Theoretical Receiver Operating Characteristics of Two-Stage Change Detector for Synthetic Aperture Radar Images

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.