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According to the underwater image formation model, the degraded underwater image could be separated into three parts, the directed component, the back and forward scattering components. The latter two parts can be considered as scattering. The directed component is constrained to have a low rank. After that, the restored underwater image is obtained. The quantitative and qualitative analyses illustrate that the proposed method performed equivalent or better than the state-of-the-art methods. Yet, it\u2019s simple to implement without the training process.<\/jats:p>","DOI":"10.1142\/s0218001421540227","type":"journal-article","created":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T01:49:39Z","timestamp":1612403379000},"page":"2154022","source":"Crossref","is-referenced-by-count":3,"title":["Underwater Image Enhancement with the Low-Rank Nonnegative Matrix Factorization Method"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4822-2721","authenticated-orcid":false,"given":"Xiaopeng","family":"Liu","sequence":"first","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 265205, P.\u00a0R.\u00a0China"}]},{"given":"Cong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Science, Nanjing University of Science and Technology, Nanjing 210094, P.\u00a0R.\u00a0China"},{"name":"CAD\/CAM Fujian Province University Engineering Research Center, Putian University, Putian 350000, P.\u00a0R.\u00a0China"}]},{"given":"Xiaochen","family":"Liu","sequence":"additional","affiliation":[{"name":"Shandong Hi-speed Architectural Design Co., Ltd., Jinan 250000, P.\u00a0R.\u00a0China"}]}],"member":"219","published-online":{"date-parts":[[2021,3,8]]},"reference":[{"issue":"99","key":"S0218001421540227BIB001","first-page":"379","volume":"27","author":"Ancuti C. 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