Regularized Nonparametric Estimation of Covariance Kernels for High-Dimensional Interferometric Data

Sentinel-1 satellites offer extensive synthetic aperture radar data globally, revisiting locations every six days. Leveraging these data, differential interferometric processing techniques yield high-resolution ground displacement images that are accurate to millimeter precision, enabling comprehensive monitoring of large areas prone to environmental hazards. Nonetheless, challenges arise when single pixels or entire areas of the images have missing information consistently over time. As typical reconstruction techniques from functional and spatial statistics ground on the second-order structure of the target field, we address the challenge of estimating the spatial covariance operator in a highly non-stationary, non-parametric setting. By grounding in the theory of functional data analysis, we discuss a flexible, non-parametric methodology which accounts for the non-stationarity of the field and ensures continuity of the reconstructed operator through a second-order regularization. The methodology is showcased on ground displacement images collected in the Phlegraean Fields, Italy, a region vulnerable to seismic and bradyseismic activity.