Low rank and collaborative representation for hyperspectral anomaly detection via robust dictionary construction

Hyperspectral anomaly detection methods based on representation model have attracted much attention in recent years. In the method, a background dictionary is used to represent each pixel linearly, and the residual is taken as the abnormal level of the pixel. Therefore, building a functional model with strong representation ability and a matching background dictionary is an important factor for success of the method. In the existing methods, the lack of feature utilization, the contamination of background dictionary and the dependence on prior knowledge lead to the instability of anomaly detection results, which are difficult to be applied in practice. To address the issues, this paper proposed a novel hyperspectral anomaly detection method which consists of two interconnected components: a new anomaly detection function model through the combination of LRR and CR, and the supporting background dictionary which does not need prior knowledge. The new anomaly detection model decomposed a two-dimensional normalized hyperspectral image into background and anomaly components, and reconstructed the background through a background dictionary and the corresponding coefficient matrix. The representation coefficient matrix was constrained by global low-rank and local collaborative attributes which helps background modeling. A distance weight matrix was also included to enhance the dense representation of background dictionary atoms which are similar to the testing pixel. The anomaly part was constrained by column sparsity simultaneously due to the global sparsity of anomalous targets in hyperspectral images. To further clarify the physical meaning of the model, another version that imposes non-negative and sum-to-one constraints on coefficient matrix was also proposed. The supporting background dictionary was designed for practical and reliable purposes and was implemented by dual mean shift clustering which automatically estimates parameter without prior-knowledge. The experimental results show that the proposed method can effectively improve the result of anomaly detection, and has the best ROC, AUC, and separation degree between background and anomalies for four real datasets. The average AUC of four datasets of the proposed algorithm is 2.6% higher than the method based on CR and 3.2% higher than the method based on LRR. Moreover, the proposed algorithm has stability and reliability under complex background, as well as the application on a larger hyperspectral scene shows that it offers great potential in practical use.