A Test Statistic for Block-Diagonal Covariance Matrix Structure in polSAR Data

We report on a complex Wishart distribution-based test statistic $\boldsymbol {Q}$ for block-diagonality in Hermitian matrices such as the ones analyzed in polarimetric synthetic aperture radar (polSAR) image data in the covariance matrix formulation. We also give an improved probability measure $\boldsymbol {P}$ associated with the test statistic. This is used in a case with simulated data to demonstrate the superiority of the new expression for $\boldsymbol {P}$ and to illustrate the dependence of results on the choice of covariance matrix, its dimensionality, the equivalent number of looks, and two parameters in the improved $\boldsymbol {P}$ measure. We also give two cases with acquired data. One case is with airborne F-SAR polarimetric data, where we test for reflection symmetry, another case is with (spaceborne) dual-pol Sentinel-1 data, where we test if the data are diagonal-only. The absence of block-diagonal structure occurs mostly for man-made objects. In the example with Sentinel-1 data, some objects (e.g., buildings, cars, aircraft, and ships) are detected, others (e.g., some bridges) are not.