# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
###### Abstract  
Due to the constant increase in Earth Observation (EO) data collections, the monitoring of land cover is facilitated by the temporal diversity of the satellite images datasets. Due to the capacity of Synthetic Aperture Radar (SAR) sensors to operate independently of sunlight and weather conditions, SAR image time series offer the possibility to form a dataset with almost regular temporal sampling. This paper aims at mining the SAR image time series for an analysis of target's behavior from the perspective of both temporal evolution and coherence. The authors present a two-level analytical approach envisaging the assessment of global (related to perceivable structures on the ground) and local (related to changes occurred within a perceivable structure on the ground) evolution inside the scene. The Latent Dirichlet Allocation (LDA) model is implemented to identify the categories of evolution present in the analyzed scene, while the statistical and coherent proprieties of the dataset's images are exploited in order to identify the structures with stable electromagnetic response, the so-called Persistent Scatterers (PS). A comparative study of the two algorithms' classification results is conducted on ERS and Sentinel-1 data. At global scale, the results fit human perception, as most of the points which can be exploited for Persistent Scatterers Interferometry (PS-InSAR) are classified within the same class, referring to stable structures. At local scale, the LDA classification demands for an extended number of classes (defined through a perplexity-based analysis), enabling further differentiation inside the evolutional character of those stable structures. The comparison against the map of detected PS reveals which classes present higher temporal correlation, determining a stable evolutionary character, opening new perspectives for validation of both PS detection and SITS analysis algorithms. SAR image time series analysis; Latent Dirichlet Allocation; categories of evolution; PSInSAR data analytics; evolutionary character of Persistent Scatterers 201810103390/rs1009143610.3390/rs1009143610. the multispectral images with respect to an object when analyzing a time series contributes to a better understanding of the evolution phenomena itself. Optical data provide a great amount of detail and representation with visual significance [4]. Unfortunately, sparsity and irregular time sampling hinders a coherent analysis. Due to the sensors' nature, multispectral data is available only on cloud-free days, such that the temporal behavior is not totally correlated with land transformations. Yet, applications such as agriculture assessment, forest monitoring, or urbanism rely on the exploration of optical SITS [5]. Opposite to the multispectral sensors, the Synthetic Aperture Radars (SAR) are active illuminating systems, which operate in the microwave domain [6], being one of the most exploited instruments in the remote sensing field [7]. The large data volume of SAR systems is a consequence of the former spaceborne missions (European Remote Sensing--ERS, Envisat) whose data still can be exploited for validation of experimental concepts, with a significant number of active missions (Sentinel-1, TerraSAR-X, and TanDEM-X, COSMO-SkyMed, RADARSAT, and PALSAR). More satellites are planned to be launched in the immediate period (Sentinel-1C and 1D, COSMO-SkyMed second generation, and RADARSAT constellation), accelerating the increase of data volume. Their main advantages over optical systems rely on the fact that they can operate independently of sunlight and almost independent of weather conditions. Therefore, the generation of SAR SITS is overcoming the problems of time sampling and is not bound by cloud cover, as in the case of optical imagery. They consist of a radar mounted on a platform which moves with constant velocity relative to the illuminated scene.