Test Statistics for Reflection Symmetry: Applications to Quad-Polarimetric SAR Data for Detection of Man-Made Structures

In polarimetric synthetic aperture radar (SAR) images, speckle is removed by multilooking and the local covariance matrix is the main parameter of interest. In the covariance matrix from a backscatter with reflection symmetry, the terms
${\langle \boldsymbol{S}_{hh}\boldsymbol{S}_{hv}^*\rangle }$
,
${\langle \boldsymbol{S}_{vv}\boldsymbol{S}_{hv}^*\rangle }$
, and their complex conjugates are 0. The backscatter from natural covers, such as fields and forested areas, is typically reflection-symmetric, as these four elements have near-zero values. The backscatter from urban areas and man-made structures is substantially different, and the backscatter from buildings not aligned with the radar line of sight usually does not have reflection symmetry. A novel block-diagonality test statistic for reflection symmetry with a constant false alarm rate property is proposed. It is compared to an approximate test built on a change detection test statistic for Wishart-distributed covariance matrices. Their use on quad-polarimetric data in different situations shows their high potential for man-made structure detection. Applied after an orientation correction of the covariance matrices, these test statistics highlight with high-contrast buildings and urban areas. We also apply this test for ship detection at sea, and show that while the results are unconvincing at X-band, it can also be applied at longer wavelengths such as L-band.