Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal Environment
The monitoring of coastal areas using remote sensing techniques is an important issue to determine the bio-optical properties of the water column and the seabed composition. New hyperspectral satellite sensors (e.g., PRISMA, DESIS or EnMap) are developed to periodically observe ecosystems. The uncer...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/15/9/2242 |
| _version_ | 1797601817802047488 |
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| author | Mireille Guillaume Audrey Minghelli Malik Chami Manchun Lei |
| author_facet | Mireille Guillaume Audrey Minghelli Malik Chami Manchun Lei |
| author_sort | Mireille Guillaume |
| collection | DOAJ |
| description | The monitoring of coastal areas using remote sensing techniques is an important issue to determine the bio-optical properties of the water column and the seabed composition. New hyperspectral satellite sensors (e.g., PRISMA, DESIS or EnMap) are developed to periodically observe ecosystems. The uncertainties in the retrieved geophysical products remain a key issue to release reliable data useful for the end-users. In this study, an analytical approach based on Information theory is proposed to investigate the Cramér–Rao lower Bounds (CRB) for the uncertainties in the ocean color parameters. Practically, during the inversion process, an <i>a priori</i> knowledge on the estimated parameters is used since their range of variation is supposed to be known. Here, a Bayesian approach is attempted to handle such <i>a priori</i> knowledge. A Bayesian CRB (BCRB) is derived using the Lee et al. semianalytical radiative transfer model dedicated to shallow waters. Both environmental noise and bio-optical parameters are supposed to be random vectors that follow a Gaussian distibution. The calculation of CRB and BCRB is carried out for two hyperspectral images acquired above the French mediterranean coast. The images were obtained from the recently launched hyperspectral sensors, namely the DESIS sensor (DLR Earth Sensing Imaging Spectrometer, German Aerospace Center), and PRISMA (Precursore IpperSpettrale della Mission Applicativa—ASI, Italian Space Adjency) sensor. The comparison between the usual CRB approach, the proposed BCRB approach and experimental errors obtained for the retrieved bathymetry shows the better ability of the BCRB to determine minimum error bounds. |
| first_indexed | 2024-03-11T04:08:01Z |
| format | Article |
| id | doaj.art-82e21e15957545b083bd7a1a5dadcb2f |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-11T04:08:01Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-82e21e15957545b083bd7a1a5dadcb2f2023-11-17T23:37:27ZengMDPI AGRemote Sensing2072-42922023-04-01159224210.3390/rs15092242Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal EnvironmentMireille Guillaume0Audrey Minghelli1Malik Chami2Manchun Lei3Aix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel, F-13013 Marseille, FranceLaboratoire d’Informatique et Système (LIS), Université de Toulon, CNRS UMR 7020, F-83041 Toulon, FranceUniversité Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 96 Boulevard de l’Observatoire, CS 34229, CEDEX 4, F-06304 Nice, FranceLASTIG, Université Gustave Eiffel, ENSG, IGN, F-94160 Saint-Mandé, FranceThe monitoring of coastal areas using remote sensing techniques is an important issue to determine the bio-optical properties of the water column and the seabed composition. New hyperspectral satellite sensors (e.g., PRISMA, DESIS or EnMap) are developed to periodically observe ecosystems. The uncertainties in the retrieved geophysical products remain a key issue to release reliable data useful for the end-users. In this study, an analytical approach based on Information theory is proposed to investigate the Cramér–Rao lower Bounds (CRB) for the uncertainties in the ocean color parameters. Practically, during the inversion process, an <i>a priori</i> knowledge on the estimated parameters is used since their range of variation is supposed to be known. Here, a Bayesian approach is attempted to handle such <i>a priori</i> knowledge. A Bayesian CRB (BCRB) is derived using the Lee et al. semianalytical radiative transfer model dedicated to shallow waters. Both environmental noise and bio-optical parameters are supposed to be random vectors that follow a Gaussian distibution. The calculation of CRB and BCRB is carried out for two hyperspectral images acquired above the French mediterranean coast. The images were obtained from the recently launched hyperspectral sensors, namely the DESIS sensor (DLR Earth Sensing Imaging Spectrometer, German Aerospace Center), and PRISMA (Precursore IpperSpettrale della Mission Applicativa—ASI, Italian Space Adjency) sensor. The comparison between the usual CRB approach, the proposed BCRB approach and experimental errors obtained for the retrieved bathymetry shows the better ability of the BCRB to determine minimum error bounds.https://www.mdpi.com/2072-4292/15/9/2242hyperspectral imagingocean color remote sensingradiative transferseabed analysisestimationuncertainty |
| spellingShingle | Mireille Guillaume Audrey Minghelli Malik Chami Manchun Lei Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal Environment Remote Sensing hyperspectral imaging ocean color remote sensing radiative transfer seabed analysis estimation uncertainty |
| title | Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal Environment |
| title_full | Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal Environment |
| title_fullStr | Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal Environment |
| title_full_unstemmed | Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal Environment |
| title_short | Determination of Bayesian Cramér–Rao Bounds for Estimating Uncertainties in the Bio-Optical Properties of the Water Column, the Seabed Depth and Composition in a Coastal Environment |
| title_sort | determination of bayesian cramer rao bounds for estimating uncertainties in the bio optical properties of the water column the seabed depth and composition in a coastal environment |
| topic | hyperspectral imaging ocean color remote sensing radiative transfer seabed analysis estimation uncertainty |
| url | https://www.mdpi.com/2072-4292/15/9/2242 |
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