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Gap-filling based on iterative EOF analysis of temporal covariance : application to InSAR displacement time series

An iterative method, namely EM-EOF (Expectation Maximization-Empirical Orthogonal Functions) is proposed for the first time to retrieve missing values in InSAR displacement time series. The method decomposes the temporal covariance into different EOF modes by solving the eigenvalue problem, and then selects an optimal number of EOF modes to reconstruct the time series. After an appropriate initialization of missing values, the proposed method performs (i) a cross-validation error minimization to find an estimate of the optimal number of EOF modes used in the reconstruction and (ii) an iterative update of missing values which gives the best estimate of missing data points according to the cross-validation error. Results on a time series of Sentinel-1 A/B unwrapped interferograms over the Gorner glacier from November 2016 to March 2017 demonstrate the high efficiency of the proposed method at retrieving missing values and denoising the time series, even in case of time series with limited size and spatio-temporally correlated gaps.