Hyperspectral Anomaly Detection Based on Tensor Truncated Nuclear Norm and Linear Total Variation Regularization.

Hyperspectral image (HSI) anomaly detection aims to separate abnormal targets and background, traditional HSI processing approaches are based on the matrixes and vectors. However, the spatial-spectral structure is destroyed in this way. In contrast with matrix-based methods, HSI, owing to its own structural characteristics, can use third-order tensor to describe its spatial-spectrum features more accurately. In this paper, we proposed a novel method based on tensor truncated nuclear norm and linear total variation regularization, and achieved outstanding result. Specifically, the background part is expressed linearly with the elements in the dictionary matrix, and the representation coefficients are stored in a tensor, which has low-dimensional structure and constrained by tensor truncated nuclear norm. As truncated nuclear norm removed the influence of smaller singular values of background tensor, the robustness of the model has been enhanced. What’s more, linear total variation regularization (LTV) is adopted to exploit the smooth prior knowledge of the background tensor and a specific norm regularization is used to constrain the sparse property of the anomaly tensor in our model. Finally, extensive experiments demonstrate that proposed method and optimal algorithm are both effective.