  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.
