Background Density Nonparametric Estimation With Data-Adaptive Bandwidths for the Detection of Anomalies in Multi-Hyperspectral Imagery

This letter presents a scheme for detecting global anomalies, in which a likelihood ratio test based decision rule is applied in conjunction with an automated data-driven estimation of the background probability density function (PDF). The latter is reliably estimated with a nonparametric variable-band width kernel density estimator (VKDE), without making any distributional assumption. With respect to conventional fixed bandwidth KDE (FKDE), which lacks adaptivity due to the use of a bandwidth that is fixed across the entire feature space, VKDE lets the bandwidths adaptively vary pixel by pixel, tailoring the amount of smoothing to the local data density. Two multispectral images are employed to explore the potential of VKDE background PDF estimation for detecting anomalies in a scene with respect to conventional nonadaptive FKDE.

I. Introduction

Several studies have shown the usefulness of exploiting the information extracted from multiple spectral bands when searching for targets and objects in a remotely sensed scene. Here, we are interested in detecting global anomalies, i.e., small rare objects that are anomalous with respect to the global background, embodied by most of image pixels. In doing so, no previous knowledge about the nature of anomalies is assumed other than that they are very sparsely and scarcely represented in the image [4], [8], and [13].