Hyperspectral anomaly detection (HAD), a crucial approach for many civilian and military applications, seeks to identify pixels with spectral signatures that are anomalous relative to a preponderance of background signatures. Significant effort has been made to improve HAD techniques, but challenges arise due to complex real-world environments and, by definition, limited prior knowledge of potential signatures of interest. This paper introduces a novel HAD method by proposing a transport-based mathematical model to describe the pixels comprising a given hyperspectral image. In this approach, hyperspectral pixels are viewed as observations of a template pattern undergoing unknown deformations that enables their representation in the signed cumulative distribution transform (SCDT) domain. An unsupervised subspace modeling technique is then used to construct a model of abundant background signals in this domain, whereupon anomalous signals are detected as deviations from the learned model. Comprehensive evaluations across five distinct datasets illustrate the superiority of our approach compared to state-of-the-art methods.