Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval
The log-ratio model (LRM) with three model parameters (<inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_1},$</tex-math></inline-for...
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| Format: | Article |
| Language: | English |
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IEEE
2021-01-01
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| Series: | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9582775/ |
| _version_ | 1831666854701039616 |
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| author | Jiawei Qi Dianjun Zhang Zhaoyu Ren Aijun Cui Fei Yin Jian Qin Jie Zhan Jinshan Zhu |
| author_facet | Jiawei Qi Dianjun Zhang Zhaoyu Ren Aijun Cui Fei Yin Jian Qin Jie Zhan Jinshan Zhu |
| author_sort | Jiawei Qi |
| collection | DOAJ |
| description | The log-ratio model (LRM) with three model parameters (<inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_1},$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_0}$</tex-math></inline-formula>) has been widely used in shallow water bathymetry of multispectral images. At present, obtaining LRM model parameters by optimization algorithms depends on the setting of initial values [<inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0)$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_1}(0),$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_0}(0)$</tex-math></inline-formula>] or initial value ranges. However, how to set the initial value can obtain model parameters more effectively and credibly, and the significance of each initial value in the optimization process is very important for LRM bathymetric retrieval method. In this article, remote sensing images and bathymetric data were used to determine the initial value ranges of credible model parameters, and then the sensitivity of each parameter was analyzed in the algorithm optimization process from the partial differential perspective, and the bathymetry was retrieved in the sea area near Ganquan Island. The results show that according to the partial differential analysis of model parameters, <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}$</tex-math></inline-formula>, with the smallest change rate in three LRM parameters and the rate of <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_1}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_0}$</tex-math></inline-formula> is at least five times of it. So <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0)$</tex-math></inline-formula> needs more iterations to achieve the optimal. Therefore, the initial value <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0)$</tex-math></inline-formula> determines whether the optimization method can obtain credible LRM model parameters and the algorithm convergence speed. And when <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0) \in ({1/{{\boldsymbol{R}}_{{{\bf min}}}},\ 1000} ]$</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">${{\boldsymbol{R}}_{{{\bf min}}}}$</tex-math></inline-formula> is the minimum reflectance in blue and green bands), there must be a credible model parameter solution. The bathymetric retrieval results of the sea area with coral and sand substrates show the applicability of our initial value ranges in different substrate area. |
| first_indexed | 2024-12-19T20:00:01Z |
| format | Article |
| id | doaj.art-f89f3fd64a564d079d859abc9393a641 |
| institution | Directory Open Access Journal |
| issn | 2151-1535 |
| language | English |
| last_indexed | 2024-12-19T20:00:01Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| spelling | doaj.art-f89f3fd64a564d079d859abc9393a6412022-12-21T20:07:42ZengIEEEIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing2151-15352021-01-0114108751088810.1109/JSTARS.2021.31214469582775Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry RetrievalJiawei Qi0https://orcid.org/0000-0001-8379-3293Dianjun Zhang1https://orcid.org/0000-0003-3270-8794Zhaoyu Ren2Aijun Cui3Fei Yin4Jian Qin5https://orcid.org/0000-0002-4507-8229Jie Zhan6https://orcid.org/0000-0001-7100-2394Jinshan Zhu7https://orcid.org/0000-0003-0102-7603College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, ChinaSchool of Marine Science and Technology, Tianjin University, Tianjin, ChinaCollege of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, ChinaCollege of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, ChinaCollege of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, ChinaCollege of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, ChinaSchool of Marine Science and Technology, Tianjin University, Tianjin, ChinaCollege of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, ChinaThe log-ratio model (LRM) with three model parameters (<inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_1},$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_0}$</tex-math></inline-formula>) has been widely used in shallow water bathymetry of multispectral images. At present, obtaining LRM model parameters by optimization algorithms depends on the setting of initial values [<inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0)$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_1}(0),$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_0}(0)$</tex-math></inline-formula>] or initial value ranges. However, how to set the initial value can obtain model parameters more effectively and credibly, and the significance of each initial value in the optimization process is very important for LRM bathymetric retrieval method. In this article, remote sensing images and bathymetric data were used to determine the initial value ranges of credible model parameters, and then the sensitivity of each parameter was analyzed in the algorithm optimization process from the partial differential perspective, and the bathymetry was retrieved in the sea area near Ganquan Island. The results show that according to the partial differential analysis of model parameters, <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}$</tex-math></inline-formula>, with the smallest change rate in three LRM parameters and the rate of <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_1}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{m}}_0}$</tex-math></inline-formula> is at least five times of it. So <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0)$</tex-math></inline-formula> needs more iterations to achieve the optimal. Therefore, the initial value <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0)$</tex-math></inline-formula> determines whether the optimization method can obtain credible LRM model parameters and the algorithm convergence speed. And when <inline-formula><tex-math notation="LaTeX">${\boldsymbol{n}}(0) \in ({1/{{\boldsymbol{R}}_{{{\bf min}}}},\ 1000} ]$</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">${{\boldsymbol{R}}_{{{\bf min}}}}$</tex-math></inline-formula> is the minimum reflectance in blue and green bands), there must be a credible model parameter solution. The bathymetric retrieval results of the sea area with coral and sand substrates show the applicability of our initial value ranges in different substrate area.https://ieeexplore.ieee.org/document/9582775/Bathymetryinitial valuesLevenberg–Marquardt methodoptimization |
| spellingShingle | Jiawei Qi Dianjun Zhang Zhaoyu Ren Aijun Cui Fei Yin Jian Qin Jie Zhan Jinshan Zhu Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Bathymetry initial values Levenberg–Marquardt method optimization |
| title | Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval |
| title_full | Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval |
| title_fullStr | Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval |
| title_full_unstemmed | Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval |
| title_short | Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval |
| title_sort | determination of the initial value ranges of nonlinear solutions for a log ratio bathymetric inversion model and bathymetry retrieval |
| topic | Bathymetry initial values Levenberg–Marquardt method optimization |
| url | https://ieeexplore.ieee.org/document/9582775/ |
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