On Semiparametric Clutter Estimation for Ship Detection in Synthetic Aperture Radar Images

The statistical behavior of the sea clutter in synthetic aperture radar (SAR) images is characterized by both the marginal distribution and spatial correlation. However, simultaneous modeling of the joint information remains a difficult job because of the non-Gaussian clutter nature. In this paper, a semiparametric approach is proposed for addressing this problem with the two-fold purpose. First, we investigate the applicability of the nonparametric kernel density estimator (KDE) for marginal distribution estimation of the SAR clutter and show that the KDE is most applicable in the log-intensity domain. Second, we propose to separately estimate the underlying correlation structure with a copula approach and show that the Gaussian copula is a sufficiently accurate model. Consequently, the KDE together with the Gaussian copula, offers a full characterization of the joint probability distribution, based on which a quadratic detector of null distribution is governed by the well-known chi-square law can be conveniently designed for constant false alarm rate (CFAR) detection. In the experiment, results with both simulated and real SAR data demonstrate that, compared with the single-point detector using only the marginal distribution, the proposed method, which incorporates spatial correlation, significantly improves the detection performance with regard to either the receiver operating characteristic (ROC) curve or detected target pixels. The tradeoff, however, lies in a loss of false alarm rate (FAR) control resulting from increased uncertainty in estimating higher dimensional distributions.