Reconstruction of Sentinel-2 Time Series Using Robust Gaussian Mixture Models -- Application to the Detection of Anomalous Crop Development in wheat and rapeseed crops

Missing data is a recurrent problem in remote sensing, mainly due to cloud coverage for multispectral images and acquisition problems. This can be a critical issue for crop monitoring, especially for applications relying on machine learning techniques, which generally assume that the feature matrix does not have missing values. This paper proposes a Gaussian Mixture Model (GMM) for the reconstruction of parcel-level features extracted from multispectral images. A robust version of the GMM is also investigated, since datasets can be contaminated by inaccurate samples or features (e.g., wrong crop type reported, inaccurate boundaries, undetected clouds, etc). Additional features extracted from Synthetic Aperture Radar (SAR) images using Sentinel-1 data are also used to provide complementary information and improve the imputations. The robust GMM investigated in this work assigns reduced weights to the outliers during the estimation of the GMM parameters, which improves the final reconstruction. These weights are computed at each step of an Expectation-Maximization (EM) algorithm by using outlier scores provided by the isolation forest algorithm. Experimental validation is conducted on rapeseed and wheat parcels located in the Beauce region (France). Overall, we show that the GMM imputation method outperforms other reconstruction strategies. A mean absolute error (MAE) of 0.013 (resp. 0.019) is obtained for the imputation of the median Normalized Difference Index (NDVI) of the rapeseed (resp. wheat) parcels. Other indicators (e.g., Normalized Difference Water Index) and statistics (for instance the interquartile range, which captures heterogeneity among the parcel indicator) are reconstructed at the same time with good accuracy. In a dataset contaminated by irrelevant samples, using the robust GMM is recommended since the standard GMM imputation can lead to inaccurate imputed values.