An Adaptive SurrogateAssisted Endmember Extraction Framework Based on Intelligent Optimization Algorithms for Hyperspectral Remote Sensing Images
Abstract
:1. Introduction
 (1)
 This paper solves the endmember extraction problem with the proposed ASAEE framework. The overall convergence characteristics and the timeconsuming issue can be significantly improved by the proposed framework.
 (2)
 Three algorithms of ASAEEGA, ASAEEPSO and ASAEEDE based on the ASAEE framework are specifically designed. The experimental results of these three algorithms have been greatly improved compared with the corresponding stateoftheart intelligentbased endmember extraction algorithms.
 (3)
 An adaptive weight surrogateassisted model selection algorithm is designed, which is able to automatically adjust the weights of different surrogateassisted models according to the characteristics of different intelligent optimization algorithms.
 (4)
 We also transfer the ASAEE framework to other intelligentbased endmember extraction algorithms, which greatly reduces the expensive time cost while maintaining the accuracy.
2. Related Work
2.1. IntelligentBased Endmember Extraction Algorithms
2.2. Brief Introduction of the SurrogateAssisted Models
3. Proposed Method
3.1. Motivation
3.2. Initialization and Objective Optimization Function
3.3. ASAEE Framework
Algorithm 1 The ASAEE Framework 
Input:Y: the original hyperspectral image, Maxgen: the max generation number, K: the population size. Output:$\widehat{\mathit{E}}$: the endmember set for reconstructing the remixed image.

3.4. Evolution Strategies
3.4.1. ASAEEGA
3.4.2. ASAEEPSO
3.4.3. ASAEEDE
4. Experimental Results
4.1. Data Sets Description
4.2. Experiments on the Proposed ASAEE Framework
4.3. Comparison of the Proposed ASAEE with Other Methods
4.4. Transfer to Other IntelligentBased Endmember Extraction Algorithms
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Attributes  SNR  20  30  40  

Methods  RMSE  Time (s)  RMSE  Time (s)  RMSE  Time (s)  
PPI  0.6062  3.100  0.6069  3.365  0.6055  3.599  
Geometrialbased  NFINDR  0.0823  1.436  0.0263  1.522  0.0183  1.626 
VCA  0.0735  0.910  0.0232  0.936  0.0173  0.980  
GOP  0.0784  1558.228  0.0224  1835.942  0.0109  2212.031  
DPSO  0.0811  1429.519  0.0196  1701.182  0.0115  2064.372  
Intelligentbased  ADEE  0.0809  1291.413  0.0171  1534.217  0.0098  1727.190 
QPSO  0.0739  1357.904  0.0157  1660.213  0.0091  1882.512  
IQPSO  0.0717  1332.013  0.0138  1653.510  0.0072  1861.607  
ASAEEGA  0.0731  66.706  0.0171  70.272  0.0095  74.264  
ASAEEbased  ASAEEPSO  0.0722  59.958  0.0143  62.391  0.0080  66.220 
ASAEEDE  0.0697  43.331  0.0114  45.447  0.0061  47.059 
Attributes  SNR  20  30  40  

Methods  RMSE  Time (s)  RMSE  Time (s)  RMSE  Time (s)  
PPI  0.5132  4.522  0.5063  4.642  0.5051  4.723  
Geometrialbased  NFINDR  0.0805  1.995  0.0336  2.061  0.0218  2.102 
VCA  0.0711  1.236  0.0306  1.309  0.0189  1.381  
GOP  0.0780  2050.407  0.0295  2273.227  0.0113  2587.485  
DPSO  0.0802  1813.623  0.0305  2099.171  0.0136  2392.728  
Intelligentbased  ADEE  0.0759  1472.874  0.0273  1651.492  0.0101  1884.253 
QPSO  0.0724  1668.131  0.0262  1891.692  0.0098  2105.269  
IQPSO  0.0679  1613.092  0.0240  1810.125  0.0082  2080.572  
ASAEEGA  0.0702  74.408  0.0273  78.559  0.0094  83.952  
ASAEEbased  ASAEEPSO  0.0684  67.945  0.0265  71.623  0.0089  75.798 
ASAEEDE  0.0658  54.151  0.0208  58.847  0.0075  62.801 
Attributes  Endmember  5  10  15  20  

Methods  RMSE  Time (s)  RMSE  Time (s)  RMSE  Time (s)  RMSE  Time (s)  
PPI  20.7768  30.774  18.3991  42.293  16.8536  57.495  14.3208  65.473  
Geometrialbased  NFINDR  5.8611  26.633  4.0298  34.205  3.8376  48.465  3.2275  59.217 
VCA  5.5463  25.495  3.8370  32.197  3.5101  43.151  2.9383  57.542  
GOP  5.2643  1.590 × 10${}^{6}$  3.8251  1.985 × 10${}^{6}$  3.5212  2.308 × 10${}^{6}$  2.9180  2.820 × 10${}^{6}$  
DPSO  4.5321  1.373 × 10${}^{6}$  3.3797  1.764 × 10${}^{6}$  3.0944  2.081 × 10${}^{6}$  2.7488  2.556 × 10${}^{6}$  
Intelligentbased  ADEE  4.2970  1.24 × 10${}^{6}$  3.3102  1.586 × 10${}^{6}$  3.0206  1.912 × 10${}^{6}$  2.6831  2.401 × 10${}^{6}$ 
QPSO  4.1542  1.270 × 10${}^{6}$  3.1326  1.600 × 10${}^{6}$  2.9437  2.005 × 10${}^{6}$  2.6704  2.493 × 10${}^{6}$  
IQPSO  4.0720  1.258 × 10${}^{6}$  3.0327  1.581 × 10${}^{6}$  2.7794  1.990 × 10${}^{6}$  2.5925  2.451 × 10${}^{6}$  
ASAEEGA  4.3364  954.296  3.4417  1309.780  3.1561  1613.094  2.7436  1940.092  
ASAEEbased  ASAEEPSO  4.0862  826.323  3.1058  1198.461  2.8456  1436.977  2.6024  1805.624 
ASAEEDE  3.7321  751.325  2.8469  984.226  2.5564  1318.374  2.2613  1705.950 
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Wang, Z.; Li, J.; Liu, Y.; Xie, F.; Li, P. An Adaptive SurrogateAssisted Endmember Extraction Framework Based on Intelligent Optimization Algorithms for Hyperspectral Remote Sensing Images. Remote Sens. 2022, 14, 892. https://doi.org/10.3390/rs14040892
Wang Z, Li J, Liu Y, Xie F, Li P. An Adaptive SurrogateAssisted Endmember Extraction Framework Based on Intelligent Optimization Algorithms for Hyperspectral Remote Sensing Images. Remote Sensing. 2022; 14(4):892. https://doi.org/10.3390/rs14040892
Chicago/Turabian StyleWang, Zhao, Jianzhao Li, Yiting Liu, Fei Xie, and Peng Li. 2022. "An Adaptive SurrogateAssisted Endmember Extraction Framework Based on Intelligent Optimization Algorithms for Hyperspectral Remote Sensing Images" Remote Sensing 14, no. 4: 892. https://doi.org/10.3390/rs14040892