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

Area of Science:

• Signal Processing
• Information Geometry
• Machine Learning

Background:

• Non-stationary signal detection is challenging due to information embedded in local time-frequency structures, not global statistics.
• Existing methods struggle when discriminative information is not captured by energy, mean spectra, or covariance.
• Analyzing local directional organization and anisotropy is crucial for robust signal detection.

Purpose of the Study:

• To propose a novel information-geometric detector for non-stationary signals.
• To leverage symmetric positive definite (SPD) structure fields for characterizing local time-frequency organization.
• To develop a detection statistic based on aggregated local evidence from SPD objects.

Main Methods:

• Transforming time-frequency patches into spatially distributed fields of second-order tensors (SPD structure fields).
• Employing a locally isotropic Riemannian Gaussian approximation on the SPD manifold.
• Calculating local distance-difference evidence, monotonically related to an approximate log-likelihood ratio.
• Aggregating local evidence into a sample-level detection statistic.

Main Results:

• The proposed SPD structure-field representation significantly drives performance gains in non-stationary signal detection.
• The information-geometric approach provides an effective interpretation of detection evidence.
• The Riemannian metric offers secondary refinement to the detection statistic.
• Experiments on a controlled benchmark validate the effectiveness of the SPD structure-field representation.

Conclusions:

• The proposed information-geometric detector effectively utilizes local SPD structure fields for non-stationary signal detection.
• The SPD structure-field representation is the primary contributor to improved detection performance.
• This approach offers a new paradigm for analyzing complex signal structures in time-frequency domains.