Improved SAR Coherence Magnitude Estimates in Scenarios with Low Coherence and Small Sample Size

Kurzfassung

Interferometric Synthetic Aperture Radar (SAR) (InSAR) is a well-established method for measuring the topography of the Earth and the displacements of its surface with millimeter accuracy. As this information is essential for infrastructure safety, there are numerous operational SAR missions, InSAR processing systems and InSAR-based monitoring services. The SAR coherence magnitude is an essential parameter in InSAR. It is directly related to the signal-to-noise ratio and is therefore synonymous with it. It is also used to characterize InSAR systems, as the statistics of the interferometric measurements are parameterized by the coherence magnitude. And more recently, with SqueeSAR and CAESAR, it became the fundamental weighting for analyzing long time series from observations of distributed scatterers (DSs). The latter application, in particular, requires accurate coherence estimation to minimize error propagation and provide an accurate measurement of ground motion. Estimators of the coherence magnitude, e.g., the sample estimator, are biased, and the smaller the coherence and the number of available samples, the more biased they are. The objective of this thesis is to develop new coherence magnitude estimators of jointly complex circular Gaussian (CCG) signals and to describe, characterize, and demonstrate the methods. In addition, Bayesian coherence priors are developed, which are applicable in everyday InSAR processing. Bayesian methods are well-established in statistical inference and estimation, and allow to include prior information. However, there are currently no publications on methods for coherence magnitude estimation using this principle. Therefore, an empirical Bayesian estimation is developed. Another technique that has not yet been studied for coherence magnitude estimation is machine learning (ML). Two estimators are developed for this principle, and they are adapted to support prior information. Using simulations, the estimators are characterized with respect to various sample sizes and the underlying true coherence by the corresponding bias, standard deviation, and root mean squared error (RMSE). Also, the respective performance is compared with the conventional sample estimator. Furthermore, the new methods are demonstrated on real Sentinel-1 data as a proof of concept. In this thesis, the use of prior knowledge on the coherence is demonstrated for the first time, and all developed estimators support prior information. The more information is used and the stricter the prior, the more accurate the coherence estimate will be. The developed estimators offer two main advantages compared to the conventional sample estimator. All improve the estimation of small coherences. And, they better estimate the coherence from small sample sizes. The empirical Bayesian estimator works advantageously up to 15 InSAR samples. The direct ML method is advantageous up to 30 samples, and the composite estimator was demonstrated to be advantageous for 200 InSAR samples. The performance and advantages are the reasons why the composite estimator is suitable and recommended for implementation in operational InSAR systems. It supports small and large sample sizes and has the best estimation performance compared to the other methods. An advantage worth emphasizing is its estimation performance even without prior. This makes the estimator universally applicable and comparable with the conventional sample estimator.