Discriminative coefficient analysis-based collaborative representation with enhanced Background-Anomaly separation for hyperspectral anomaly detection

Various anomaly detection (AD) methods focus on the background feature extraction and suppression from hyperspectral images (HSIs). However, this process is susceptible to anomaly signals. As a typical example, the collaborative representation (CR) model incorporates contextual information into a linear approximation of the central pixel, but suffers severely from anomaly contamination from the local neighborhood. How to remove potential anomalies in the complete lack of prior knowledge is a crucial problem, yet there is currently no reliable solution due to the limited background-anomaly separation in the original HSI space. In this paper, inspired by the unique coefficient distribution in the coefficient domain, a discriminative coefficient analysis (DCA)-based collaborative representation method is proposed for hyperspectral AD. By projecting the HSI into a local coefficient domain relative to the central pixel, an interesting observation occurs that the coefficients of dominant background atoms exhibit a smooth and stable distribution pattern, while those of few anomalous atoms deviate significantly from the mainstream. Accordingly, by designing a pair of background coefficient boundaries, neighboring atoms with coefficient lying outside are considered suspicious anomalies and thus removed. The remaining atoms, corresponding to one homogeneous or few categories of local background materials, finally contribute to accurate anomaly judgment on the central pixel. Different from existing studies, the main contribution lies in the novel perspective of discriminative coefficient domain with enhanced background-anomaly separation. Experiments on one synthetic and five real-world HSI data sets demonstrate the effectiveness of the proposed method.