A New Biorthogonal Spline Wavelet-Based K-Layer Network for Underwater Image Enhancement
Abstract
:1. Introduction
2. Related Work
3. Methodology
3.1. A New Biorthogonal Cubic Special Spline Wavelet (BCS-SW)
3.1.1. Cubic Special Spline Algorithm
3.1.2. Constructing Biorthogonal Cubic Special Spline Wavelet (BCS-SW)
Algorithm 1 BCS-SW Filter Algorithm |
Input: L: sum of the vanishing moment order of and by Equations (8) and (9), and ; : defined by Equation (11); : axis angel; n: integer, the subscript of the low-pass filter coefficient; Output: : the set of corresponding low-pass filter coefficients of ; : the set of corresponding low-pass filter coefficients of ;
|
3.2. K-Layer Network
4. Experiments
4.1. Implementation Details
4.2. BCS-SW vs. Other Wavelets in Underwater Image Related Tasks
4.3. KLN vs. Other Underwater Image Enhancement Algorithms
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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N | |||
---|---|---|---|
2 | 1417/1969, 737/1491, 389/2760, 5/907, −1/1415, 1/6154, −1/19,642, 1/51,496… | 2 | 813/731, 63/298, −419/1066, 91/1301, 81/992, −8/273, 3/689, −1/647, 1/1482, −1/3011, 1/5619… |
3 | 330/317, 38/141, −157/398, −3/488, 137/972, −13/669, −17/1051, 7/1205, −1/1437, 1/4657, −1/12,080 … | ||
4 | 645/643, 96/319, −231/593, −45/733, 143/838, 3/610, −3/83, 7/1030, 5/1491, −1/819, 1/8087… | ||
5 | 483/493, 319/994, −589/1535, −65/634, 93/502, 23/749, −25/496, 1/369, 3/308, −1/479, −1/1397… |
Image | Haar | BCS-SW | ||
---|---|---|---|---|
PSNR | SSIM | PSNR ↑ | SSIM ↑ | |
Figure 4a | 31.7752 | 0.9922 | 32.7565 | 0.9938 |
Figure 4b | 36.6892 | 0.9820 | 40.8069 | 0.9928 |
Figure 4c | 40.3920 | 0.9979 | 42.1529 | 0.9986 |
Figure 4d | 27.8036 | 0.9121 | 30.3055 | 0.9477 |
Image | Haar | Bior3.5 | DB2 | BCS-SW | ||||
---|---|---|---|---|---|---|---|---|
PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR ↑ | SSIM ↑ | |
Figure 5a | 22.00 | 0.6166 | 21.80 | 0.5366 | 22.89 | 0.6664 | 23.36 | 0.6911 |
Figure 5b | 22.11 | 0.5597 | 21.89 | 0.5521 | 23.12 | 0.6232 | 23.76 | 0.6547 |
Figure 5c | 24.62 | 0.6159 | 23.53 | 0.5824 | 25.92 | 0.7137 | 27.00 | 0.7484 |
Figure 5d | 22.31 | 0.5626 | 21.83 | 0.5335 | 23.19 | 0.6205 | 23.85 | 0.6528 |
Original | CLAHE (1994) | UCDP (2013) | GDCP (2018) | Ucolor (2021) | MLLE (2022) | TOPAL (2022) | U-Shape (2023) | WWPF (2023) | Semi-UIR (2023) | OURS | |
---|---|---|---|---|---|---|---|---|---|---|---|
UIQM ↑ | 2.4745 | 2.7409 | 2.0180 | 2.0995 | 3.0305 | 1.9561 | 2.8994 | 3.0141 | 2.3900 | 2.9503 | 2.8546 |
UCIQE ↑ | 0.5031 | 0.5527 | 0.5860 | 0.6141 | 0.5709 | 0.6216 | 0.5726 | 0.5748 | 0.6341 | 0.6188 | 0.6089 |
PCQI ↑ | — | 1.2036 | 0.9324 | 1.0161 | 1.1033 | 1.2242 | 1.1377 | 1.0866 | 1.2187 | 1.1704 | 1.2516 |
PSNR ↑ | — | 23.9048 | 14.0771 | 15.5725 | 21.5026 | 15.3689 | 22.2745 | 21.9905 | 15.8602 | 19.3214 | 25.6162 |
SSIM ↑ | — | 0.9114 | 0.6379 | 0.7581 | 0.8984 | 0.5848 | 0.9028 | 0.8528 | 0.6345 | 0.8005 | 0.9538 |
Original | CLAHE (1994) | UCDP (2013) | GDCP (2018) | Ucolor (2021) | MLLE (2022) | TOPAL (2022) | U-Shape (2023) | WWPF (2023) | Semi-UIR (2023) | OURS | |
---|---|---|---|---|---|---|---|---|---|---|---|
UIQM ↑ | 2.4641 | 2.6795 | 2.1315 | 2.4002 | 2.9963 | 2.4112 | 2.8644 | 2.9705 | 2.6591 | 2.9582 | 2.7684 |
UCIQE ↑ | 0.4321 | 0.4761 | 0.5128 | 0.5467 | 0.5317 | 0.5829 | 0.5004 | 0.5456 | 0.5958 | 0.5667 | 0.5897 |
PCQI ↑ | — | 1.2268 | 1.1041 | 1.2127 | 1.2121 | 1.3304 | 1.0899 | 1.2035 | 1.3002 | 1.2911 | 1.2616 |
U-Shape | Semi-UIR | OURS | |
---|---|---|---|
Flops (G) | 26.11 | 36.44 | 207.8 |
Total Parameters (M) | 31.6 | 1.68 | 57.24 |
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Zhou, D.; Cai, Z.; He, D. A New Biorthogonal Spline Wavelet-Based K-Layer Network for Underwater Image Enhancement. Mathematics 2024, 12, 1366. https://doi.org/10.3390/math12091366
Zhou D, Cai Z, He D. A New Biorthogonal Spline Wavelet-Based K-Layer Network for Underwater Image Enhancement. Mathematics. 2024; 12(9):1366. https://doi.org/10.3390/math12091366
Chicago/Turabian StyleZhou, Dujuan, Zhanchuan Cai, and Dan He. 2024. "A New Biorthogonal Spline Wavelet-Based K-Layer Network for Underwater Image Enhancement" Mathematics 12, no. 9: 1366. https://doi.org/10.3390/math12091366
APA StyleZhou, D., Cai, Z., & He, D. (2024). A New Biorthogonal Spline Wavelet-Based K-Layer Network for Underwater Image Enhancement. Mathematics, 12(9), 1366. https://doi.org/10.3390/math12091366