One of the major challenges in optical-based remote sensing is the presence of clouds, which imposes a hard constraint on the use of multispectral or hyperspectral satellite imagery for earth observation. While some studies have used interpolation models to remove cloud affected data, relatively few aim at restoration via the use of multi-temporal reference images. This paper proposes not only the use of image time-series, but also the implementation of a geostatistical model that considers the spatiotemporal correlation between them to fill the cloud-related gaps. Using Hyperion hyperspectral images, we demonstrate a capacity to reconstruct cloud-affected pixels and predict their underlying surface reflectance values. To do this, cloudy pixels were masked and a parametric family of non-separable covariance functions was automated fitted, using a composite likelihood estimator. A subset of cloud-free pixels per scene was used to perform a kriging interpolation and to predict the spectral reflectance per each cloud-affected pixel. The approach was evaluated using a benchmark dataset of cloud-free pixels, with a synthetic cloud superimposed upon these data. An overall root mean square error (RMSE) of between 0.5% and 16% of the reflectance was achieved, representing a relative root mean square error (rRMSE) of between 0.2% and 7.5%. The spectral similarity between the predicted and reference reflectance signatures was described by a mean spectral angle (MSA) of between 1° and 11°, demonstrating the spatial and spectral coherence of predictions. The approach provides an efficient spatiotemporal interpolation framework for cloud removal, gap-filling, and denoising in remotely sensed datasets.