论文标题
随机功能分析和多级矢量场异常检测
Stochastic Functional Analysis and Multilevel Vector Field Anomaly Detection
论文作者
论文摘要
大量矢量场数据集在多光谱光学传感器和雷达传感器中很常见，以及许多其他新兴应用领域。在本文中，我们开发了一种新型的随机功能（数据）分析方法，用于基于跨域的标称随机行为的协方差结构来检测异常。最佳矢量场karhunen-loeve扩展应用于此类随机字段数据。一系列的多级正交功能子空间是根据域的几何形状构建的，该域的几何形状是根据KL扩展的。通过在多级基础上检查随机场的投影来实现检测。此外，还形成了可靠的假设检验，这些测试不需要先前关于数据概率分布的假设。该方法应用于亚马逊森林中森林砍伐和退化的重要问题。这是一个复杂的非单调过程，因为森林可以降解和恢复。使用Sentinel-2的多光谱卫星数据，构造了多级过滤器，并将异常视为与森林初始状态的偏差。通过可靠的假设检验对森林异常进行定量。我们的方法显示了在矢量化复合物中使用多个数据频段的优点，从而超过了基于标量的方法的能力，从而使更好的异常检测。
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.
