On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging
We propose a mathematical study of the statistics of chlorophyll fluorescence indices. While most of the literature assumes Gaussian distributions for these indices, we demonstrate their fundamental non-Gaussian nature. Indeed, while the noise in the raw fluorescence images can be assumed as Gaussia...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
|
| Series: | Remote Sensing |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2072-4292/15/2/528 |
| _version_ | 1797437403496972288 |
|---|---|
| author | Angelina El Ghaziri Nizar Bouhlel Natalia Sapoukhina David Rousseau |
| author_facet | Angelina El Ghaziri Nizar Bouhlel Natalia Sapoukhina David Rousseau |
| author_sort | Angelina El Ghaziri |
| collection | DOAJ |
| description | We propose a mathematical study of the statistics of chlorophyll fluorescence indices. While most of the literature assumes Gaussian distributions for these indices, we demonstrate their fundamental non-Gaussian nature. Indeed, while the noise in the raw fluorescence images can be assumed as Gaussian additive, the deterministic ratio between them produces nonlinear non-Gaussian distributions. We investigate the states in which this non-Gaussianity can affect the statistical estimation when wrongly approached with linear estimators. We provide an expectation–maximization estimator adapted to the non-Gaussian distributions. We illustrate the interest of this estimator with simulations from images of chlorophyll fluorescence indices.. We demonstrate the benefits of our approach by comparison with the standard Gaussian assumption. Our expectation–maximization estimator shows low estimation errors reaching seven percent for a more pronounced deviation from Gaussianity compared to Gaussianity assumptions estimators rising to more than 70 percent estimation error. These results show the importance of considering rigorous mathematical estimation approaches in chlorophyll fluorescence indices. The application of this work could be extended to various vegetation indices also made up of a ratio of Gaussian distributions. |
| first_indexed | 2024-03-09T11:19:42Z |
| format | Article |
| id | doaj.art-f565364abe6e4abbb88637ba06f3992b |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-09T11:19:42Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-f565364abe6e4abbb88637ba06f3992b2023-12-01T00:23:15ZengMDPI AGRemote Sensing2072-42922023-01-0115252810.3390/rs15020528On the Importance of Non-Gaussianity in Chlorophyll Fluorescence ImagingAngelina El Ghaziri0Nizar Bouhlel1Natalia Sapoukhina2David Rousseau3Institut Agro, Université d’Angers, INRAE, IRHS, SFR QuaSaV, 49000 Angers, FranceInstitut Agro, Université d’Angers, INRAE, IRHS, SFR QuaSaV, 49000 Angers, FranceInstitut Agro, Université d’Angers, INRAE, IRHS, SFR QuaSaV, 49000 Angers, FranceLARIS, UMR INRAe IRHS, Université d’Angers, 62 Avenue Notre Dame du Lac, 49000 Angers, FranceWe propose a mathematical study of the statistics of chlorophyll fluorescence indices. While most of the literature assumes Gaussian distributions for these indices, we demonstrate their fundamental non-Gaussian nature. Indeed, while the noise in the raw fluorescence images can be assumed as Gaussian additive, the deterministic ratio between them produces nonlinear non-Gaussian distributions. We investigate the states in which this non-Gaussianity can affect the statistical estimation when wrongly approached with linear estimators. We provide an expectation–maximization estimator adapted to the non-Gaussian distributions. We illustrate the interest of this estimator with simulations from images of chlorophyll fluorescence indices.. We demonstrate the benefits of our approach by comparison with the standard Gaussian assumption. Our expectation–maximization estimator shows low estimation errors reaching seven percent for a more pronounced deviation from Gaussianity compared to Gaussianity assumptions estimators rising to more than 70 percent estimation error. These results show the importance of considering rigorous mathematical estimation approaches in chlorophyll fluorescence indices. The application of this work could be extended to various vegetation indices also made up of a ratio of Gaussian distributions.https://www.mdpi.com/2072-4292/15/2/528<i>Arabidopsis</i>Bayesian inferenceExpectation–Maximization (EM) algorithmparameter estimationplant imagingstatistics |
| spellingShingle | Angelina El Ghaziri Nizar Bouhlel Natalia Sapoukhina David Rousseau On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging Remote Sensing <i>Arabidopsis</i> Bayesian inference Expectation–Maximization (EM) algorithm parameter estimation plant imaging statistics |
| title | On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging |
| title_full | On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging |
| title_fullStr | On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging |
| title_full_unstemmed | On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging |
| title_short | On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging |
| title_sort | on the importance of non gaussianity in chlorophyll fluorescence imaging |
| topic | <i>Arabidopsis</i> Bayesian inference Expectation–Maximization (EM) algorithm parameter estimation plant imaging statistics |
| url | https://www.mdpi.com/2072-4292/15/2/528 |
| work_keys_str_mv | AT angelinaelghaziri ontheimportanceofnongaussianityinchlorophyllfluorescenceimaging AT nizarbouhlel ontheimportanceofnongaussianityinchlorophyllfluorescenceimaging AT nataliasapoukhina ontheimportanceofnongaussianityinchlorophyllfluorescenceimaging AT davidrousseau ontheimportanceofnongaussianityinchlorophyllfluorescenceimaging |