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Anomaly detection (AD), which aims to distinguish targets with significant spectral differences from the background, has become an important topic in hyperspectral imagery (HSI) processing. In this paper, a novel anomaly detection algorithm via dictionary construction-based low-rank representation (LRR) and adaptive weighting is proposed. This algorithm has three main advantages. First, based on the consistency with AD problem, the LRR is employed to mine the lowest-rank representation of hyperspectral data by imposing a low-rank constraint on the representation coefficients. Sparse component contains most of the anomaly information and can be used for anomaly detection. Second, to better separate the sparse anomalies from the background component, a background dictionary construction strategy based on the usage frequency of the dictionary atoms for HSI reconstruction is proposed. The constructed dictionary excludes possible anomalies and contains all background categories, thus spanning a more reasonable background space. Finally, to further enhance the response difference between the background pixels and anomalies, the response output obtained by LRR is multiplied by an adaptive weighting matrix. Therefore, the anomaly pixels are more easily distinguished from the background. Experiments on synthetic and real-world hyperspectral datasets demonstrate the superiority of our proposed method over other AD detectors.

Sparse representation-based methods, as an important branch of anomaly detection (AD) technologies for hyperspectral imagery (HSI), have attracted extensive attention. How to construct an overcomplete background dictionary containing all background categories and excluding anomaly signatures is the focus. Traditional background dictionary construction methods first convert HSI into a two-dimensional matrix composed of independent spectral vectors, and then execute the subsequent construction operations. In this way, only spectral anomalies can be excluded from the background dictionary, whereas spatial anomalies still exist. To alleviate this problem, this paper proposes a novel AD algorithm through sparse representation with tensor decomposition-based dictionary construction and adaptive weighting. It has three main advantages. First, tensor representation allows the spectral and spatial characteristics of HSI to be preserved simultaneously, and Tucker decomposition achieves excellent separation between the background part and anomaly part by distinguishing them along three modes. Second, the K-means++ clustering operation is implemented on the background part so that the background dictionary used for sparse representation contains all background categories. Finally, an adaptive weighting matrix derived from the anomaly part further improves the distinction between background pixels and anomalies. Experiments on synthetic and real HSI datasets demonstrate the superiority of our proposed algorithm.