Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing
Abstract
:1. Introduction
- A sparse constrained regularization is proposed to explore the sparse structure of the HSI differential image in the horizontal and vertical directions. In addition, weight coefficients are used to enhance sparsity.
- The norm is utilized to constrain the sparse regularizer, and the norm is embedded in the NTF framework to maintain the sparsity of the abundance tensor.
- The proposed algorithm WSCTF uses the alternating direction method of multipliers to iteratively optimize. Experiments on three real data prove the effectiveness of our algorithm.
2. Related Work
2.1. Notation
2.2. NTF Unmixing Method
3. Proposed Method
3.1. WSCTF Model
3.2. Optimization
Algorithm 1 The proposed method SCLT |
Input: —the mixing hyperspectral data; P—the number of endmembers; Parameter , and .
Output: —the abundance tensor; —the endmember matrix. |
4. Experiments
4.1. Sythetic Data
4.2. Real Datasets
4.3. Parameter Analysis
4.4. Complexity Analysis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Data | SNR | SULRSR-TV | NMF-QMV | MV-NTF | NL-TSUn | ULTRA-V | WSCTF |
---|---|---|---|---|---|---|---|
10 dB | 0.0995 ± 0.0049 | 0.0960 | 0.1906 ± 0.0041 | 0.1447 ± 0.0621 | 0.2339 ± 0.0031 | 0.0827 ± 0.0019 | |
DS1 | 20 dB | 0.0805 ± 0.0077 | 0.0723 | 0.1500 ± 0.0420 | 0.1024 ± 0.0352 | 0.1701 ± 0.0214 | 0.0682 ± 0.0241 |
30 dB | 0.0797 ± 0.0051 | 0.0624 | 0.1456 ± 0.0164 | 0.0828 ± 0.0614 | 0.2291 ± 0.0510 | 0.0621 ± 0.0146 | |
10 dB | 0.1433 ± 0.0143 | 0.1200 | 0.1256 ± 0.0091 | 0.1326 ± 0.0312 | 0.1980 ± 0.0312 | 0.1126 ± 0.0321 | |
DS2 | 20 dB | 0.1366 ± 0.0106 | 0.1193 | 0.1580 ± 0.0217 | 0.1273 ± 0.0318 | 0.1876 ± 0.0021 | 0.1004 ± 0.0021 |
30 dB | 0.1344 ± 0.0054 | 0.0942 | 0.1005 ± 0.0032 | 0.0987 ± 0.0021 | 0.1690 ± 0.0410 | 0.0911 ± 0.0039 |
Data | SNR | SULRSR-TV | NMF-QMV | MV-NTF | NL-TSUn | ULTRA-V | WSCTF |
---|---|---|---|---|---|---|---|
10 dB | 0.1115 ± 0.0139 | 0.3624 | 0.5127 ± 0.0164 | 0.1326 ± 0.0052 | 0.1427 ± 0.0216 | 0.0920 ± 0.0031 | |
DS1 | 20 dB | 0.0453 ± 0.0014 | 0.0867 | 0.4023 ± 0.0121 | 0.0952 ± 0.0143 | 0.1214 ± 0.0126 | 0.0434 ± 0.0108 |
30 dB | 0.0134 ± 0.0004 | 0.0920 | 0.3210 ± 0.0114 | 0.0623 ± 0.2432 | 0.0737 ± 0.0601 | 0.0126 ± 0.0245 | |
10 dB | 0.1977 ± 0.0928 | 0.2325 | 0.5232 ± 0.0088 | 0.4329 ± 0.0621 | 0.3172 ± 0.0241 | 0.1920 ± 0.0314 | |
DS2 | 20 dB | 0.1688 ± 0.0794 | 0.0861 | 0.5161 ± 0.0128 | 0.4061 ± 0.0051 | 0.3202 ± 0.0152 | 0.0827 ± 0.0021 |
30 dB | 0.1423 ± 0.0366 | 0.0184 | 0.3237 ± 0.0672 | 0.2846 ± 0.0601 | 0.3110 ± 0.0031 | 0.0094 ± 0.0017 |
SULRSR-TV | NMF-QMV | MV-NTF | NL-TSUn | ULTRA-V | WSCTF | |
---|---|---|---|---|---|---|
Tree | 0.2012 ± 0.0187 | 0.2571 | 0.2416 ± 0.0136 | 0.2081 ± 0.0306 | 0.0502 ± 0.0003 | 0.0495 ± 0.0476 |
Soil | 0.2336 ± 0.0011 | 1.1890 | 0.2601 ± 0.0089 | 0.2334 ± 0.0001 | 0.1422 ± 0.0342 | 0.1071 ± 0.1660 |
Water | 0.6194 ± 0.1761 | 0.1386 | 0.1586 ± 0.0956 | 0.4929 ± 0.2715 | 0.5641 ± 0.0013 | 0.3977 ± 0.0072 |
Road | 0.2943 ± 0.0722 | 0.1840 | 0.4544 ± 0.0706 | 0.3665 ± 0.1179 | 0.0362 ± 0.0033 | 0.2461 ± 0.0303 |
Mean | 0.3863 ± 0.0357 | 0.4421 | 0.3024 ± 0.0396 | 0.3723 ± 0.0482 | 0.3002 ± 0.0010 | 0.2406 ± 0.0434 |
SULRSR-TV | NMF-QMV | MV-NTF | NL-TSUn | ULTRA-V | WSCTF | |
---|---|---|---|---|---|---|
Tree | 0.0247 ± 0.0121 | 0.0337 | 0.0433 ± 0.0129 | 0.0288 ± 0.0161 | 0.0340 ± 0.0272 | 0.0201 ± 0.0024 |
Soil | 0.0495 ± 0.0011 | 0.0732 | 0.0953 ± 0.0011 | 0.0496 ± 0.0001 | 0.0566 ± 0.0090 | 0.0685 ± 0.0102 |
Water | 0.1299 ± 0.0004 | 1.4831 | 0.2810 ± 0.0050 | 0.1289 ± 0.0003 | 0.2401 ± 0.0221 | 0.0675 ± 0.0021 |
Mean | 0.0818 ± 0.0019 | 0.8575 | 0.1733 ± 0.0036 | 0.0825 ± 0.0026 | 0.1438 ± 0.0154 | 0.0611 ± 0.0105 |
SULRSR-TV | NMF-QMV | MV-NTF | NL-TSUn | ULTRA-V | WSCTF | |
---|---|---|---|---|---|---|
Alunite | 0.0966 ± 0.0739 | 0.0860 | 0.0748 ± 0.0875 | 0.0783 ± 0.0243 | 0.1897 ± 0.0722 | 0.0735 ± 0.0134 |
Andradite | 0.1353 ± 0.0157 | 0.1212 | 0.0661 ± 0.0207 | 0.0958 ± 0.0376 | 0.0971 ± 0.0323 | 0.0631 ± 0.0369 |
Buddingtonite | 0.0699 ± 0.0174 | 0.0797 | 0.0718 ± 0.0193 | 0.0982 ± 0.0183 | 0.1097 ± 0.0193 | 0.0669 ± 0.0217 |
Chalcedony | 0.1482 ± 0.0230 | 0.1428 | 0.1652 ± 0.0304 | 0.1253 ± 0.0444 | 0.1212 ± 0.0307 | 0.0829 ± 0.0317 |
Dumortierite | 0.0855 ± 0.0152 | 0.1108 | 0.0984 ± 0.0208 | 0.1709 ± 0.0240 | 0.0936 ± 0.0158 | 0.0944 ± 0.0258 |
Kaolinite#1 | 0.0718 ± 0.0155 | 0.0795 | 0.0841 ± 0.0070 | 0.0738 ± 0.0095 | 0.1300 ± 0.0137 | 0.0859 ± 0.0104 |
Kaolinite#2 | 0.0678 ± 0.0187 | 0.1014 | 0.0786 ± 0.0098 | 0.0625 ± 0.0126 | 0.0391 ± 0.0160 | 0.0638 ± 0.0154 |
Montmorillonite | 0.0504 ± 0.0132 | 0.1114 | 0.0535 ± 0.0065 | 0.0720 ± 0.0124 | 0.0508 ± 0.0134 | 0.0501 ± 0.0143 |
Muscovite | 0.1066 ± 0.0450 | 0.0811 | 0.2518 ± 0.0498 | 0.0925 ± 0.0457 | 0.1257 ± 0.0389 | 0.1719 ± 0.0461 |
Nontronite | 0.0730 ± 0.0193 | 0.0715 | 0.1086 ± 0.0111 | 0.0813 ± 0.0156 | 0.0835 ± 0.0246 | 0.0702 ± 0.0271 |
Pyrope | 0.1876 ± 0.0521 | 0.1812 | 0.1431 ± 0.0598 | 0.1501 ± 0.0464 | 0.1737 ± 0.0535 | 0.1326 ± 0.0574 |
Sphene | 0.0663 ± 0.0564 | 0.1879 | 0.0700 ± 0.0673 | 0.1642 ± 0.0137 | 0.2306 ± 0.0506 | 0.0744 ± 0.0829 |
Mean | 0.1042 ± 0.0062 | 0.1190 | 0.1176 ± 0.0135 | 0.1054 ± 0.0066 | 0.1317 ± 0.0089 | 0.0925 ± 0.0134 |
Data | ||
---|---|---|
DS1 | 0.015 | 0.010 |
DS2 | 0.015 | 0.010 |
Jasper | 0.02 | 0.015 |
Samon | 0.015 | 0.010 |
Cuprite | 0.010 | 0.010 |
SULRSR-TV | NMF-QMV | MV-NTF | NL-TSUn | ULTRA-V | WSCTF | |
---|---|---|---|---|---|---|
Jasper Ridge Data | 6 | 10 | 170 | 55 | 26 | 5 |
Samon Data | 5 | 9 | 135 | 29 | 14 | 4 |
Cuprite Data | 34 | 293 | 904 | 194 | 209 | 17 |
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Feng, X.; Han, L.; Dong, L. Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing. Remote Sens. 2022, 14, 383. https://doi.org/10.3390/rs14020383
Feng X, Han L, Dong L. Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing. Remote Sensing. 2022; 14(2):383. https://doi.org/10.3390/rs14020383
Chicago/Turabian StyleFeng, Xinxi, Le Han, and Le Dong. 2022. "Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing" Remote Sensing 14, no. 2: 383. https://doi.org/10.3390/rs14020383
APA StyleFeng, X., Han, L., & Dong, L. (2022). Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing. Remote Sensing, 14(2), 383. https://doi.org/10.3390/rs14020383