.879 0.437 0.34 5.6 0.816 0.57 3.7 0.55 0.36
    ISeDiLSR (ours)
    PSNR 35.56 32.05 29.72 32.062 29.01 27.1 31.35 28.53 26.99
    SSIM 0.954 0.903 0.849 0.918 0.83 0.76 0.9 0.81 0.734
    Time 2.829 0.444 0.315 5.596 0.82 0.576 3.69 0.619 0.39
  • Table 2   The super-resolution results of the datasets of LFW, ORL and Yale
    Bicubic SeDiLSR (ours) ASeDiLSR (ours) ISeDiLSR (ours)
    PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM
    2
    LFW 35.122 0.9616 35.5396 0.968 36.3721 0.9698 35.9968 0.9661
    ORL 30.3001 0.9123 30.5224 0.9195 30.7368 0.9209 30.7202 0.9201
    Yale 26.2624 0.8817 26.1103 0.8817 26.5393 0.8854 26.8538 0.8873
    3
    LFW 29.9856 0.8849 30.2636 0.8961 30.6429 0.8984 30.7381 0.8986
    ORL 27.6624 0.8345 27.8313 0.8433 27.9484 0.8444 27.9499 0.8435
    Yale 23.0754 0.7635 23.0021 0.7624 23.502 0.7735 23.8688 0.7892
    4
    LFW 27.0311 0.7886 27.2905 0.8043 27.4714 0.806 27.6124 0.8102
    ORL 26.0258 0.7593 26.2167 0.7691 26.2728 0.7698 26.3004 0.7704
    Yale 20.9202 0.4181 20.8746 0.4188 21.3545 0.5681 21.7321 0.5265
  • Table 3   The time consumption for the facial images in LFW, ORL and Yale (s)
    Algorithm 2 3 4
    LFW ORL Yale LFW ORL Yale LFW ORL Yale
    SeDiLSR (ours) 0.095 0.0841 0.138 0.0984 0.0703 0.07 0.0949 0.091 0.0581
    ASeDiLSR (ours) 0.0522 0.0827 0.0168 0.028 0.0848 0.052 0.0287 0.1292 0.027
    ISeDiLSR (ours) 0.0906 0.0826 0.1826 0.0964 0.0843 0.0796 0.0844 0.1268 0.1805