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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Autores principales:	Jiawei Qi, Dianjun Zhang, Zhaoyu Ren, Aijun Cui, Fei Yin, Jian Qin, Jie Zhan, Jinshan Zhu
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Bathymetry initial values Levenberg–Marquardt method optimization Ocean engineering TC1501-1800 Geophysics. Cosmic physics QC801-809
Acceso en línea:	https://doaj.org/article/f89f3fd64a564d079d859abc9393a641
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spelling	oai:doaj.org-article:f89f3fd64a564d079d859abc9393a6412021-11-05T23:00:10ZDetermination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval2151-153510.1109/JSTARS.2021.3121446https://doaj.org/article/f89f3fd64a564d079d859abc9393a6412021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9582775/https://doaj.org/toc/2151-1535The 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.Jiawei QiDianjun ZhangZhaoyu RenAijun CuiFei YinJian QinJie ZhanJinshan ZhuIEEEarticleBathymetryinitial valuesLevenberg–Marquardt methodoptimizationOcean engineeringTC1501-1800Geophysics. Cosmic physicsQC801-809ENIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol 14, Pp 10875-10888 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bathymetry initial values Levenberg–Marquardt method optimization Ocean engineering TC1501-1800 Geophysics. Cosmic physics QC801-809
spellingShingle	Bathymetry initial values Levenberg–Marquardt method optimization Ocean engineering TC1501-1800 Geophysics. Cosmic physics QC801-809 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
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.
format	article
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
title	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_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_sort	determination of the initial value ranges of nonlinear solutions for a log ratio bathymetric inversion model and bathymetry retrieval
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/f89f3fd64a564d079d859abc9393a641
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Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval

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