{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T16:46:43Z","timestamp":1778258803135,"version":"3.51.4"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,3,23]],"date-time":"2019-03-23T00:00:00Z","timestamp":1553299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The log-ratio (LR) operator is well suited for change detection in synthetic aperture radar (SAR) amplitude or intensity images. In applying the LR operator to change detection in multi-temporal SAR images, a crucial problem is how to develop precise models for the LR statistics. In this study, we first derive analytically the probability density function (PDF) of the LR operator. Subsequently, the PDF of the LR statistics is parameterized by three parameters, i.e., the number of looks, the coherence magnitude, and the true intensity ratio. Then, the maximum-likelihood (ML) estimates of parameters in the LR PDF are also derived. As an example, the proposed statistical model and corresponding ML estimation are used in an operational application, i.e., determining the constant false alarm rate (CFAR) detection thresholds for small target detection between SAR images. The effectiveness of the proposed model and corresponding ML estimation are verified by applying them to measured multi-temporal SAR images, and comparing the results to the well-known generalized Gaussian (GG) distribution; the usefulness of the proposed LR PDF for small target detection is also shown.<\/jats:p>","DOI":"10.3390\/s19061431","type":"journal-article","created":{"date-parts":[[2019,3,25]],"date-time":"2019-03-25T06:56:52Z","timestamp":1553497012000},"page":"1431","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Small-Target Detection between SAR Images Based on Statistical Modeling of Log-Ratio Operator"],"prefix":"10.3390","volume":"19","author":[{"given":"Chao","family":"Chen","sequence":"first","affiliation":[{"name":"College of System Engineering, National University of Defense Technology, Sanyi Avenue, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kuihua","family":"Huang","sequence":"additional","affiliation":[{"name":"College of System Engineering, National University of Defense Technology, Sanyi Avenue, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gui","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Traffic Engineering, Hunan University of Technology, Zhuzhou 412007, China"},{"name":"Faculty of Geoscience and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1080\/01431169108929656","article-title":"Change detection in SAR imagery","volume":"12","author":"White","year":"1990","journal-title":"Int. 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