Robust Hyperspectral Anomaly Detection via Bootstrap Sampling-based Subspace Modeling in the Signed Cumulative Distribution Transform Domain

This paper introduces an approach that combines a transport-based model of hyperspectral pixels and a bootstrap sampling strategy to construct an ensemble of background subspaces in the signed cumulative distribution transform (SCDT) domain for robust anomaly detection in hyperspectral images characterized by complex and varied background clutter. Each spectral signal (i.e., pixel) is treated as an observation of an unknown background template pattern that has undergone unknown, but restricted, deformation due to factors such as shadowing, look angle, or atmospheric absorption. When combined with the SCDT—a transport-based transform with close connections to one-dimensional Wasserstein embedding—the model induces convexity of hyperspectral pixel representations in the SCDT space and facilitates the construction of subspace models that characterize dominant background signals. A bootstrap sampling strategy in the ambient domain yields an ensemble of background subspace models in SCDT domain and anomalies are subsequently detected as pixels that do not conform to any of the learned subspace models. Experiments on six benchmark hyperspectral datasets demonstrate that the approach effectively captures spectral variability and reliably detects anomalies with low false alarm rates, outperforming state-of-the-art comparison methods in most cases. These results underscore the potential of transport-based subspace representations for robust and interpretable hyperspectral anomaly detection across diverse imaging scenarios. Finally, the geodesic properties of the SCDT embedding are leveraged to provide a geometric interpretation of the method via visualization of paths between test signals and their subspace projections.