Point Coherence Estimation (PCE) in SAR interferometry
Authors: Costantini Mario , Minati Federico , Vecchioli Francesco , Zavagli Massimo 
Published: March 2024

Synthetic aperture radar (SAR) interferometry (InSAR) is a well-established technology for precise monitoring of ground motions (due to subsidence, landslides, volcanic and seismic phenomena) with millimeter accuracy from time series of satellite SAR images. A crucial aspect of this technology involves identifying points exhibiting interferometric phase coherence across acquisitions in an image stack, typically corresponding to man-made structures, rocks, or bare soil, irrespective of the scattering mechanism (point-like or distributed). Coherent point identification faces challenges, particularly due to atmospheric and other systematic disturbances affecting the phase. Various techniques have been presented in the scientific literature, relying on statistics of stack image amplitudes (such as amplitude dispersion and signal-to-clutter ratio) and/or phases in spatial and temporal domains.This work presents a new algorithm we have recently developed, named Point Coherence Estimation (PCE), for identification of coherent points. The temporal coherence (related to phase noise) of each point is derived from the coherences between pairs of points, directly calculable, through an effective and clean procedure, without the need for spatial averages, amplitude/phase calibrations, or critical assumptions.The algorithm begins by examining phase differences between neighboring points, within tens or hundreds of meters. As known, temporal coherences of these point pairs can be estimated exploiting the cancellation of spatially correlated components in phase differences (such as atmospheric and orbital artifacts, large scale motions) and determining temporally correlated components related to ground motion and elevation. The temporal coherence of each point pair primarily depends on the phase noises (temporal, spectral, geometric decorrelations, thermal noises) of the two points.Assuming statistically independent phase noises in neighboring points (possibly excluding the nearest neighboring pixels if the images are oversampled), the expected value of temporal coherence for each pair is shown to be the product of the temporal coherence expected values for the two paired points. By taking the logarithm of these equations, an overdetermined system of linear equations is derived, which can be solved by minimizing the equation residuals according to the L1 or L2 norm, using existing efficient solvers such as linear or quadratic (LP or QP) programming solvers. The solution provides a reliable estimate of the temporal coherence for each point.Importantly, the PCE method operates without assuming any probability distribution of phase noise. Moreover, the PCE algorithm can be applied to full-resolution data as well as to data with degraded resolution for a previous multi-look or distributed scattering processing. In addition, the algorithm provides consistent results if applied to preselected candidate coherent points to reduce computational time (however absolutely affordable even without point preselection).Extensive testing, including stacks of Sentinel-1 interferometric SAR images over different scenarios, showcased the method effectiveness. PCE provided reliable measurements of temporal coherence and phase noise variance for each point, enabling detection of coherent points with minimal missing or false detections. The tested areas, affected by diverse displacement phenomena, showcased the algorithm applicability across different land cover types and geological features.The PCE method will be made available to the geoscience community as software as a service (SaaS).