# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
###### Abstract
The sensor transmits a set of coherent impulses in the scene's direction and integrates the reflected echoes to focus a complex bidimensional image of the scene [8]. Compared to classical radars, SAR systems allow the 2D localization of targets in the range-azimuth plane of the focused images [7], while the relative movement between sensor and targets leads to an azimuth resolution improvement [9]. The lack of a direct association, valid in case of optical sensors, is compensated by some particularities of SAR imagery. The use of polarized waves allows for the assessment of a target's structure by studying their polarimetric signatures. The employment of quadrature modulation offers the possibility to extract information related to terrain's characteristics from the phase of the focused images by means of coherent processing. For this purpose, a wide range of coherent processing algorithms has been developed, from classical SAR interferometry to advanced multitemporal techniques. Initial approaches of SAR interferometry [10] exploited the phase difference between two images of the same area, acquired from different sensor positions, to estimate the topography of the illuminated scene. Interferometric phase also contains a component proportional to the terrain's displacements; this propriety represents the basics of SAR differential interferometry. In order to estimate the scene's dislocations, a topographic component must be subtracted from the interferometric phase. This operation can be implemented either by employing an external digital elevation model (DEM)--2-pass differential interferometry, or using an elevation model estimated from a couple of SAR images--3 or 4 pass differential interferometry. Multitemporal interferometric methods study the interferometric phase variation along a dataset of multiple SAR acquisitions, allowing a better estimation of its residual component and offering the possibility to estimate and monitor the linear deformation rates of the analyzed scene over wider temporal intervals. SAR tomography [11] combines both amplitude and phase information from a multi-baseline dataset, to reconstruct the 3D profile of the scene by estimating the reflectivity function's variation in elevation direction. There is an extended area in the literature for research and applications with respect to SAR SITS. Important effort has been made for the measurement of scene displacements, the most popular methods being Persistent Scatterers Interferometry (PS-InSAR) [12; 13], small baselines subsets (SBAS) [14], and SqueeSAR [15]. However, there is more to develop with respect to SAR SITS processing. The analysis of scene evolution will open new perspectives for monitoring applications. In a past paper [16], the authors used data analytics and interactive learning techniques to evaluate the manner in which a land structure was dynamically transforming over time. One of the algorithms that proved to be very efficient for multispectral SITS analysis [17], but also for single scene classification, regardless the type of imagery [18; 19; 20], is the Latent Dirichlet Allocation (LDA) model. The secret lies in the way one defines analogies between the analyzed data and notions like word, document, and corpus. A generative model introduced at first to deal with text analysis, LDA can easily be adjusted to various uses, as long as relevant associations can be established. Considering the adaptability of the algorithm, this paper encourages SAR SITS handling by means of LDA modeling. This new approach aims at discovering categories of evolution to highlight the temporal behavior of land cover, as perceived by SAR systems. The temporal behavior captured through SAR SITS is not limited to the extraction of categories of evolutions based on scene transformations. There is a perpetual character of the scene that can be emphasized using SAR SITS, where structures that are not changing over time are identified based on their coherence.