Interferometric SAR Coherence Magnitude Estimation by Machine Learning

Abstract

Current interferometric wide area ground motion services require the estimation of the coherence magnitude as accurately and computationally effectively as possible. However, a precise and at the same time computationally efficient method is missing. Therefore, the objective of this article is to improve the empirical Bayesian coherence magnitude estimation in terms of accuracy and computational cost. Precisely, this article proposes the interferometric coherence magnitude estimation by Machine Learning (ML). It results in a non-parametric and automated statistical inference. However, applying ML in this estimation context is not straightforward. The number and the domain of possible input processes is infinite and it is not possible to train all possible input signals. It is shown that the expected channel amplitudes and the expected interferometric phase cause redundancies in the input signals allowing to solve this issue. Similar to the empirical Bayesian methods, a single parameter for the maximum underlaying coherence is used to model the prior. However, no prior or any shape of prior probability is easy to implement within the ML framework. The article reports on the bias, the standard deviation and the root mean square error (RMSE) of the developed estimators. It was found that ML estimators improve the coherence estimation RMSE from small samples ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2 N &lt; 30$</tex-math></inline-formula> ) and for small underlaying coherence compared to the conventional and empirical Bayes estimators. For three interferometric samples ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N = 3$</tex-math></inline-formula> ) and a zero coherence magnitude, the bias related to the sample estimator improves from 0.53 to 0.39 by 27.8%. Assuming the maximum underlaying coherence is 0.6, the bias is reduced by 33.0% to 0.36 for the less strict and by 45.5% to 0.29 for the strict prior. The developed ML coherence magnitude estimators are suitable and recommended for operational InSAR systems. For the estimation, the ML model is extremely fast evaluated because no iteration, numeric integration or Bootstrapping is needed.