{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T09:54:21Z","timestamp":1781603661731,"version":"3.54.5"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T00:00:00Z","timestamp":1781222400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2023YFF0717402"],"award-info":[{"award-number":["2023YFF0717402"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013frequency structures. This paper proposes an information-geometric detector defined on local symmetric positive definite (SPD) structure fields. Time\u2013frequency 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\u2013Pearson 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.<\/jats:p>","DOI":"10.3390\/e28060679","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T09:06:52Z","timestamp":1781600812000},"page":"679","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Information-Geometric Detection via Local SPD Structure Fields in the Time\u2013Frequency Domain"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-7416-3948","authenticated-orcid":false,"given":"Yaohao","family":"Yue","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Shandong University, Qingdao 266237, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjie","family":"Wei","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5825-2575","authenticated-orcid":false,"given":"Yang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Shandong University, Qingdao 266237, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,12]]},"reference":[{"key":"ref_1","unstructured":"Kay, S.M. 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