Spatiotemporal Filling of Missing Data in Remotely Sensed Displacement Measurement Time Series

Abstract

Missing data is a critical pitfall in the investigation of remotely sensed displacement measurement because it prevents from a full understanding of the physical phenomenon under observation. In the sight of reconstructing incomplete displacement data, this letter presents a data-driven spatiotemporal gap-filling method, which is an extension of the expectation–maximization-empirical orthogonal function (EM-EOF) method. The presented method decomposes an augmented spatiotemporal covariance of a displacement time series into EOF modes and then selects the optimal set of EOF modes to reconstruct the time series. This selection is based on the cross-validation root-mean-square error and a confidence index associated with each eigenvalue. The estimated missing values are then iteratively updated until convergence. Results on displacement time series derived from cross correlation of Sentinel-2 optical images over Fox Glacier in New-Zealand’s Alps show that the reconstruction accuracy is improved compared with the EM-EOF method. The proposed extension can tackle challenging cases, i.e., short time series with heterogeneous displacement behaviors corrupted by a large amount of missing data and noise.