Massive vector field datasets are common in multi-spectral optical and radar sensors and modern multimodal MRI data, among many other areas of application. In this paper we develop a novel stochastic functional analysis approach for detecting anomalies based on the covariance structure of nominal stochastic behavior across a domain with multi-band vector field data. An optimal vector field Karhunen-Loeve (KL) 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. The anomalies can be quantified in suitable normed spaces based on local and global information. In addition, reliable hypothesis tests are formed with controllable distributions that do not require prior assumptions on probability distributions of the data. Only the covariance function is needed, which makes for significantly simpler estimates. Furthermore this approach allows stochastic vector-based fusion of anomalies without any loss of information. 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. This particular problem is further compounded by the presence of clouds that are hard to remove with current masking algorithms. 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 and distinguished from false variations such as cloud cover. 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现代多式云性磁共振数据中常见的大规模矢量实地数据集,是多谱光学和雷达传感器以及现代多式云性磁共振数据中常见的。在本文件中,我们开发了一个新型的随机功能分析方法,以根据一个域的表面随机行为以及多波段矢量的实地数据共变异结构结构来检测异常现象。一个最佳的矢量字段Karhunen-Loev (KL) 扩展适用于这种随机的外地数据。一系列多层次或地心功能子空间是从域的地貌测量中构建出来的,从KLL扩张的初始的地貌变异性中改造。通过在多层次上对随机字段的预测进行检测。这种异常现象可以在基于本地和全球信息的适当规范空间中量化。此外,在可靠的假设分布上,不需要事先对数据的概率分布进行假设。只有复变异功能才适用于这种随机的功能。此外,这个方法还允许在不丢失任何信息的情况下对基于初始变异性的矢量方法进行分解。该方法适用于在多层次的野野野场野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野野生物,,,,,,,,,,,,,, 的地,在使用在使用新的地,在使用着地,在使用一个复杂的地,在使用新的森林的地,,,,在使用新的森林的地,,在使用地, 的地, 的地, 根基化地, 的变地, 的变地, 地, 的变地, 地, 地, 地, 地, 地, 地, 地, 地, 地, 地, 根基地, 地基地基地, 地, 地, 地, 地, 地, 地, 地, 地, 根基地, 地, 地, 地, 地, 地, 地,