Joint Velocity Spectral Analysis and APS Compensation in Ground-Based SAR via k-means clustering

Interferometric ground-based synthetic aperture radars (GB-SARs) are widely used for their capability to measure small displacements with optimal illumination geometry and short revisit times. However, achieving high-precision displacement measurements requires to remove phase disturbances, particularly those induced by variations in atmospheric refractivity, which manifest as an atmospheric phase screen (APS) in the interferometric images. Traditional APS estimation relies on model-based approaches, which assume the presence of motionless pixels and estimate APS through polynomial regression or spatial spectral analysis. These methods require that most of the scene remains stable and spatially homogeneous, which is often not the case. In this work, we propose a novel time-domain spectral analysis approach to estimate the average velocity of pixels exhibiting similar phase characteristics. The estimated velocity component is then removed in the complex domain, allowing APS evaluation over all pixels as if they were virtually motionless. Subsequently, APS is corrected in the original interferograms. To group pixels with similar phase behaviour, a ks-means clustering strategy is adopted. The proposed algorithm was assessed through simulations and validated with experimental datasets acquired in two distinct scenarios: an open-pit copper mine and a glacier.