# Spatiotemporal Image Fusion in Remote Sensing
## 2 Fusion Methods to Increase Spatiotemporal Resolution of Satellite Images
### Unmixing-Based Spatiotemporal Image Fusion Methods  
The need to fuse images from very heterogeneous environments has been systematically addressed by the unmixing-based spatiotemporal image fusion methods. Spectral unmixing methods rely on the linear spectral mixture to extract endmembers and abundances, i.e., proportion, at the sub-pixel level [36]. The number of endmembers and abundances is obtained from a high-resolution data set, and the spectral signature of the endmembers is unmixed from the coarse resolution images. Linear mixed methods assume that \"the reflectance of each coarse spatial resolution pixel is a linear combination of the responses of each land cover class contributing to the mixture\" [52]. Thus, spectral reflectance of coarse resolution pixels \(CR(i,t_{i})\) consisting of \(n\) land cover classes is weighted by classes abundance as follows [52]:  
\[CR(i,t_{i})=\sum_{c=0}^{n}f_{c}(i,c)\times\overline{r}_{f}(c,t_{i})+\varepsilon (i,t_{i}) \tag{7}\]  
where \(f\)(\(i\),\(c\)) is the abundance of land cover class \(c\) in coarse pixel \(i\); \(\overline{r}_{f}\)(\(c\),\(t_{i}\)) is the mean reflectance of pixels from the fine resolution images belonging to land cover class \(c\) at time \(t_{i}\); and \(\varepsilon\)(\(i\),\(t_{i}\)) is the residual. Unmixing-based methods usually start with the classification of the image with high spatial resolution using unsupervised methods such as \(k\)-means (or fuzzy \(k\)-means), followed by the spectral unmixing of the image with high temporal frequency by making use of the classification information obtained during the first step [36; 61]. Alternatively, up-to-date land cover/land use maps can be used to identify the endmembers as shown by [PERSON] et al. [53]. A comparison between unmixing-based image fusion and reconstruction-based methods is provided by [PERSON] et al. [36]. The authors also implemented a Bayesian unmixing-based fusion method to downscale coarse resolution images to the spatial resolution of fine resolution images using one base fine-coarse resolution image pair. This method outperformed those proposed by [32] when fewer input fine resolution images area used. Given the landscape heterogeneity and complexity caused by different geomorphological conditions or anthropogenic activities, land cover change is expected during the period of blended images [62]. To address this problem, [50] proposed a spatiotemporal image fusion method based on unmixing and using two or more image pairs. The authors assumed that the spectral information of pixels belonging to the same class have the same temporal variation. This method has been successfully used for high-resolution (i.e., 30 m) leaf area index estimation [63], for generating daily synthetic Landsat imagery [52] or for land surface temperature [64]. Since it neglects the differences among different sensors and thus the window size is fixed, [PERSON] et al. [52] introduced a modified spatial and temporal data fusion method by including adaptive window size and moving steps selection for disaggregating coarse pixels. The method requires fine resolution images acquired at the beginning and end of the observation period, coarse resolution reflectance data acquired on the same date as fine resolution data and land cover data to predict daily fine resolution images. [PERSON] et al. [51] described an image fusion method capable to account for both phenological and land-cover changes. The method requires two pairs of fine-coarse resolution images at the beginning and end of the observation period and a coarse resolution image for the prediction date. Proposed data fusion is sensitive to the scale parameter used to delineate homogeneous change regions from fine resolution images through segmentation. It proved, however, to perform better than reconstruction-based [32] and other spectral unmixing based methods [44], mainly because it relies on neighboring spatial information for blending the images, whereas the other evaluated methodsconsider linear land cover change during the observation period.