{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:09:40Z","timestamp":1773655780666,"version":"3.50.1"},"reference-count":68,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2015,12,17]],"date-time":"2015-12-17T00:00:00Z","timestamp":1450310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE), which is based on the combination of Fractional Fourier Transform (FRFT) and Shannon entropy. Afterwards, the Welch\u2019s t-test (WTT) and Mahalanobis distance (MD) were harnessed to select distinguishing features. Finally, we introduced an advanced classifier: twin support vector machine (TSVM). Results: A 10 \u00d7 K-fold stratified cross validation test showed that this proposed \u201cFRFE + WTT + TSVM\u201d yielded an accuracy of 100.00%, 100.00%, and 99.57% on datasets that contained 66, 160, and 255 brain images, respectively. Conclusions: The proposed \u201cFRFE + WTT + TSVM\u201d method is superior to 20 state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/e17127877","type":"journal-article","created":{"date-parts":[[2015,12,17]],"date-time":"2015-12-17T10:47:37Z","timestamp":1450349257000},"page":"8278-8296","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":67,"title":["Pathological Brain Detection by a Novel Image Feature\u2014Fractional Fourier Entropy"],"prefix":"10.3390","volume":"17","author":[{"given":"Shuihua","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Nanjing Normal University, Nanjing 210023, China"},{"name":"School of Psychology, Nanjing Normal University, Nanjing 210023, China"},{"name":"Jiangsu Key Laboratory of 3D Printing Equipment and Manufacturing, Nanjing 210042, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4870-1493","authenticated-orcid":false,"given":"Yudong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Nanjing Normal University, Nanjing 210023, China"},{"name":"School of Psychology, Nanjing Normal University, Nanjing 210023, China"},{"name":"Jiangsu Key Laboratory of 3D Printing Equipment and Manufacturing, Nanjing 210042, China"},{"name":"Guangxi Key Laboratory of Manufacturing System &amp; Advanced Manufacturing Technology, College of Mechanical Engineering, Guangxi University, Nanning 530021, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0009-4599","authenticated-orcid":false,"given":"Xiaojun","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou 221008, China"}]},{"given":"Ping","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, The City College of New York, City University of New York, New York, NY 10031, USA"}]},{"given":"Zhengchao","family":"Dong","sequence":"additional","affiliation":[{"name":"Translational Imaging Division &amp; MRI Unit, Columbia University and New York State Psychiatric Institute, New York, NY 10032, USA"}]},{"given":"Aijun","family":"Liu","sequence":"additional","affiliation":[{"name":"W. P. Carey School of Business, Arizona State University, P.O. Box 873406, Tempe, AZ 85287, USA"}]},{"given":"Ti-Fei","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Nanjing Normal University, Nanjing 210023, China"},{"name":"School of Psychology, Nanjing Normal University, Nanjing 210023, China"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ins.2015.06.017","article-title":"Exponential Wavelet Iterative Shrinkage Thresholding Algorithm for compressed sensing magnetic resonance imaging","volume":"322","author":"Zhang","year":"2015","journal-title":"Inf. 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