# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
## 4 Experimental Setup
### Overview of SITS Temporal Analysis  
Once the preprocessing is completed, the SITS is ready for temporal analysis. The proposed methodology includes two independent processes: the PS detection (identification of persistent structures in the scene) and the categories of evolution extraction (characterization of the evolving structures in the scene), as presented in Figure 7.  
At first, we concentrate on the identification of stable targets. Amplitude statistics of each pixel values across the images dataset are computed. Points which present a MSR above 1.3 are selected in this step. For large data stacks (over 25 acquisitions, as was the case for both ERS and Sentinel-1 datasets), this method should be reliable since suitable conditions for statistics estimations are created. Figure 7: Proposed methodology for Satellite Image Time Series (SITS) temporal analysis. However, for a supplementary validation, the power spectral density of the selected points, computed according to the Wiener-Hincin theorem, is also analyzed. Points with unstable spectral phases were eliminated. From the retrained points, those which present an amplitude higher than the mean of the neighboring points will form the final PS set. Stable targets are expected to be found in areas characterized by high temporal correlation, pointing out to stable structures from the urban area. This approach could provide a reference for the scene classification and it can be used to verify the precision in urban area delimitation. In order to differentiate the structures in the scene based on their transformation over time, we use the LDA analysis on the SITS to define categories of evolution. This kind of information is hidden to human perception, as a visual interpretation is hard to perform in this respect. All the images in the time series must be observed at the same time in order to understand if any transformation occurred in the area and to establish the extent of it with respect to the structures on the ground. Figure 8 illustrates four categories of evolution. In these particular examples, whether the urban and forest areas present no major transformations, both agriculture and water show significant variations within a specific period of time. During SITS analysis, the focus shall turn towards of land transformations that might appear over the analyzed period. We propose two approaches for the LDA classification: at global level (where we target evolutions matching the structures on the ground distinguishable by visual perception) and at local level (where we plan to determine the set of elementary categories of evolution that can express the content scene  
Figure 8: Categories of evolutions that we can extract from the Buzū scene: (**A**) agricultural evolution, (**B**) forest evolution, (**C**) urban evolution, and (**D**) water evolution. variability in terms of changes). The only difference between the approaches refers to the selection process of the evolution categories number. In the visual approach, the number of classes is chosen based on how many categories have been perceptible to the human user in the analyzed scenes. The second approach computes the perplexity curve, which is then exploited to determine the optimal number of evolution categories. Those two methods are described below. First, we plan to see how much the categories of evolution fit the semantic classes perceivable during a visual inspection of the scene: water, roads, built-up area, forest, and agricultural fields (as exemplified in Figure 9) were identified. A strong validation measure for the case of the built-up area will be provided by the list of detected PSs. Temporal analysis goes beyond visual land use classes; the consequences of major phenomena will be observed. Moreover, the scene rich content at a 10 m spatial resolution, combined with the SAR image complexity and the sensor's ability to capture differently or sense multiple echoes coming from the same area at various moments of time, enable the identification of seasonal or more frequent transformations.