On the evaluation of second order phase statistics in SAR interferogram stacks

Document Type : Original Article


Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, the Netherlands


During the last decades, time-series interferometric synthetic aperture radar (InSAR) has been emerged as a powerful technique to measure various surface deformation phenomena of the earth. The multivariate statistics of interferometric phase stacks plays an important role in the performance of different InSAR methodologies and also in the final quality description of InSAR derived products. The multivariate phase statistics are ideally described by a joint probability distribution function (PDF) of interferometric phases, whose closed-form evaluation in a generic form is very complicated and is not found in the literature. Focusing on the first two statistical moments, the stack phase statistics can be effectively described by a full (co)variance matrix. Although a closed-form expression of interferometric phase variances has been derived in literature for single-looked pixels, there is no such an expression for neither the variances of the multilooked pixels nor the covariances among interferometric phases. This paper presents two different approaches for evaluation of the full covariance matrix: one based on the numerical Monte-Carlo integration and the other based on an analytical approximation using nonlinear error propagation. We first, clarify on the noise components that are the subject of statistical models of this paper. Then, the complex statistics in SAR stacks and the phase statistics in a single interferogram are reviewed, followed by the phase statistics in InSAR stacks in terms of second statistical moments. The Monte-Carlo approach and the derivation of an analytical closed-form evaluation of InSAR second-order phase statistics are then introduced in details. Finally, the two proposed methods are validated against each other.


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