  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.
