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.

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