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Synthetic aperture radar tomography (TomoSAR) is a useful tool for retrieving the three-dimensional structure of buildings in urban areas, especially for datasets with a high spatial resolution. However, among the previous TomoSAR estimators, some cannot retrieve the 3-D structure of objects with a high elevation resolution, some cannot maintain the spatial resolution, and some require the selection of a hyperparameter. To overcome these limitations, this paper proposes a new nonparametric iterative adaptive approach with a model selection tool based on the Bayesian information criterion (IAA-BIC) for the application of TomoSAR in urban areas. IAA-BIC employs weighted least squares to acquire a high elevation resolution and works well for both distributed and coherent scatterers, even with single-look. Concurrently, IAA-BIC does not require the user to make any difficult selection regarding a hyperparameter. The proposed IAA-BIC estimator was tested in simulated experiments, and the results confirmed the advantages of the IAA-BIC estimator. Moreover, the three-dimensional structure of the Hubei Science and Technology Venture building in Wuhan, China, was retrieved through the IAA-BIC method with nine very high spatial resolution TerraSAR-X images. The height estimation accuracy for this building was about 1% and 4% relative to its real height for single-look and multi-look, respectively. In addition, a comparison between the IAA-BIC estimator and some of the typical existing TomoSAR estimators (Capon, MUSIC, and compressed sensing (CS)) was also carried out. The results indicate that the IAA-BIC estimator obtains a better resolution for coherent sources than Capon and MUSIC; notably, the IAA-BIC estimator obtains a similar performance to CS, but in less computation time.

Synthetic aperture radar tomography (TomoSAR) is a useful tool for retrieving the three-dimensional structure of buildings in urban areas, especially for datasets with a high spatial resolution. However, among the previous TomoSAR estimators, some cannot retrieve the 3-D structure of objects with a high elevation resolution, some cannot maintain the spatial resolution, and some require the selection of a hyperparameter. To overcome these limitations, this paper proposes a new nonparametric iterative adaptive approach with a model selection tool based on the Bayesian information criterion (IAA-BIC) for the application of TomoSAR in urban areas. IAA-BIC employs weighted least squares to acquire a high elevation resolution and works well for both distributed and coherent scatterers, even with single-look. Concurrently, IAA-BIC does not require the user to make any difficult selection regarding a hyperparameter. The proposed IAA-BIC estimator was tested in simulated experiments, and the results confirmed the advantages of the IAA-BIC estimator. Moreover, the three-dimensional structure of the Hubei Science and Technology Venture building in Wuhan, China, was retrieved through the IAA-BIC method with nine very high spatial resolution TerraSAR-X images. The height estimation accuracy for this building was about 1% and 4% relative to its real height for single-look and multi-look, respectively. In addition, a comparison between the IAA-BIC estimator and some of the typical existing TomoSAR estimators (Capon, MUSIC, and compressed sensing (CS)) was also carried out. The results indicate that the IAA-BIC estimator obtains a better resolution for coherent sources than Capon and MUSIC; notably, the IAA-BIC estimator obtains a similar performance to CS, but in less computation time. [ABSTRACT FROM AUTHOR]