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Gap-Filling Based on EOF Analysis of Spatio-Temporal Covariance of Satellite Image Derived Displacement Time Series

An iterative method, namely extended EM-EOF (Expectation Maximization - Empirical Orthogonal Functions) is proposed to retrieve missing values in satellite derived displacement time series. The method constructs the spatio-temporal covariance of a displacement time series, decomposes it into different EOF modes by solving the eigenvalue problem and then selects an optimal number of EOF modes to reconstruct the time series based on cross validation errors. The latter are also used as convergence criterion in an EM-like algorithm. A confidence index associated with each eigenvalue, estimated from the eigenvalue uncertainty, is introduced as a metric for refining the estimated optimal number of EOF modes. Results on simulated displacement time series perturbed by spatially correlated noise demonstrate the potential of extended EM-EOF to impute spatio-temporal missing values even in case of a reduced size of time series.