Spatial Invariant Tensor Self-Representation Model for Hyperspectral Anomaly Detection

With the development of hyperspectral imaging technology, the hyperspectral anomaly has attracted considerable attention due to its significant role in many applications. Hyperspectral images (HSIs) with two spatial dimensions and one spectral dimension are intrinsically three-order tensors. However, most of the existing anomaly detectors were designed after converting the 3-D HSI data into a matrix, which destroys the multidimension structure. To solve this problem, in this article, we propose a spatial invariant tensor self-representation (SITSR) hyperspectral anomaly detection algorithm, which is derived based on the tensor-tensor product (t-product) to preserve the multidimension structure and achieve a comprehensive description of the global correlation of HSIs. Specifically, we exploit the t-product to integrate spectral information and spatial information, and the background image of each band is represented as the sum of the t-product of all bands and their corresponding coefficients. Considering the directionality of the t-product, we utilize two tensor self-representation methods with different spatial modes to obtain a more balanced and informative model. To depict the global correlation of the background, we merge the unfolding matrices of two representative coefficients and constrain them to lie in a low-dimensional subspace. Moreover, the group sparsity of anomaly is characterized by l_2.1.1 norm regularization to promote the separation of background and anomaly. Extensive experiments conducted on several real HSI datasets demonstrate the superiority of SITSR compared with state-of-the-art anomaly detectors.