Effective Anomaly Space for Hyperspectral Anomaly Detection

Due to unavailability of prior knowledge about anomalies, background suppression (BS) is a crucial factor in anomaly detection (AD) evaluation. The difficulty in dealing with BS arises from the fact that anomalies are generally sandwiched between background (BKG) and noise. This article presents a new concept, called effective anomaly space (EAS), to resolve this dilemma. To accomplish this goal, the well-known independent component analysis (ICA) is used to address between BKG and anomalies issue by removing the first two orders of data statistics (2OS), while sparsity cardinality (SC) is used to address between anomalies and noise issue by removing non-Gaussian noises and interferers from anomalies. Specifically, SC is rederived as fixed SC (FSC) corresponding to fixed length coding for a spectral vector and a spatial band and variable SC (VSC) for a corresponding to variable length coding for a spectral–spatial sample and spatial–spectral band from an information theory point of view. Combining ICA and the new derived SC versions allows EAS not only to remove BKG-characterized by 2OS including Gaussian-distributed signal sources but also to remove non-Gaussian noises/interferers from anomalies. As a consequence, EAS can significantly increase anomaly detectability. In particular, one of great benefits resulting from EAS is that EAS can also improve current low-rank and sparse representation (LRaSR)-based methods used for AD.

I. Introduction

One of the fundamental tasks in hyperspectral imaging is anomaly detection (AD) because anomalies cannot be known priori but provide crucial and vital information for image analysis [1]–[5]. It is very challenging in the sense that anomalies generally possess the following unique properties. First, anomalies usually cannot be identified by visual inspection or prior knowledge. Second, the presence of anomalies is unexpected. Third, the probability of occurrence of anomalies is relatively low. Fourth, once anomalies occur, their populations cannot be too many. Most importantly, due to the nature of anomalies, the number of anomalies present in the data will be very limited, in which case anomalies cannot constitute Gaussian distributions by statistics.