# Hyperspectral and Multispectral Remote Sensing Image Fusion Based on Endmember Spatial Information

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. The Proposed Method Overview

#### 2.2. Regional Mask of the LSR-HS Image and HSR-HS Image Variation Area

#### 2.3. LSR-HS Image Endmember Extracting

#### 2.4. HSR-MS Image Unmixing

## 3. Experiments and Results

#### 3.1. Performance Evaluation Metrics

- PSNRPSNR is for measuring the spatial quality of each band. It is the ratio between the maximum pixel value and the mean square error of the reconstructed image in each band. The PSNR of the i-th band is defined as:$$\mathrm{PSNR}\left({\mathbf{z}}_{i},{\widehat{\mathbf{z}}}_{i}\right)=10\xb7{log}_{10}\left(\frac{max{\left({\mathbf{z}}_{i}\right)}^{2}}{{\u2225{\mathbf{z}}_{i}-{\widehat{\mathbf{z}}}_{i}\u2225}_{2}^{2}/\phantom{{\u2225{\mathbf{z}}_{i}-{\widehat{\mathbf{z}}}_{i}\u2225}_{2}^{2}N}\phantom{\rule{0.0pt}{0ex}}N}\right)$$
- SAMSAM [32] is for quantifying the spectral similarity between the estimated and reference spectra in each pixel. The smaller of the SAM value indicates the higher spectral quality, the smaller spectral distortion.$$\mathrm{SAM}=\frac{1}{{L}_{h}}\sum arccos\frac{{\widehat{\mathbf{z}}}_{i}^{\mathrm{T}}{\mathbf{z}}_{i}}{{\u2225{\mathbf{z}}_{i}\u2225}_{2}{\u2225{\widehat{\mathbf{z}}}_{i}\u2225}_{2}}$$
- ERGASEGRAS index [33] describes the global statistical quality of the fused data, the smaller the better.$$\mathrm{ERGAS}=100S\sqrt{\frac{1}{N}{\sum}_{i=1}^{N}{\left(\frac{{\u2225{\widehat{\mathbf{Z}}}_{i}-{\mathbf{Z}}_{i}\u2225}_{2}^{2}}{\frac{1}{L}{\sum}_{i=1}^{L}{\mathbf{Z}}_{i}}\right)}^{2}}$$
- Q2nQ2n is a generalization of the universal image quality index (UIQI) [34] to measure the spatial and spectral quality in monochromatic images. The UIQI between reference image $\mathbf{Z}$ and fused image $\widehat{\mathbf{Z}}$ is defined as:$$\mathrm{Q}{2}^{\mathrm{n}}=\frac{4{\sigma}_{\widehat{\mathbf{z}},\mathbf{z}}\overline{\widehat{}}\mathbf{z}\xb7\overline{\mathbf{z}}}{\left({\sigma}_{\widehat{\mathbf{z}}}^{2}+{\sigma}_{\mathbf{z}}^{2}\right){\left({\overline{\widehat{}}\mathbf{z}}^{2}+{\overline{\mathbf{z}}}^{2}\right)}^{\prime}}$$

#### 3.2. Experiment Data Sets

- ROSIS Pavia center datasetThe city center scene in Pavia is in the northern Italy, and the image was obtained by the Reflective Optics System Imaging Spectrometer (ROSIS-3) sensor with high spatial resolution (1.3 m) and the spectrum range is 430–834 nm (http://www.ehu.eus/ccwintco/index.php). There are 102 effective bands with a size of $1096\times 715$ pixels in the image, and in this experiment we use the $480\times 480$ pixels in the bottom right part the original image as the experiment data. The number of endmembers in this dataset is six.
- HYDICE Urban datasetThe Urban dataset was obtained by the Hyperspectral Digital Imagery Collection Experiment (HYDICE) over the urban in Copperas Cove (http://www.erdc.usace.army.mil/Media/FactSheets/FactSheetArticleView/tabid/9254/Article/610433/hypercube.aspx). The image includes 210 bands with high spatial resuolution (2 m) and the spectrum range is 400 to 2400 nm. After the removal of low-SNR and water absorption bands (1–4, 76, 87, 101–111, 136–153 and 198–210), 162 bands remain. The image size is $307\times 307$ pixels, and in order to get a integer scale, we subset the in image as $304\times 304$ pixels. The number of endmembers in this dataset is six.We use the original datasets as reference images $\mathbf{Z}$. To obtain the LSR-HS images ${\mathbf{X}}_{h}$, the reference images are first blurred by $9\times 9$ Gaussian kernel in the spatial domain and then downsampled by a ratio of 4. As to obtain HSR-MS ${\mathbf{X}}_{m}$, we directly select the bands whose center wavelengths are the same as landsat 8 from the original reference images. We choose the blue, green, red and NIR channel to simulate the HSR-MS images. For Pavia center dataset, we choose 478 nm, 558 nm, 658 nm and 830 nm, for Urban dataset, we choose 481 nm, 555 nm, 650 nm and 859 nm. Because an HS image with lower spatial resolution contains more noise than an HSR-MS image, we add Gaussian white noises with standard deviation 0.1 and 0.04, respectively [35].
- Worldview-3 and OHS Hengqin datasetThe third dataset is Hengqin island area of Guangdong Province, China. The HSR-MS image was captured by worldview-3 on 15 January 2018. The data includes four bands: blue, green, red and NIR, with a spatial resolution of 1.332 m. The LSR-MS image was captured by OHS sensor, which commercial satellites launched by Zhuhai Orbita Aerospace Science and Technology Company in 28 April 2018 carry. The LSR-HS image has 32 bands with 2.5 nm spectral resolution, the spectrum range is 400–1000 nm, and the spatial resolution is 10 m. We discard the 32-th band for the noise, so there are 31 bands left. In this experiment, we choose the area with small change of surface features, which includes water body, vegetation, residential area, highway, etc. The size of HSR-MS image and LSR-HS image in the same experimental area is $500\times 500$ and $69\times 69$, respectively. For the convenience of comparative experiment, LSR-HS image was resampled to $100\times 100$ (shown in Figure 3). In this experiment, $thresh1$ is set as 1.3, and the number of endmembers in this dataset is six.

#### 3.3. Experimental Results

- CNMF [23] is a well-known HS–MS fusion method based on the spectral unmixing theory.
- FUSE [18] is one of the Bayesian-based HS–MS fusion algorithms with lower computational cost.
- GLP [17] determines the difference between the high-resolution image and its low-pass version, and multiplies the gain factor to obtain the spatial details of each low-resolution band.
- GSA [16] is an adaptive Gram–Schmidt algorithm, which better preserves the spectral information.
- HySure [20] preserves the edges of the fused image and uses total variation regularization to smooth out noise in homogeneous regions.
- MAPSMM [21] is the classic baysein-based HS–MS fusion method.

#### 3.3.1. Simulated Dataset Fusion Results

#### 3.3.2. Real Dataset Fusion Results

## 4. Discussion

#### 4.1. Results Discussion

#### 4.2. Time Complexity

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Overall flowchart of the proposed hyperspectral–multispectral (HS–MS) fusion method (Image in the flowchart has six endmembers).

**Figure 2.**Pure pixel in low spatial resolution (LSR)-HS image and high spatial resolution (HSR)-MS image.

**Figure 3.**Experiment datasets. ((

**a**)Pavia HSR-MS image (B:13, G:33, R:58); (

**b**) Pavia LSR-HS image (downsampled ratio:4, add noise); (

**c**) Urban HSR-MS image (B:17, G:37, R:50); (

**d**) Urban LSR-HS image (downsampled ratio:4, add scale); (

**e**) Hengqin HSR-MS image (B:2, G:3, R:4); (

**f**) Hengqin LSR-HS image (B:8, G:13, R:27). Scale 4 is the downsampled ratio.)

**Figure 4.**HS–MS fusion results among seven compared methods and ground truth on ROSIS Pavia Center dataset with one demarcated areas zoomed in 1.5 times for easy observation. The composite HSIs are shown with bands 58-33-13 as R-G-B. (

**a**) Coupled nonnegative matrix factorization (CNMF). (

**b**) Fast fusion based on Sylvester equation (FUSE). (

**c**) Generalized Laplacian pyramid (GLP). (

**d**) Gram–Schmidt (GS). (

**e**) HS Superresolution (HySure). (

**f**) MAPSMM. (

**g**) Proposed method. (

**h**) Ground truth.

**Figure 5.**HS–MS fusion Spectral Angle Mapper (SAM) map results among seven compared methods on ROSIS Pavia Center dataset. (

**a**) CNMF. (

**b**) FUSE. (

**c**) GLP. (

**d**) GS. (

**e**) HySure. (

**f**) MAPSMM. (

**g**) Proposed method. The color scale denotes the spectral angle difference of each pixel between the ground truth to the fused image (from 0 to 1).

**Figure 6.**HS–MS fusion results among seven compared methods and ground truth on HYDICE Urban dataset with one demarcated areas zoomed in 1.5 times for easy observation. The composite HSIs are shown with bands 50-37-17 as R-G-B. (

**a**) CNMF. (

**b**) FUSE. (

**c**) GLP. (

**d**) GS. (

**e**) HySure. (

**f**) MAPSMM. (

**g**) Proposed method. (

**h**) Ground truth.

**Figure 7.**HS–MS fusion SAM map results among seven compared methods on HYDICE Urban dataset. (

**a**) CNMF. (

**b**) FUSE. (

**c**) GLP. (

**d**) GS. (

**e**) HySure. (

**f**) MAPSMM. (

**g**) Proposed method. The color scale denotes the spectral angle difference of each pixel between the ground truth to the fused image (from 0 to 1).

**Figure 8.**Spectral value curves of the pixel in (45, 98) pixel of Pavia dataset and (88, 16) pixel of Urban dataset, respectively, using the seven compared methods compared to the ground truth.

**Figure 9.**HS–MS fusion results among seven compared methods on Hengqin dataset with one demarcated areas zoomed in 1.5 times for easy observation. The composite HSIs are shown with bands 27-13-8 as R-G-B. (

**a**) CNMF. (

**b**) FUSE. (

**c**) GLP. (

**d**) GS. (

**e**) HySure. (

**f**) MAPSMM. (

**g**) Proposed method. (

**h**) HSR-MS image. (

**i**) LSR-HS image.

**Table 1.**Experimental evaluation metrics among seven compared methods on two simulated Dataset (Bold numbers indicate the best performance).

Data | Index | Method | ||||||
---|---|---|---|---|---|---|---|---|

CNMF | FUSE | GLP | GSA | HySure | MAPSMM | Proposed | ||

Pavia | PSNR | 31.747 | 26.766 | 27.838 | 30.636 | 28.061 | 26.255 | 32.860 |

SAM | 6.357 | 13.646 | 8.643 | 11.774 | 11.876 | 9.629 | 5.700 | |

ERGAS | 4.973 | 8.667 | 7.448 | 5.460 | 7.334 | 8.922 | 4.799 | |

Q2n | 0.929 | 0.836 | 0.852 | 0.935 | 0.888 | 0.792 | 0.942 | |

Urban | PSNR | 25.890 | 23.223 | 25.370 | 27.235 | 24.183 | 24.002 | 29.083 |

SAM | 8.665 | 15.190 | 8.689 | 11.307 | 13.946 | 9.546 | 8.827 | |

ERGAS | 7.361 | 10.240 | 7.715 | 6.180 | 9.008 | 9.028 | 5.745 | |

Q2n | 0.863 | 0.772 | 0.817 | 0.886 | 0.802 | 0.772 | 0.933 |

**Table 2.**MG and SAM of HS–MS fusion results among seven compared methods on Hengqin dataset (Bold numbers indicate the best performance).

Method | Hengqin | ||||||
---|---|---|---|---|---|---|---|

CNMF | FUSE | GLP | GSA | HySure | MAPSMM | Proposed | |

MG | 57.743 | 6.852 | 7.791 | 14.812 | 57.570 | 9.996 | 69.575 |

SAM | 4.407 | 80.276 | 1.546 | 4.589 | 8.239 | 2.435 | 4.849 |

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## Share and Cite

**MDPI and ACS Style**

Feng, X.; He, L.; Cheng, Q.; Long, X.; Yuan, Y.
Hyperspectral and Multispectral Remote Sensing Image Fusion Based on Endmember Spatial Information. *Remote Sens.* **2020**, *12*, 1009.
https://doi.org/10.3390/rs12061009

**AMA Style**

Feng X, He L, Cheng Q, Long X, Yuan Y.
Hyperspectral and Multispectral Remote Sensing Image Fusion Based on Endmember Spatial Information. *Remote Sensing*. 2020; 12(6):1009.
https://doi.org/10.3390/rs12061009

**Chicago/Turabian Style**

Feng, Xiaoxiao, Luxiao He, Qimin Cheng, Xiaoyi Long, and Yuxin Yuan.
2020. "Hyperspectral and Multispectral Remote Sensing Image Fusion Based on Endmember Spatial Information" *Remote Sensing* 12, no. 6: 1009.
https://doi.org/10.3390/rs12061009