On the Reality of the Coherence Matrix in SAR Interferometry

Abstract:
We argue that the hypothesis of “phase consistency” for a set of N SAR images can be checked by studying the coherence matrix associated with a distributed scatterer. We show that phase consistency is just a consequence of having a coherence matrix similar (in algebraic sense) to a real matrix and where the unknown variations of the optical paths between the different SAR acquisitions correspond to a phase modulation of a complex gaussian process characterized by a real covariance matrix. The problem of testing an InSAR dataset for phase consistency can then be cast as testing the reality of a covariance matrix. The analysis can shed new light also on how to reduce the bias in the estimation of coherence values.