Information-Geometric Detection via Local SPD Structure Fields in the Time-Frequency Domain

Non-stationary signal detection is challenging when discriminative information is not reflected in global energy, mean spectra, or a single covariance statistic, but is instead embedded in the organization of local time-frequency structures. This paper proposes an information-geometric detector defined on local symmetric positive definite (SPD) structure fields. Time-frequency patches are transformed into a spatially distributed field of second-order tensors to characterize local directional organization and anisotropy. Under a locally isotropic Riemannian Gaussian approximation on the SPD manifold, the local distance-difference evidence is monotonically related to an approximate log-likelihood ratio, providing an information-geometric interpretation without implying strict Neyman-Pearson optimality. Instead of forming a single global statistic or stacking patch-level features, the proposed method constructs a spatially distributed field of structured SPD objects and derives local distance-difference evidence, which is subsequently aggregated into a sample-level detection statistic. Experiments under a controlled SPD structure-field locality benchmark show that performance gains are primarily driven by the proposed SPD structure-field representation, with the Riemannian metric providing only secondary refinement.