Empirical Bayesian Estimation of the Interferometric SAR Coherence Magnitude
SAR interferometry has developed rapidly in recent years and now allows measurements of subtle deformation of the Earth's surface with millimeter accuracy. All state-of-the-art processing methods require a precise coherence estimate. However, this estimate is a random variable and biased...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
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| Online Access: | https://ieeexplore.ieee.org/document/9835014/ |
| _version_ | 1818497349835554816 |
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| author | Nico Adam |
| author_facet | Nico Adam |
| author_sort | Nico Adam |
| collection | DOAJ |
| description | SAR interferometry has developed rapidly in recent years and now allows measurements of subtle deformation of the Earth's surface with millimeter accuracy. All state-of-the-art processing methods require a precise coherence estimate. However, this estimate is a random variable and biased toward higher values. Up to now, little is published on the Bayesian estimation of the degree of coherence. The objective of the article is to develop empirical Bayesian estimators and to assess their characteristics by simulations. Bayesian estimation is understood as a regularization of the maximum likelihood estimation. The more information is used and the stricter the general prior, the more accurate the estimate will be. Three levels of prior information are developed: (1) an uninformative prior and an informative prior which can be implemented as (2a) less strict prior and (2b) strict prior. The informative priors are described by a single parameter only i.e., the maximum underlaying coherence. The article reports on the bias, the standard deviation and the root-mean-square error of the developed estimators. It was found that all empirical Bayes estimators improve the coherence estimation from small samples and for small underlaying coherences compared to the conventional sample estimator, e.g., a zero underlaying coherence is estimated by the expected <italic>a posteriori</italic> estimator without additional information with a 33.3% reduced bias using three samples only. Assuming the maximum underlaying coherence is 0.6, the bias is reduced by 51.3% for the strict prior and by 36.6% for the less strict prior. In addition, it was found that the methods work very well even for the extremely small sample size of only two values. |
| first_indexed | 2024-12-10T18:44:33Z |
| format | Article |
| id | doaj.art-62e34fa37ed04e43b82b681b52132ef1 |
| institution | Directory Open Access Journal |
| issn | 2151-1535 |
| language | English |
| last_indexed | 2024-12-10T18:44:33Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| spelling | doaj.art-62e34fa37ed04e43b82b681b52132ef12022-12-22T01:37:32ZengIEEEIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing2151-15352022-01-01156306632310.1109/JSTARS.2022.31928949835014Empirical Bayesian Estimation of the Interferometric SAR Coherence MagnitudeNico Adam0https://orcid.org/0000-0002-6053-0105German Aerospace Center (DLR), Wessling, GermanySAR interferometry has developed rapidly in recent years and now allows measurements of subtle deformation of the Earth's surface with millimeter accuracy. All state-of-the-art processing methods require a precise coherence estimate. However, this estimate is a random variable and biased toward higher values. Up to now, little is published on the Bayesian estimation of the degree of coherence. The objective of the article is to develop empirical Bayesian estimators and to assess their characteristics by simulations. Bayesian estimation is understood as a regularization of the maximum likelihood estimation. The more information is used and the stricter the general prior, the more accurate the estimate will be. Three levels of prior information are developed: (1) an uninformative prior and an informative prior which can be implemented as (2a) less strict prior and (2b) strict prior. The informative priors are described by a single parameter only i.e., the maximum underlaying coherence. The article reports on the bias, the standard deviation and the root-mean-square error of the developed estimators. It was found that all empirical Bayes estimators improve the coherence estimation from small samples and for small underlaying coherences compared to the conventional sample estimator, e.g., a zero underlaying coherence is estimated by the expected <italic>a posteriori</italic> estimator without additional information with a 33.3% reduced bias using three samples only. Assuming the maximum underlaying coherence is 0.6, the bias is reduced by 51.3% for the strict prior and by 36.6% for the less strict prior. In addition, it was found that the methods work very well even for the extremely small sample size of only two values.https://ieeexplore.ieee.org/document/9835014/Bayesian inferencecoherence magnitudedegree of coherencedistributed scatterers in SqueeSAR or CESAR or phase linkingempirical Bayes methodExpected <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX">$a \, posteriori$</tex-math> </inline-formula> </named-content> (EAP) estimation |
| spellingShingle | Nico Adam Empirical Bayesian Estimation of the Interferometric SAR Coherence Magnitude IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Bayesian inference coherence magnitude degree of coherence distributed scatterers in SqueeSAR or CESAR or phase linking empirical Bayes method Expected <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX">$a \, posteriori$</tex-math> </inline-formula> </named-content> (EAP) estimation |
| title | Empirical Bayesian Estimation of the Interferometric SAR Coherence Magnitude |
| title_full | Empirical Bayesian Estimation of the Interferometric SAR Coherence Magnitude |
| title_fullStr | Empirical Bayesian Estimation of the Interferometric SAR Coherence Magnitude |
| title_full_unstemmed | Empirical Bayesian Estimation of the Interferometric SAR Coherence Magnitude |
| title_short | Empirical Bayesian Estimation of the Interferometric SAR Coherence Magnitude |
| title_sort | empirical bayesian estimation of the interferometric sar coherence magnitude |
| topic | Bayesian inference coherence magnitude degree of coherence distributed scatterers in SqueeSAR or CESAR or phase linking empirical Bayes method Expected <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX">$a \, posteriori$</tex-math> </inline-formula> </named-content> (EAP) estimation |
| url | https://ieeexplore.ieee.org/document/9835014/ |
| work_keys_str_mv | AT nicoadam empiricalbayesianestimationoftheinterferometricsarcoherencemagnitude |