Anomaly Detection in Satellite-Borne Push-Broom Hyperspectral Imagery Based on Joint Low-Rank Tensor Approximation

Hyperspectral anomaly detection aims to detect potential targets of interest in hyperspectral images (HSIs). In this article, we propose a joint low-rank tensor approximation-based anomaly detection method that incorporates the distinct physical characteristics of satellite-borne push-broom HSIs. In our method, an HSI is decomposed into a background tensor and an anomaly tensor. For the background tensor, the spatial correlations between pixels give it a low-rank characteristic in frontal slices, while the spectral correlations among adjacent bands and similar ground materials give it low-rank properties in horizontal slices. Therefore, in order to simultaneously and flexibly exploit the correlations in both the spatial and spectral dimensions of the background tensor, we design a joint low-rank constraint term of the background tensor, using the weighted tensor nuclear norm based on tensor singular value decomposition (t-SVD), which applies to both the background tensor and its permutation tensor. In addition, considering the homogeneity of adjacent pixels in the background, which results in spatial piecewise smoothness of the background tensor, we incorporate a linear total variation norm regularization term to more accurately characterize the background tensor. For the anomaly tensor, an <inline-formula> <tex-math notation="LaTeX">$ \boldsymbol {l}_{ \boldsymbol {1,1,2}}$ </tex-math></inline-formula>-norm regularization term is employed to characterize its tubewise sparsity. We incorporate all regularization terms and a fidelity term into a nonconvex framework and solve it using the alternating direction method of multipliers. The experimental results using real HSIs from the GaoFen-5 and ZiYuan1–02D satellites demonstrated that the proposed method outperforms seven comparison methods.