Regularized covariance estimation from partially observed interferometric data

2026-06-17

AI Summary

This study addresses the challenge of covariance estimation in Small Baseline Subset (SBAS) interferometry caused by systematic, large-scale data gaps. Viewing two-dimensional partial observations as fragmented functional data, the authors introduce a novel “fragmented observation mechanism” framework from the perspective of functional data analysis. They propose a Laplacian-regularized matrix completion method that enables nonparametric covariance estimation without requiring assumptions of stationarity or isotropy. The approach demonstrates consistently low estimation errors across diverse covariance structures in simulations and is successfully applied to real SBAS-derived surface deformation data from the Phlegraean Fields. The method effectively recovers spatial dependence patterns, offering robust support for environmental risk monitoring.

Abstract

The Small BAseline Subset technique provides remote measurements of ground displacement with high spatial resolution, making it a key tool for monitoring geophysical processes in hazard-prone areas. An effective analysis of this type of data requires reliable estimation of their second-order structure, which is difficult to achieve because the measurements are systematically missing over relatively large portions of the investigated areas. We tackle the problem from a functional data analysis perspective and treat the observations as partially observed functional data with two-dimensional domain. To properly characterize the data, we introduce the fragmented regime of partial observation, where parts of the curves are systematically missing across replicates. For this regime, we propose a novel method for covariance estimation, formulating the task as a matrix completion problem with Laplacian regularization. The estimator is nonparametric and free from stationarity or isotropy assumptions. Extensive simulations show that our method achieves consistently low estimation error across a range of covariance structures. Application to ground displacement data relative to the Phlegraean Fields demonstrates its ability to recover meaningful spatial dependence patterns, highlighting its potential for environmental risk assessment and monitoring.

Problem

• covariance estimation
• partially observed data
• interferometric data
• Small BAseline Subset
• functional data analysis

Innovation

• covariance estimation
• matrix completion
• Laplacian regularization
• functional data analysis
• partial observation