Theoretical Analysis of a Symmetric Two-Stage Change Detector for SAR Images

Abstract

A procedure is developed to generate theoretical receiver operating characteristic (ROC) curves for the two-stage change detector proposed by Cha <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , in order to compare its detection performance with other detectors. A modification, however, to the first stage of the two-stage detector is proposed, which introduces a symmetry that significantly simplifies analysis. The probability density function (pdf) for this symmetric two-stage detector is derived, and using this pdf, an approach for determining thresholds is proposed. The symmetric two-stage detector introduces a new parameter that effectively weights each statistic making up its two individual stages. Detection performance is explored versus this new parameter. The two-stage detector is shown to yield overall better detection performance than the sample variance ratio, Berger’s alternative coherence estimator, and the classical coherence estimator. When applied to real synthetic aperture radar (SAR) data, the two-stage detector and Berger’s estimator yield binary change images with more easily visible areas of change. Finally, we derive an expression for the pdf of the optimal log-likelihood ratio statistic that is simpler than that given by Preiss <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i>