Invariant rules for multi-polarization SAR change detection

This paper deals with coherent (in the sense that both amplitudes and relative phases of the polarimetric returns are used to construct the decision statistic), multi-polarization SAR change detection assuming the availability of reference and test images collected from N multiple polarimetric channels. At the design stage, the change detection problem is formulated as a binary hypothesis testing problem and the principle of invariance is used to come up with decision rules sharing the Constant False Alarm Rate (CFAR) property. The maximal invariant statistic and the maximal invariant in the parameter space are obtained. Hence, the optimum invariant test is devised proving that a Uniformly Most Powerful Invariant (UMPI) detector does not exist. Based on this, the class of sub-optimum invariant receivers, which also includes the Generalized Likelihood Ratio Test (GLRT), is considered. At the analysis stage, the performance of some tests, belonging to the aforementioned class, is assessed and compared with the optimum clairvoyant invariant detector. Finally, detection maps on real high resolution SAR data are computed showing the effectiveness of the considered invariant decision structures.