Massive vector field datasets are common in multi-spectral optical and radar sensors, among many other emerging areas of application. In this paper we develop a novel stochastic functional (data) analysis approach for detecting anomalies based on the covariance structure of nominal stochastic behavior across a domain. An optimal vector field Karhunen-Loeve expansion is applied to such random field data. A series of multilevel orthogonal functional subspaces is constructed from the geometry of the domain, adapted from the KL expansion. Detection is achieved by examining the projection of the random field on the multilevel basis. In addition, reliable hypothesis tests are formed that do not require prior assumptions on probability distributions of the data. The method is applied to the important problem of deforestation and degradation in the Amazon forest. This is a complex non-monotonic process, as forests can degrade and recover. Using multi-spectral satellite data from Sentinel-2, the multilevel filter is constructed and anomalies are treated as deviations from the initial state of the forest. Forest anomalies are quantified with robust hypothesis tests. Our approach shows the advantage of using multiple bands of data in a vectorized complex, leading to better anomaly detection beyond the capabilities of scalar-based methods.
翻译:多光谱光学和雷达传感器以及其他许多新兴应用领域中常见的大规模矢量场数据集。在本文件中,我们开发了一种新型的随机功能(数据)分析方法,以根据一个域内名义随机行为共变结构来检测异常现象。一个最佳的矢量场Karhunen-Loeve扩展适用于这种随机实地数据。从KL扩展后改制的多光谱光学和雷达传感器,从域的几何学中建立了一系列多级正方位功能子空间。通过在多级基础上审查随机场的预测,可以进行探测。此外,还形成了一种可靠的假设测试,不需要事先假设数据的概率分布。该方法适用于亚马孙森林的砍伐和退化这一重要问题。这是一个复杂的非移动过程,因为森林可以降解和复原。使用Sentinel-2的多谱卫星数据,构建了多级过滤器,异常点被作为偏离森林初始状态的偏差处理。森林异常点通过可靠的假设测试量化。我们的方法表明,在基于病媒的复杂检测能力之外,使用多种矢量波段数据的好处。