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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">radioelectronics</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений России. Радиоэлектроника</journal-title><trans-title-group xml:lang="en"><trans-title>Journal of the Russian Universities. Radioelectronics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1993-8985</issn><issn pub-type="epub">2658-4794</issn><publisher><publisher-name>Saint Petersburg Electrotechnical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.32603/1993-8985-2024-27-5-41-53</article-id><article-id custom-type="elpub" pub-id-type="custom">radioelectronics-931</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>РАДИОЛОКАЦИЯ И РАДИОНАВИГАЦИЯ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>RADAR AND NAVIGATION</subject></subj-group></article-categories><title-group><article-title>Определение характеристик морской поверхности по радиолокационным изображениям с использованием градиентных методов</article-title><trans-title-group xml:lang="en"><trans-title>Measurement of Sea Surface Characteristics from Radar Images Using Gradient Methods</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0008-2110-0568</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лаптев</surname><given-names>К. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Laptev</surname><given-names>K. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Лаптев Кирилл Юрьевич – магистр по направлению "Инфокоммуникационные технологии и системы связи" (2024), аспирант кафедры радиотехнических систем.</p><p>Ул. Проф. Попова, д. 5 Ф, Санкт-Петербург, 197022</p></bio><bio xml:lang="en"><p>Kirill Yu. Laptev - Master in Infocommunication Technology and Communications Systems (2024), Postgraduate student of the Department of Radio Engineering Systems.</p><p>5 F, Professor Popov St., St Petersburg 197022</p></bio><email xlink:type="simple">kirikill76@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Соколов</surname><given-names>Н. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Sokolov</surname><given-names>N. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Соколов Никита Владимирович – специалист по направлению "Радиоэлектронные системы и комплексы".</p><p>Ул. Проф. Попова, д. 5 Ф, Санкт-Петербург, 197022</p></bio><bio xml:lang="en"><p>Nikita V. Sokolov - Specialist in "Radioelectronic systems and complexes".</p><p>5 F, Professor Popov St., St Petersburg 197022</p></bio><email xlink:type="simple">falconsnv@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8155-9310</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Михайлов</surname><given-names>В. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Mikhailov</surname><given-names>V. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михайлов Вячеслав Николаевич – инженер по специальности "Радиотехника" (2000), старший научный сотрудник научно-образовательного центра "Цифровые телекоммуникационные технологии".</p><p>Ул. Проф. Попова, д. 5 Ф, Санкт-Петербург, 197022</p></bio><bio xml:lang="en"><p>Viacheslav N. Mikhailov - Enginer in Radiotechnics (2000), Senior Researcher of the Scientific and Educational Center "Digital Telecommunication Technologies".</p><p>5 F, Professor Popov St., St Petersburg 197022</p></bio><email xlink:type="simple">vnmikhaylov@etu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-0356-5651</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Богачев</surname><given-names>М. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Bogachev</surname><given-names>M. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Богачев Михаил Игоревич – доктор технических наук (2018), доцент (2011), профессор кафедры радиотехнических систем, главный научный сотрудник научно-образовательного центра "Цифровые телекоммуникационные технологии".</p><p>Ул. Проф. Попова, д. 5 Ф, Санкт-Петербург, 197022</p></bio><bio xml:lang="en"><p>Mikhail I. Bogachev - Dr Sci. (Eng.) (2018), Associate Professor (2011), Professor of the Department of Radio Engineering Systems, Chief Researcher of the Scientific and Educational Center "Digital Telecommunication Technologies".</p><p>5 F, Professor Popov St., St Petersburg 197022</p></bio><email xlink:type="simple">rogex@yandex.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6637-2374</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Воробьев</surname><given-names>Е. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Vorobev</surname><given-names>E. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Воробьев Евгений Николаевич – кандидат технических наук (2022), доцент кафедры радиотехнических систем.</p><p>Ул. Проф. Попова, д. 5 Ф, Санкт-Петербург, 197022</p></bio><bio xml:lang="en"><p>Evgenii N. Vorobev - Cand. Sci. (Eng.) (2022), Associate Professor of the Department of Radio Engineering Systems, Senior Researcher at the Research Institute "Prognoz".</p><p>5 F, Professor Popov St., St Petersburg 197022</p></bio><email xlink:type="simple">envorobev@etu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В.И. Ульянова (Ленина)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Saint Petersburg Electrotechnical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>21</day><month>11</month><year>2024</year></pub-date><volume>27</volume><issue>5</issue><fpage>41</fpage><lpage>53</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Лаптев К.Ю., Соколов Н.В., Михайлов В.Н., Богачев М.И., Воробьев Е.Н., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Лаптев К.Ю., Соколов Н.В., Михайлов В.Н., Богачев М.И., Воробьев Е.Н.</copyright-holder><copyright-holder xml:lang="en">Laptev K.Y., Sokolov N.V., Mikhailov V.N., Bogachev M.I., Vorobev E.N.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://re.eltech.ru/jour/article/view/931">https://re.eltech.ru/jour/article/view/931</self-uri><abstract><sec><title>Введение</title><p>Введение. Дистанционное зондирование и мониторинг морской поверхности имеют огромное значение в контексте решения задач оперативной океанографии, экологического мониторинга и ряда др. Возможность оперативной оценки состояния морской поверхности особенно актуальна в зонах, представляющих опасность для судоходства, где быстрое и точное реагирование становится критически важным. Современные радиолокационные станции (РЛС) при обзоре формируют последовательности цифровых радиолокационных изображений (РЛИ), аналогичные последовательностям кадров в видеопотоке, что обусловливает возможность применения для их вторичной обработки градиентных методов, зарекомендовавших себя при анализе видеоданных.</p></sec><sec><title>Цель работы</title><p>Цель работы. Определение характеристик морского волнения по РЛИ с использованием методов градиентной оценки движения. Использование градиентных методов позволит реализовать дополнительные инструменты обработки изображений, формируемых при отражении зондирующих сигналов от морской поверхности.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. Для оценки характеристик морской поверхности по РЛИ использованы градиентные методы. Для их обучения служили серии синтезированных изображений морской поверхности, полученные методом математического моделирования. Эффективность градиентных методов оценивалась по экспериментальным РЛИ, предоставленным ИО РАН им. Ширшова.</p></sec><sec><title>Результаты</title><p>Результаты. С помощью градиентных методов вычислены направление и скорость волнения по нескольким последовательным обзорам РЛС. Построены регрессионные модели зависимости вычисленных значений от заданных. При определении направления волнения высокую эффективность продемонстрировали методы Fаrnеback и TV-L1.</p></sec><sec><title>Заключение</title><p>Заключение. Алгоритм вычисления скорости и направления смещения морской поверхности с помощью градиентных методов был предварительно обучен с применением модельных данных. Выполнена верификация реализованных методов и алгоритмов оценки скорости и направления морского волнения на предмет адекватности и реалистичности получаемых результатов сравнением с экспериментальными изображениями, найденными с использованием корабельных РЛС.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. Remote sensing and monitoring of the sea surface are of great importance in such fields, as operational oceanography, environmental monitoring, etc. The ability to quickly assess the state of the sea surface is particularly relevant in areas that pose a danger to shipping, where rapid and accurate response becomes critical. Modern radars represent information as digital image series largely reminiscent to a frame series in a video stream, thus enabling the use of gradient methods originally designed for and proven successful in video analysis.</p></sec><sec><title>Aim</title><p>Aim. Determination of sea wave characteristics from radar images using gradient motion estimation methods. The use of gradient methods will allow implementing additional tools for processing radar image series obtained from sea backscatter.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. To assess the characteristics of the sea surface from radar images, gradient methods were used. To train the methods, a series of synthetic images of the sea surface obtained by mathematical modeling were used. To evaluate the effectiveness of the gradient methods, two representative experimental radar image series provided by the Institute of Oceanography RAS were employed.</p></sec><sec><title>Results</title><p>Results. Using gradient methods, the direction and speed of waves were calculated from several consecutive radar observations. Regression models of the dependence of calculated values on the specified ones were constructed. The Farneback and TV-L1 methods proved to be effective especially for obtaining the direction of the sea waves.</p></sec><sec><title>Conclusion</title><p>Conclusion. An algorithm for evaluating speed and direction of the sea surface displacement using gradient methods was pre-trained using simulated model data. The implemented methods and algorithms for assessing the speed and direction of sea waves were validated using two experimental image series obtained from shipborne navigational radars.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>радиолокация</kwd><kwd>морская поверхность</kwd><kwd>алгоритм Лукаса–Канаде</kwd><kwd>алгоритм Farnebäck</kwd><kwd>TV-L1</kwd><kwd>линейная регрессия</kwd></kwd-group><kwd-group xml:lang="en"><kwd>radar</kwd><kwd>sea surface</kwd><kwd>Lucas–Kanade algorithm</kwd><kwd>Farnebäck algorithm</kwd><kwd>TV-L1</kwd><kwd>linear regression</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при поддержке Минобрнауки РФ в рамках темы Государственного задания FSEE-2020-0002</funding-statement><funding-statement xml:lang="en">This study was supported by the Ministry of Science and Higher Education in the framework of the state assignment FSEE-2020-0002</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Horn B. 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