🤖 AI Summary
This work addresses the challenge of robust covariance matrix estimation under the scale-invariant random vector (SIRV) model in the presence of ignorable missing data. The authors propose a novel expectation-maximization (EM) algorithm that introduces an inverse-Gamma prior on the scale variables, thereby recasting the observation model as a complex multivariate Student-t distribution. This formulation enables, for the first time within the SIRV framework, closed-form updates in both the E-step and M-step. The method further incorporates numerical optimizations—including Hermitian positive semi-definite constraints, regularized matrix inversion, and computational reuse—to significantly enhance numerical stability and efficiency. Experimental results demonstrate that the proposed approach effectively reconstructs missing entries and achieves superior denoising performance under both missing completely at random (MCAR) and missing not at random (MNAR) mechanisms, making it well-suited for processing Sentinel-1 InSAR time-series data.
📝 Abstract
This paper presents a robust Expectation-Maximization framework for covariance estimation in Scale-Invariant Random Vector (SIRV) models with missing data under ignorable missingness mechanisms. By adopting an inverse-gamma prior on the scale variables, the resulting observation model leads to a complex multivariate Student-t distribution and allows closed-form E-step and M-step updates. The proposed algorithm incorporates numerical robustness techniques such as computation reuse for common observation patterns, regularized matrix inversions, and explicit enforcement of Hermitian positive semidefinite structure. Experiments on synthetic data and Sentinel-1 interferograms show effective missing value reconstruction and denoising performance under both MCAR and MNAR scenarios.