# Potential of Resolution-Enhanced Hyperspectral Data for Mineral Mapping Using Simulated EnMAP and Sentinel-2 Images

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## Abstract

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## 1. Introduction

_{3}at 2.32–2.35 µm [6].

## 2. Hyperspectral and Multispectral Image Fusion

#### 2.1. Related Work

#### 2.2. The CNMF Algorithm

**B**and

**R**, can be estimated from the observed data sources when they are not given as prior knowledge [32].

**X**is formulated as

**N**is the residual. The endmember spectra and abundance fractions are nonnegative. By substituting Equation (3) into Equations (1) and (2), ${\mathbf{Y}}_{h}$ and ${\mathbf{Y}}_{m}$ can be approximated as

**E**) and the corresponding high-resolution abundance maps (

**A**) by the coupled spectral unmixing of the low-spatial-resolution hyperspectral image (${\mathbf{Y}}_{h}$) and the high-spatial-resolution multispectral image (${\mathbf{Y}}_{m}$). CNMF alternately unmixes ${\mathbf{Y}}_{h}$ and ${\mathbf{Y}}_{m}$ in the framework of nonnegative matrix factorization (NMF) [34,35] to estimate

**E**and

**A**under the constraints of the relative sensor characteristics given by Equations (6) and (7). NMF decomposes a nonnegative data matrix into a product of two nonnegative matrices, and it has been shown to be effective for spectral unmixing satisfying physical constraints without assuming the presence of pure pixels. The squared Frobenius norm of a residual matrix in a linear spectral mixture model is commonly used for a cost function. NMF unavoidably converges to local minima depending on the initialization. CNMF alternately takes advantage of the two images, i.e., the spectral resolution of the hyperspectral image and the spatial resolution of the multispectral image, to initialize the other spectral unmixing so that the optimization can converge to a better local minimum.

**E**can be initialized using endmember extraction methods, for example, vertex component analysis (VCA) [36]. In this work, since our interest is focused on the SWIR range of fused data, this endmember extraction process is carried out using only SWIR bands.

**E**and ${\mathbf{A}}_{h}$ are then alternately optimized by Lee and Seung’s multiplicative update rules [35]. Next,

**A**is estimated from the multispectral image. ${\mathbf{E}}_{m}$ is set by Equation (7) and

**A**is initialized by the spatially up-sampled matrix of ${\mathbf{A}}_{h}$ obtained by bilinear interpolation. The sequential unmixing for the hyperspectral image is performed after initializing ${\mathbf{A}}_{h}$ by Equation (6). After that, the two images are alternately unmixed until convergence. Finally, the target image is obtained by the multiplication of

**E**and

**A**. More details of the implementation are given in [18].

## 3. Materials and Validation Methods

#### 3.1. Study Area and Data Preparation

^{−2}and a rural aerosol model. The spatial and spectral modules include resampling of an image in the spatial and spectral domains using the sensor specific PSFs and SRFs, respectively. The radiometric module transformed the at-sensor radiance to DN by simulating instrumental noise and calibration coefficients. The modules are coupled with a backward simulation branch consisting of calibration modules such as nonlinearity, dark current and absolute radiometric calibration and a series of preprocessing modules such as radiometric calibration, co-registration, orthorectification and atmospheric correction. In case of Sentinel-2, all bands of the Level-1c- and Level-2a-products were spatially resampled to a uniform 10 m pixel grid. A reference hyperspectral image with a 10 m GSD for all bands was also prepared by applying only spatial and spectral resampling to the HyMap at-surface reflectance data. The HyMap data were spectrally resampled to a 1 nm resolution before the SRFs were applied for simulating the EnMAP and reference images.

#### 3.2. Validation Methods

**X**denote a fused image and a reference image, respectively.

- (1)
- CC is a characterization of geometric distortion obtained for each band with an ideal value of 1. We used an average value of CCs for all bands, which is defined as$$\text{CC}\left(\widehat{X},\mathbf{X}\right)=\frac{1}{L}{\displaystyle \sum _{i=1}^{L}}\frac{{\sum}_{j=1}^{P}\left({\widehat{X}}_{ij}-\frac{1}{P}{\sum}_{j\prime =1}^{P}{\widehat{X}}_{ij\prime}\right)\left({X}_{ij}-\frac{1}{P}{\sum}_{j\prime =1}^{P}{X}_{ij\prime}\right)}{\sqrt{{\sum}_{j=1}^{P}{\left({\widehat{X}}_{ij}-\frac{1}{P}{\sum}_{j\prime =1}^{P}{\widehat{X}}_{ij\prime}\right)}^{2}{\sum}_{j=1}^{P}{\left({X}_{ij}-\frac{1}{P}{\sum}_{j\prime =1}^{P}{X}_{ij\prime}\right)}^{2}}}$$
- (2)
- SAM is a measure for the shape preservation of a spectrum calculated at each pixel with a unit degree and 0 as the ideal value. An average value of a whole image is defined as$$\text{SAM}\left(\widehat{X},\mathbf{X}\right)=\frac{1}{P}{\displaystyle \sum _{i=1}^{P}}\text{arccos}\left(\frac{{\widehat{x}}_{i}^{T}{\mathbf{x}}_{i}}{\Vert {\widehat{x}}_{i}\Vert \Vert {\mathbf{x}}_{i}\Vert}\right)$$
**X**and ‖·‖ is the ${l}_{2}$ norm. - (3)
- RMSE is calculated at each pixel as the difference of spectra between the fused image and the reference image. We used an average value of RMSEs for all pixels, which is defined as$$\text{RMSE}\left(\widehat{X},\mathbf{X}\right)=\frac{1}{P}{\displaystyle {\sum}_{j=1}^{P}}\sqrt{\frac{1}{L}{\displaystyle {\sum}_{i=1}^{L}}{\left({\widehat{X}}_{ij}-{X}_{ij}\right)}^{2}}$$

- (4)
- ERGAS provides a global statistical measure of the quality of fused data with the best value at 0, which is defined as$$\text{ERGAS}\left(\widehat{X},\mathbf{X}\right)=100\sqrt{\frac{P}{{P}_{h}}}\sqrt{\frac{1}{L}{\sum}_{i=1}^{L}{\left(\sqrt{\frac{1}{P}{\sum}_{j=1}^{P}{\left({\widehat{X}}_{ij}-{X}_{ij}\right)}^{2}}/\frac{1}{P}\sum _{j=1}^{P}{X}_{ij}\right)}^{2}}$$

## 4. Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**

**Top**: Schematic surface alteration map of the study area (modified from [38]). The dotted rectangle indicates the approximate outline of the study area;

**Bottom**: The scene is displayed in false color composite (R: 750 nm, G: 550 nm, B: 450 nm) made from the original HyMap image. Bright red represents cultivated cropland, and shades of red show distribution of various vegetated land covers. Numbered points in the enlarged image are 21 locations for validation of spectral signatures [37].

**Figure 3.**Color composite images (R: 2259 nm, G: 2201 nm, B: 2044 nm) obtained by (

**a**) nearest-neighbor interpolation; and (

**b**) bicubic interpolation of EnMAP data, and fusion of EnMAP and Sentinel-2 data using (

**c**) GSA; (

**d**) MTF-GLP; (

**e**) CNMF; and (

**f**) reference data. Shades of pink indicate the presence of minerals, such as alunite, kaolinite and smectite, Monotone areas indicate no absorption feature in the spectral range between 2259 nm and 2044 nm and brightness is influenced by topography and the sun elevation angle in addition to variations of land cover.

**Figure 4.**Color composite images (R: 2201 nm, G: 2159 nm, B: 2115 nm) of continuum removed images obtained by (

**a**) nearest-neighbor interpolation; and (

**b**) bicubic interpolation of EnMAP data; and fusion of EnMAP and Sentinel-2 data using (

**c**) GSA; (

**d**) MTF-GLP; (

**e**) CNMF; and (

**f**) reference data. Black, blue and light blue are corresponding to alunite, kaolinite and smectite, respectively.

**Figure 5.**Comparison of spectral signatures between (

**black**) reference; (

**blue**) bicubic interpolation; (

**green**) GSA; and (

**red**) CNMF images at 21 points [37].

**Figure 6.**Comparison of continuum-removed spectral signatures between (

**black**) reference; (

**blue**) bicubic interpolation; (

**green**) GSA; and (

**red**) CNMF images at 21 points [37].

**Figure 7.**Endmember spectra derived from (

**a**) reference; (

**b**) CNMF; (

**c**) GSA; and (

**d**) bicubic interpolation data.

**Figure 8.**Color composite images of abundance fractions obtained from (

**a**) nearest-neighbor interpolation; (

**b**) bicubic interpolation; (

**c**) GSA; (

**d**) CNMF; and (

**e**) reference images by MESMA for alunite (

**red**); kaolinite (

**green**); and smectite (

**blue**). Abundance fractions are linearly stretched between 0 to 0.7 for better visualization.

Band Number | Central Wavelength (nm) | Bandwidth (nm) | GSD (m) |
---|---|---|---|

1 | 443 | 20 | 60 |

2 | 490 | 65 | 10 |

3 | 560 | 35 | 10 |

4 | 665 | 30 | 10 |

5 | 705 | 15 | 20 |

6 | 740 | 15 | 20 |

7 | 783 | 20 | 20 |

8 | 842 | 115 | 10 |

8b | 865 | 20 | 20 |

9 | 945 | 20 | 60 |

10 | 1380 | 30 | 60 |

11 | 1610 | 90 | 20 |

12 | 2190 | 180 | 20 |

Data | Method | CC | SAM | RMSE | ERGAS |
---|---|---|---|---|---|

VNIR and SWIR | Cubic | 0.91749 | 2.8365 | 0.01909 | 3.3857 |

GSA | 0.98629 | 2.713 | 0.01372 | 2.0112 | |

MTF-GLP | 0.98571 | 2.692 | 0.01355 | 2.0151 | |

CNMF | 0.988 | 2.6994 | 0.01349 | 1.9793 | |

SWIR | Cubic | 0.90549 | 1.6368 | 0.01694 | 2.9814 |

GSA | 0.97374 | 1.629 | 0.01149 | 1.9339 | |

MTF-GLP | 0.97346 | 1.6381 | 0.01132 | 1.8958 | |

CNMF | 0.97329 | 1.6193 | 0.01165 | 1.9336 | |

Continuum removed SWIR | Cubic | 0.76578 | 0.65553 | 0.01015 | 0.45248 |

GSA | 0.7745 | 0.64832 | 0.01011 | 0.4504 | |

MTF-GLP | 0.7659 | 0.66141 | 0.01019 | 0.46186 | |

CNMF | 0.83494 | 0.60761 | 0.00915 | 0.40899 |

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**MDPI and ACS Style**

Yokoya, N.; Chan, J.C.-W.; Segl, K.
Potential of Resolution-Enhanced Hyperspectral Data for Mineral Mapping Using Simulated EnMAP and Sentinel-2 Images. *Remote Sens.* **2016**, *8*, 172.
https://doi.org/10.3390/rs8030172

**AMA Style**

Yokoya N, Chan JC-W, Segl K.
Potential of Resolution-Enhanced Hyperspectral Data for Mineral Mapping Using Simulated EnMAP and Sentinel-2 Images. *Remote Sensing*. 2016; 8(3):172.
https://doi.org/10.3390/rs8030172

**Chicago/Turabian Style**

Yokoya, Naoto, Jonathan Cheung-Wai Chan, and Karl Segl.
2016. "Potential of Resolution-Enhanced Hyperspectral Data for Mineral Mapping Using Simulated EnMAP and Sentinel-2 Images" *Remote Sensing* 8, no. 3: 172.
https://doi.org/10.3390/rs8030172