# An Endmember Bundle Extraction Method Based on Multiscale Sampling to Address Spectral Variability for Hyperspectral Unmixing

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## Abstract

**:**

## 1. Introduction

## 2. Relative Research Works

#### 2.1. VCA

_{k}. Then, the (k + 1)-th endmember ${\mathrm{e}}_{\mathrm{k}+1}$ can be extracted via Equation (1).

_{k}, which is calculated via Equation (3).

#### 2.2. EBE

#### 2.3. SSEBE

#### 2.4. AAEBE

## 3. Multiscale Resampling Endmember Bundle Extraction (MSREBE)

#### 3.1. Boundary Detection

#### 3.2. Sub-Images in Multiscale Generation

#### 3.3. Endmember Extraction from Each Sub-Image

#### 3.4. Stepwise Most Similar Collection (SMSC) Clustering

_{1}and N

_{2}represent the number of endmember collections and target collections, respectively, and n

_{i}and n

_{j}represent the number of spectra in collection i and j.

## 4. Experiments and Analysis

_{R}represents the RMSE between reconstructed image and original image, whereas RMSE

_{A}represents the RMSE between true abundance and estimated abundance.

#### 4.1. Synthetic Image Dataset

#### 4.2. Wetland Dataset

#### 4.3. Jasper Ridge Dataset

_{A}and MSAD show that MSREBE extracted effective endmembers of various materials which were more suitable for unmixing. The corresponding abundance maps of various methods are compared in Figure 13. It is not difficult to find that the abundance maps corresponding to MSREBE were more similar to the reference, again proving the effectiveness of the proposed method.

#### 4.4. Washington DC Mall Dataset

#### 4.5. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 8.**(

**a**) The true color image of wetland; (

**b**) the map of feature distribution in the study area.

Methods | MSAD | RMSE_{R} | RMSE_{A} |
---|---|---|---|

VCA | 0.221 | 0.178 | 0.208 |

EBE | 0.167 | 0.124 | 0.168 |

SSEBE | 0.247 | 0.072 | 0.214 |

AAEBE | 0.277 | 0.035 | 0.208 |

MSREBE | 0.155 | 0.067 | 0.037 |

Methods | MSAD | RMSE_{R} | RMSE_{A} |
---|---|---|---|

VCA | 0.279 | 0.067 | 0.382 |

EBE | 0.224 | 0.178 | 0.321 |

SSEBE | 0.312 | 0.039 | 0.349 |

AAEBE | 0.291 | 1.107 | 0.479 |

MSREBE | 0.089 | 0.019 | 0.073 |

Methods | MSAD | RMSE_{R} | RMSE_{A} |
---|---|---|---|

VCA | 0.163 | 0.159 | 0.102 |

EBE | 0.356 | 0.252 | 0.188 |

SSEBE | 0.121 | 0.109 | 0.043 |

AAEBE | 0.225 | 0.127 | 0.082 |

MSREBE | 0.099 | 0.140 | 0.036 |

Methods | MSAD | RMSE_{R} |
---|---|---|

VCA | 0.244 | 0.308 |

EBE | 0.152 | 0.016 |

SSEBE | 0.225 | 0.095 |

AAEBE | 0.143 | 0.026 |

MSREBE | 0.081 | 0.021 |

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**MDPI and ACS Style**

Ye, C.; Liu, S.; Xu, M.; Du, B.; Wan, J.; Sheng, H.
An Endmember Bundle Extraction Method Based on Multiscale Sampling to Address Spectral Variability for Hyperspectral Unmixing. *Remote Sens.* **2021**, *13*, 3941.
https://doi.org/10.3390/rs13193941

**AMA Style**

Ye C, Liu S, Xu M, Du B, Wan J, Sheng H.
An Endmember Bundle Extraction Method Based on Multiscale Sampling to Address Spectral Variability for Hyperspectral Unmixing. *Remote Sensing*. 2021; 13(19):3941.
https://doi.org/10.3390/rs13193941

**Chicago/Turabian Style**

Ye, Chuanlong, Shanwei Liu, Mingming Xu, Bo Du, Jianhua Wan, and Hui Sheng.
2021. "An Endmember Bundle Extraction Method Based on Multiscale Sampling to Address Spectral Variability for Hyperspectral Unmixing" *Remote Sensing* 13, no. 19: 3941.
https://doi.org/10.3390/rs13193941