# Spatiotemporal Image Fusion in Remote Sensing
## 2 Fusion Methods to Increase Spatiotemporal Resolution of Satellite Images
### Reconstruction-Based Spatiotemporal Image Fusion Methods  
Reconstruction-based spatiotemporal methods are also called filter-based methods [55] or weighted-function-based [56] and are used to generate synthetic spectral reflectance by means of the weighted sum of the neighboring similar pixels of the input image source. A widely-used reconstruction-based image fusion methods is the STARFM [32]. This method generates synthetic high-resolution images (e.g., 30 m resolution) on a daily basis by employing a neighborhood weighting process. It assumes the existence of co-temporal pairs of fine spatial resolution and coarse spatial resolution images and, therefore, the quality of the fused time series is dependent on the number of observations from the high temporal resolution images set [57] and on the availability of cloud-free pair images of the matching dates [46]. When no-matching dates images are found, the method starts searching for the closest image in the temporal domain to predict the value in the fine resolution output image. STARFM involves four main steps. First, coarse resolution images are co-registered and resampled to the resolution of the high spatial resolution images, e.g., 30 m for Landsat 8. In the next step, a moving window (\(w\)) is applied to identify similar pixels in the fine resolution images. In the third step, a weight is assigned to the homogeneous pixels based on the following criteria: (1) the spectral difference between the surface reflectance of the images pair; (2) the temporal differences in the dates of the coarse resolution, high frequency images (date of the pair-images and the prediction date); (3) the Euclidean distance between the neighbor and the central pixel. In the last step, the surface reflectance of the central pixel is calculated based on the following equation:  
\[ \begin{array}{c}FR\big{(}\frac{w}{2},\frac{w}{2}t_{pr}\big{)}=\sum\limits_{i =1}^{N}W_{ik}*(FR(x_{i},y_{i},t_{0})+(CR\big{(}x_{i},y_{i},t_{pr})\\ -CR(x_{i},y_{i},t_{0})\end{array}  \tag{1}\]  
where \(FR\big{(}\frac{w}{2},\frac{w}{2}t_{pr}\big{)}\) represents the central pixel of the moving window (\(w\)) to be predicted for the fine resolution images at time \(t_{pr}\), \(P\) is the total number of pixels in \(FR\) and \(CR\) images, \(N\) is the total number of pixels within the defined moving window, \(CR\big{(}x_{i},y_{i},t_{pr}\big{)}\) represents the pixels values of the coarse resolution data on the prediction date, \(FR(x_{i},y_{i},t_{0})\)_and_\(CR(x_{i},y_{i},t_{0})\) represent the pixel values of the base pair input images and \(W_{ik}\) represents the weight assigned to the similar neighboring pixels. [PERSON] et al. [44] proposed the extension of the STARFM method [32] and developed an enhanced spatial and temporal adaptive reflectance fusion method which proved to successfully predict fine resolution reflectance, especially in complex and heterogeneous landscape. The method requires two  
Figure 2: Sum of citations per year for each spatiotemporal image fusion method included in Table 1. Reported citations are recorded in the Web of Science database. or more pairs of fine-coarse resolution images collected on the same day and a series of time series coarse resolution data for prediction dates. [PERSON] et al. [58] found out that this new method performed better than the method proposed by [PERSON] et al. [32] in areas with spatial variance dominance, but is less successful in areas where the temporal variance was dominant. These methods were successfully tested for fusing Landsat-MODIS images [36]. A more generic spatiotemporal image fusion method, in terms of the used input images, was developed by [PERSON] et al. [46]. The method firstly applies a data gap-filling procedure, followed by an interpolation model for capturing the spatial information available in the image with the highest spatial resolution.