Hyperspectral Anomaly Detection through Sparse Representation with Tensor Decomposition-based Dictionary Construction and Adaptive Weighting

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.