A 3-D Spatiotemporal Model for Remote Sensing Data Cubes

Satellite images from the same scene observed over time can be composed in an image stack, which could be modeled as a 3-D cube. To handle this type of remote sensing data, on the one side, unidimensional dynamical models have been considered, modeling each pixel separately along the time (pixel-based approach), and exploring the temporal correlation. On the other side, 2-D approaches have been considered to process each image at one date, exploring the spatial correlation. In this article, we propose a new 3-D autoregressive (AR) (3-D-AR) model useful for multitemporal image interpretation exploring the correlation in three dimensions altogether. The 3-D-AR model is statistically defined, and a robust parameter estimation method is discussed. The tools for filtering, forecasting, and detecting anomalies are also introduced. A Monte Carlo simulation study is performed to evaluate the finite signal length performance of the robust estimation and its sensitivity to outliers. The proposed model is applied to a multitemporal normalized difference vegetation index (NDVI) image stack for filtering, prediction, and anomaly detection purposes. The numerical results show the importance of the proposed 3-D-AR model for spatiotemporal remote sensing data interpretation.