{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:12:50Z","timestamp":1760213570962,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2016,12,11]],"date-time":"2016-12-11T00:00:00Z","timestamp":1481414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61571145"],"award-info":[{"award-number":["61571145"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the China Postdoctoral Science Foundation","award":["2014M551221"],"award-info":[{"award-number":["2014M551221"]}]},{"name":"the Key Program of Heilongjiang Natural Science Foundation","award":["ZD201216"],"award-info":[{"award-number":["ZD201216"]}]},{"name":"the Program Excellent Academic Leaders of Harbin","award":["RC2013XK009003"],"award-info":[{"award-number":["RC2013XK009003"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["HEUCF1608"],"award-info":[{"award-number":["HEUCF1608"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Abstract: Real-time anomaly detection has received wide attention in remote sensing image processing because many moving targets must be detected on a timely basis. A widely-used anomaly detection algorithm is the Reed-Xiaoli (RX) algorithm that was proposed by Reed and Yu. The kernel RX algorithm proposed by Kwon and Nasrabadi is a nonlinear version of the RX algorithm and outperforms the RX algorithm in terms of detection accuracy. However, the kernel RX algorithm is computationally more expensive. This paper presents a novel real-time anomaly detection framework based on the kernel RX algorithm. In the kernel RX detector, the inverse covariance matrix and the estimated mean of the background data in the kernel space are non-causal and computationally inefficient. In this work, a local causal sliding array window is used to ensure the causality of the detection system. Using the matrix inversion lemma and the Woodbury matrix identity, both the inverse covariance matrix and estimated mean can be recursively derived without extensive repetitive calculations, and, therefore, the real-time kernel RX detector can be implemented and processed pixel-by-pixel in real time. To substantiate its effectiveness and utility in real-time anomaly detection, real hyperspectral data sets are utilized for experiments.<\/jats:p>","DOI":"10.3390\/rs8121011","type":"journal-article","created":{"date-parts":[[2016,12,12]],"date-time":"2016-12-12T14:43:57Z","timestamp":1481553837000},"page":"1011","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Real-Time Anomaly Detection Based on a Fast Recursive Kernel RX Algorithm"],"prefix":"10.3390","volume":"8","author":[{"given":"Chunhui","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Xifeng","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Bormin","family":"Huang","sequence":"additional","affiliation":[{"name":"Space Science and Engineering Center, University of Wisconsin, Madison, WI 53706, USA"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1109\/TNNLS.2015.2477537","article-title":"Salient band selection for hyperspectral image classification via manifold ranking","volume":"27","author":"Wang","year":"2016","journal-title":"IEEE Trans. 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