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Relaxed Collaborative Representation With Low-Rank and Sparse Matrix Decomposition for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection methods based on representation model have drawn more attention due to their simplicity and efficiency. The traditional collaborative representation (CR) model does not consider the differences between features, resulting in insufficient feature utilization. In addition, the dictionary construction of traditional CR model is from a dual window, where the dictionary is easy to be polluted by abnormal pixels. To address the abovementioned issues, this article proposes a novel relaxed collaborative representation relaxed collaborative representation (RCR) method with low-rank and sparse matrix decomposition. In the proposed approach, a relaxed regularization constraint term is imposed on the CR model, which takes into account the difference and similarity between features. In order to reduce the interference of redundant information in hyperspectral data on detection accuracy, the optimal clustering framework optimal clustering framework (OCF) is used for band selection. In terms of dictionary construction, the data with reduced dimensionality is preprocessed by low-rank and sparse matrix decomposition (LRaSMD) to realize the preliminary separation of anomalies and background. Then, the background component obtained by LRaSMD is partitioned into several categories by the improved k-means + + algorithm. Moreover, in order to enhance the contribution of useful information to the representation, according to the distance from the cluster center, logarithmic weighting is introduced to give larger weights to the atoms closer to the cluster center, so to select typical atoms to construct the dictionary. Experimental results reveal that the proposed method can attain better detection results than the existing advanced anomaly detection methods.