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.

中文翻译：

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遥感数据立方体的 3-D 时空模型

随着时间的推移观察到的同一场景的卫星图像可以组合在图像堆栈中，可以将其建模为 3-D 立方体。为了处理这种类型的遥感数据，一方面，已经考虑了一维动力学模型，沿时间分别对每个像素进行建模（基于像素的方法），并探索时间相关性。另一方面，二维方法已被考虑在一个日期处理每个图像，探索空间相关性。在本文中，我们提出了一种新的 3-D 自回归 (AR) (3-D-AR) 模型，可用于多时相图像解释，共同探索三个维度的相关性。统计定义了 3-D-AR 模型，并讨论了一种稳健的参数估计方法。还介绍了过滤、预测和检测异常的工具。执行蒙特卡罗模拟研究以评估稳健估计的有限信号长度性能及其对异常值的敏感性。所提出的模型应用于多时态归一化差异植被指数 (NDVI) 图像堆栈，用于过滤、预测和异常检测。数值结果显示了所提出的 3-D-AR 模型对时空遥感数据解释的重要性。