A Framelet-Based Iterative Pan-Sharpening Approach
Abstract
:1. Introduction
2. Related Work
3. The Proposed Method
- (1)
- For , update each by solving:
- (2)
- For , update each by solving:
- (3)
- For , update each by solving:
- (4)
- For , update each by .
- (5)
- For , update each by .
Algorithm 1 ADMM scheme for the proposed model |
Input: panchromatic image , upsampled multispectral image , . Output: high-resolution multispectral image . while not converged do for do (1) Solve by (12). (2) Solve by (14). (3) Solve by (15). (4) Update by . (5) Update by . end for end while |
Algorithm 2 The proposed iterative pan-sharpening algorithm |
Input: panchromatic image , multispectral image , . Output: high-resolution multispectral image . 1. Initialization: . for do (1) Upsample to obtain . (2) Compute by implementing Algorithm 1 ( instead of as input). (3) Update by . (4) Update by . end for 2. Compute the final output: . |
4. Results and Discussion
4.1. Visual Comparison
4.2. Quantitative Comparison
4.3. Discussion on the Number of Outer Iterations
4.4. Time Comparison with RKHS Method
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Method | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
PCA | 5.2812 | 0.7734 | 0.3895 | 21.5874 | 4.7453 | 0.7520 | 0.1246 | 18.0910 |
GS | 2.3162 | 0.8510 | 0.8345 | 12.3841 | 2.9310 | 0.9433 | 0.0715 | 22.9177 |
HPF | 2.1727 | 0.8561 | 0.8299 | 8.5465 | 2.0681 | 0.9420 | 0.0493 | 26.1392 |
MTFGLP | 2.2767 | 0.8756 | 0.8399 | 6.1273 | 1.6287 | 0.9439 | 0.0354 | 29.0296 |
PHLP | 5.0053 | 0.8184 | 0.7736 | 11.5526 | 2.9020 | 0.9077 | 0.0667 | 23.5214 |
NIHS | 2.9060 | 0.7212 | 0.7521 | 14.4955 | 3.4247 | 0.9161 | 0.0837 | 21.5503 |
RKHS | 3.0682 | 0.8725 | 0.8380 | 7.4955 | 1.9868 | 0.9413 | 0.0433 | 27.2789 |
Proposed | 2.2422 | 0.8816 | 0.8525 | 5.1265 | 1.4605 | 0.9484 | 0.0296 | 30.5785 |
Method | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
PCA | 9.5457 | 0.7829 | 0.8387 | 32.8033 | 8.0507 | 0.9276 | 0.0637 | 23.9147 |
GS | 9.1222 | 0.8336 | 0.8900 | 28.8060 | 6.4917 | 0.9645 | 0.0560 | 25.0434 |
HPF | 10.8694 | 0.8376 | 0.9243 | 27.8449 | 6.7583 | 0.9722 | 0.0541 | 25.3382 |
MTFGLP | 4.7925 | 0.9063 | 0.9653 | 14.6515 | 3.2470 | 0.9801 | 0.0285 | 30.9155 |
PHLP | 3.9558 | 0.7749 | 0.9186 | 23.6349 | 4.8308 | 0.9508 | 0.0459 | 26.7620 |
NIHS | 5.8053 | 0.7807 | 0.8954 | 32.9408 | 6.6098 | 0.9500 | 0.0640 | 23.8784 |
RKHS | 3.8294 | 0.9071 | 0.9710 | 12.0542 | 2.5088 | 0.9829 | 0.0234 | 32.6103 |
Proposed | 3.2465 | 0.9278 | 0.9775 | 10.3886 | 2.1452 | 0.9857 | 0.0202 | 33.9019 |
Method | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
PCA | 7.1137 | 0.9256 | 0.9137 | 17.4524 | 3.9960 | 0.9608 | 0.0778 | 22.1796 |
GS | 5.2254 | 0.9312 | 0.9438 | 13.1991 | 3.2049 | 0.9776 | 0.0588 | 24.6058 |
HPF | 4.1352 | 0.9185 | 0.9487 | 9.9563 | 2.4925 | 0.9832 | 0.0444 | 27.0547 |
MTFGLP | 4.3926 | 0.9372 | 0.9531 | 9.1386 | 2.3852 | 0.9857 | 0.0407 | 27.7991 |
PHLP | 4.0716 | 0.7879 | 0.9058 | 13.5540 | 3.2978 | 0.9720 | 0.0604 | 24.3753 |
NIHS | 1.7128 | 0.7751 | 0.8781 | 29.6650 | 5.6749 | 0.9645 | 0.1323 | 17.5718 |
RKHS | 5.3524 | 0.9340 | 0.9546 | 11.7716 | 2.9588 | 0.9864 | 0.0525 | 25.6000 |
Proposed | 3.5176 | 0.9441 | 0.9647 | 6.6818 | 1.7829 | 0.9879 | 0.0298 | 30.5188 |
Method | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
PCA | 8.4179 | 0.8594 | 0.9002 | 23.3863 | 6.1677 | 0.9653 | 0.0565 | 24.9547 |
GS | 7.0558 | 0.8976 | 0.9248 | 25.6653 | 5.2751 | 0.9804 | 0.0620 | 24.1470 |
HPF | 7.7539 | 0.8707 | 0.9172 | 26.0012 | 5.5211 | 0.9727 | 0.0628 | 24.0340 |
MTFGLP | 3.8118 | 0.9162 | 0.9362 | 20.5174 | 4.1687 | 0.9795 | 0.0496 | 26.0915 |
PHLP | 5.8827 | 0.7768 | 0.9044 | 21.1517 | 4.8940 | 0.9659 | 0.0511 | 25.8270 |
NIHS | 3.8008 | 0.7848 | 0.8770 | 34.3983 | 6.4343 | 0.9588 | 0.0831 | 21.6032 |
RKHS | 2.5938 | 0.9266 | 0.9530 | 11.8152 | 2.8106 | 0.9842 | 0.0286 | 30.8851 |
Proposed | 3.2818 | 0.9300 | 0.9566 | 10.8640 | 2.6335 | 0.9843 | 0.0263 | 31.6141 |
Case | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
3.6036 | 0.8633 | 0.8274 | 10.0852 | 2.5146 | 0.9393 | 0.0582 | 24.7013 | |
2.6197 | 0.8796 | 0.8468 | 6.3718 | 1.6839 | 0.9471 | 0.0368 | 28.6898 | |
2.2813 | 0.8816 | 0.8499 | 5.4827 | 1.5165 | 0.9476 | 0.0316 | 29.9951 | |
2.3563 | 0.8828 | 0.8496 | 5.2938 | 1.5354 | 0.9465 | 0.0306 | 30.2996 | |
2.2422 | 0.8816 | 0.8525 | 5.1265 | 1.4605 | 0.9484 | 0.0296 | 30.5785 | |
2.3382 | 0.8822 | 0.8500 | 5.1863 | 1.5145 | 0.9465 | 0.0299 | 30.4778 |
Case | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
5.8470 | 0.8758 | 0.9383 | 19.2451 | 4.1779 | 0.9754 | 0.0374 | 28.5467 | |
3.5671 | 0.9187 | 0.9725 | 11.8189 | 2.4454 | 0.9830 | 0.0230 | 32.7816 | |
3.4947 | 0.9244 | 0.9746 | 11.5754 | 2.3527 | 0.9839 | 0.0225 | 32.9624 | |
4.1877 | 0.9247 | 0.9731 | 12.5506 | 2.5343 | 0.9843 | 0.0244 | 32.2598 | |
3.2465 | 0.9278 | 0.9775 | 10.3886 | 2.1452 | 0.9857 | 0.0202 | 33.9019 | |
3.4306 | 0.9275 | 0.9761 | 10.9675 | 2.2676 | 0.9854 | 0.0213 | 33.4309 |
Case | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
5.2761 | 0.9338 | 0.9484 | 12.1816 | 3.0319 | 0.9816 | 0.0543 | 25.3026 | |
4.2752 | 0.9422 | 0.9608 | 8.2856 | 2.1955 | 0.9872 | 0.0369 | 28.6502 | |
3.7884 | 0.9436 | 0.9637 | 7.1468 | 1.8866 | 0.9877 | 0.0319 | 29.9344 | |
3.6676 | 0.9439 | 0.9640 | 7.3470 | 1.9681 | 0.9878 | 0.0328 | 29.6944 | |
3.5176 | 0.9441 | 0.9647 | 6.6818 | 1.7829 | 0.9879 | 0.0298 | 30.5188 | |
3.2613 | 0.9433 | 0.9652 | 6.7456 | 1.8407 | 0.9876 | 0.0301 | 30.4363 |
Case | SAM | Q4 | Q | RASE | ERGAS | CC | RMSE | PSNR |
---|---|---|---|---|---|---|---|---|
6.8677 | 0.9109 | 0.9284 | 23.4889 | 4.8319 | 0.9803 | 0.0568 | 24.9167 | |
3.6602 | 0.9270 | 0.9504 | 13.6097 | 3.1098 | 0.9824 | 0.0329 | 29.6569 | |
2.8394 | 0.9287 | 0.9535 | 10.9922 | 2.6297 | 0.9824 | 0.0266 | 31.5123 | |
2.6245 | 0.9268 | 0.9518 | 10.1182 | 2.5081 | 0.9819 | 0.0245 | 32.2318 | |
3.2818 | 0.9300 | 0.9566 | 10.8640 | 2.6335 | 0.9843 | 0.0263 | 31.6141 | |
3.8526 | 0.9295 | 0.9558 | 10.8789 | 2.6852 | 0.9841 | 0.0263 | 31.6022 |
Method | Quickbird | Pléiades | WorldView-2 | SPOT-6 |
---|---|---|---|---|
RKHS | 7263.22 | 27882.87 | 16559.93 | 31576.65 |
Proposed | 207.71 | 851.11 | 512.47 | 863.59 |
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Share and Cite
Zhang, Z.-Y.; Huang, T.-Z.; Deng, L.-J.; Huang, J.; Zhao, X.-L.; Zheng, C.-C. A Framelet-Based Iterative Pan-Sharpening Approach. Remote Sens. 2018, 10, 622. https://doi.org/10.3390/rs10040622
Zhang Z-Y, Huang T-Z, Deng L-J, Huang J, Zhao X-L, Zheng C-C. A Framelet-Based Iterative Pan-Sharpening Approach. Remote Sensing. 2018; 10(4):622. https://doi.org/10.3390/rs10040622
Chicago/Turabian StyleZhang, Zi-Yao, Ting-Zhu Huang, Liang-Jian Deng, Jie Huang, Xi-Le Zhao, and Chao-Chao Zheng. 2018. "A Framelet-Based Iterative Pan-Sharpening Approach" Remote Sensing 10, no. 4: 622. https://doi.org/10.3390/rs10040622