Estimating and modeling coherence on multi-temporal, short-revisit, long stacks of SAR data

The recent availability of large amounts of remotely sensed data requires setting up efficient paradigms for the extraction of information from long series of multi-temporal, often multi-sensor, datasets. In this field, monitoring of terrain instabilities is currently performed through algorithms which estimate millimetric displacements of stable (coherent) objects, through analysis of stacks of SAR images acquired in interferometric mode. The result is generally a decomposition of at least part of the complete complex covariance matrix obtained from all possible pairwise combinations of the images in the stack, separating its spatially- and temporally-correlated parts. The same SAR temporal data stacks can be used to apply change detection algorithms, to reveal, over potentially huge spatial scales and with high resolution, terrain surface changes due to e.g. environmental hazards (floods, fires, earthquakes). In this case, again, the temporal covariance matrix contains in practice all the information related to the environmental changes. The covariance matrix, or its normalized version, known as coherence matrix, expresses thus all the information content related to a time series of remotely sensed, coherent data. In the case of SAR data, this kind of representation offers a unified framework for the study of phenomena linked either to the presence of "periods" of persistent scattering characteristics, or to changes of backscattering patterns, hinting to variations in the terrain characteristics. The average operation, involved in the definition of the above-mentioned covariance and coherence matrices, has to be performed necessarily over "homogeneous" pixel sets. This homogeneity criterion can be intended in various ways, including the one connected to the covariance definition itself, thus leading to a sort of recursive estimation process. Moreover, such homogeneity measures are often used as a substitute for the classical Euclidean distance in nonlocal estimate implementation frameworks, used for instance in the design of effective SAR speckle filters. The coherence matrix highlights the role of the interferometric phase. After having suitably modeled various phase contributions, due to topography, atmosphere, etc., it is possible to detect periods in which a target remains stable, and can thus be used as a benchmark for estimating ground deformations or other effects related to the variations of the signal optical path. From the above discussion, it appears that a thorough, physically based modeling of the coherence over such long times series of SAR data constitutes a priority for efficient data exploitation. We illustrate some of the inference which can be made starting from a time series of more than a hundred COSMO-SkyMed (CSK) images acquired in InSAR mode over the Haiti capital of Port-Au-Prince, spanning a period of almost 3 years with short repeat times. Such tight acquisition schedule can be obtained nowadays with latest-generation SAR constellations such as CSK or (at lower resolutions) Sentinel-1A/B. On the mentioned CSK dataset, some recently proposed models for coherence have been tested over selected regions of interest, covering different terrain types, from forest, to cultivations, to man-made smooth surfaces such as tarmac lanes, to built-up areas. Coherences are estimated over homogeneous pixel sets determined through a nonlocal criterion. Results may help shed some light on the nature of constant, decaying and periodic components of the InSAR coherence.