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)
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Figure 1
The flaw chart of K-SVD algorithm
Figure 2
(Color online) The image super-resolution reconstruction based on sparse representation
Figure 3
The flow chart of separable dictionary learning based on oblique manifold
Figure 4
(Color online) The graphics of (a) dictionary and (b) sparse represent coefficients
Figure 5
The flow chart of separable dictionary learning based on 2D sparse coding and oblique manifold
Figure 6
(Color online) The super-resolution results of flower with magnification 4. (a) The original image; (b) Bicubic; (c) Zedye
Figure 7
The super-resolution results of facial images with magnification 3
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 |
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 |
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 |