Detecting areas of change between two synthetic aperture radar (SAR) images of the same scene, taken at different times is generally performed using two approaches. Non-coherent change detection is performed using the sample variance ratio detector, and displays a good performance in detecting areas of significant changes. Coherent change detection can be implemented using the classical coherence estimator, which does better at detecting subtle changes, like vehicle tracks. A two-stage detector was proposed by Cha et al., where the sample variance ratio forms the first stage, and the second stage comprises of Berger's alternative coherence estimator.

A modification to the first stage of the two-stage detector is proposed in this study, which significantly simplifies the analysis of the this detector. Cha et al. have used a heuristic approach to determine the thresholds for this two-stage detector. In this study, the probability density function for the modified two-stage detector is derived, and using this probability density function, an approach for determining the thresholds for this two-dimensional detection problem has been proposed. The proposed method of threshold selection reveals an interesting behavior shown by the two-stage detector. With the help of theoretical receiver operating characteristic analysis, it is shown that the two-stage detector gives a better detection performance as compared to the other three detectors. However, the Berger's estimator proves to be a simpler alternative, since it gives only a slightly poorer performance as compared to the two-stage detector. All the four detectors have also been implemented on a SAR data set, and it is shown that the two-stage detector and the Berger's estimator generate images where the areas showing change are easily visible.