{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T23:46:10Z","timestamp":1771458370532,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T00:00:00Z","timestamp":1730073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2022YFF1301900"],"award-info":[{"award-number":["2022YFF1301900"]}]},{"name":"National Key Research and Development Program of China","award":["2022450"],"award-info":[{"award-number":["2022450"]}]},{"name":"Youth Innovation Promote Association Cas","award":["2022YFF1301900"],"award-info":[{"award-number":["2022YFF1301900"]}]},{"name":"Youth Innovation Promote Association Cas","award":["2022450"],"award-info":[{"award-number":["2022450"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>To address the issues of image blurring and color distortion in hazy conditions, an image restoration method based on a parametric analytical modulation transfer function model is proposed under turbid atmospheric conditions. A source database is established using a numerical radiative transfer method based on discrete ordinate. Through multivariate nonlinear fitting and linear interpolation, the quantitative relationships among critical spatial frequency, turbid atmospheric MTF, and key atmospheric optical parameters\u2014such as optical thickness, single scattering albedo, and asymmetry factor\u2014are examined. A fast and efficient parametric analytical MTF model for turbid atmospheres is developed and applied to restore images affected by fog. The results demonstrate that, within the applicable range of the model, the model\u2019s maximum mean relative error and the root mean square error are 7.16% and 0.0454, respectively. The computational speed is nearly a thousand times faster than that of the numerical radiative transfer method, achieving high accuracy and ease of application. Images restored using this model exhibit enhanced clarity and quality, effectively compensating for the degradation in image quality caused by turbid atmospheres. This approach represents a novel solution to the challenges of image processing in complex atmospheric environments.<\/jats:p>","DOI":"10.3390\/rs16213998","type":"journal-article","created":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T07:04:04Z","timestamp":1730099044000},"page":"3998","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Parametric Analytical Modulation Transfer Function Model in Turbid Atmosphere with Application to Image Restoration"],"prefix":"10.3390","volume":"16","author":[{"given":"Mengxing","family":"Guo","sequence":"first","affiliation":[{"name":"Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China"},{"name":"Science Island Branch, University of Science and Technology of China, Hefei 230026, China"}]},{"given":"Pengfei","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China"},{"name":"School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei 230022, China"}]},{"given":"Zizhao","family":"Fan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China"},{"name":"School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei 230022, China"}]},{"given":"Hao","family":"Lu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China"},{"name":"Science Island Branch, University of Science and Technology of China, Hefei 230026, China"}]},{"given":"Ruizhong","family":"Rao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China"},{"name":"Science Island Branch, University of Science and Technology of China, Hefei 230026, China"},{"name":"School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei 230022, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1364\/JOSA.53.000214","article-title":"Light in the Sea","volume":"53","author":"Duntley","year":"1963","journal-title":"J. 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