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

Abstract

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.

Reconstruction of missing channel in electroencephalogram using spatiotemporal correlation-based averaging

“…The limitation of this technique is that it could be only applicable for multichannel recordings. Based on linear state transition matrix Network traffic traces ✓ Spatiotemporal covariance in order to take both temporal and spatial correlations [32] Based on decomposing a spatiotemporal covariance into different modes and then selects the optimal set of modes for reconstruction Remote sensing data ✓ Temporal covariance [33] Based on solving the eigenvalue problem, and choosing an optimal number of empirical orthogonal functions for reconstruction Remote sensing data ✓ Similarity between two temporal patterns [34] Using binary space partitioning trees Time series of multispectral images ✓ Joint probability distribution over the variables [35] Considering the mean and covariance matrix Industrial time series ✓ Spatial-temporal correlation [36] Based on low-rank matrix factorization Traffic network data ✓ Phase Space Reconstruction based on extracting linear correlation between sequences [37] Using autocorrelation function method for finding the delay time Vegetation Temperature Condition Index time series data ✓ Correlation between different neighboring sensors [38] Using linear regression models on spatially correlated measurements Distribution water network flowmeters data ✓ Spatial-spectral-temporal strategy [39] Using a local patch-based similarity Satellite image time series ✓ Spatio-temporal correlation [40] Considering binary regression Time traffic flow data…”

“…This statistical dependency, including spatiotemporal correlation patterns, is captured through a moving window and then integrated by local averaging to reconstruct the missing EEG channel. The importance of considering statistical dependencies has already been proven in a wide range of practical applications, as summarized in table 6 [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Most of these techniques focused on reconstructing data based on correlation between patterns, correlation between envelopes, and similarity between shapes and trajectories of data [24][25][26][27][28][29].…”

“…Temporal covariance [33] Based on solving the eigenvalue problem and choosing an optimal number of empirical orthogonal functions for reconstruction Remote sensing data (Continued.)…”

“…To this end, this paper aims to develop a simple imputation technique and make a more detailed analysis considering the inter-individual variations as well as the effect of increasing the number of missing channels. The method is based on the concept of statistical dependency structure in multimodal, multivariate and multisensory data with dynamically changing characteristics, the significance of which has already been proven in a wide range of practical applications [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”