A Tensor-Based Go Decomposition Method for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection (HAD) aims at effectively separating the anomaly target from the background. The low-rank and sparse matrix decomposition (LRaSMD) technique has shown great potential in HAD tasks. However, some LRaSMD models need to convert the hyperspectral data into a two-dimensional matrix. This cannot well maintain the characteristics of the hyperspectral image (his) in each dimension, thus degenerating its representation capacity. In this context, this article proposes a tensor-based Go decomposition (GODEC) model, called TGODEC. The TGODEC model supports the idea of GODEC, representing the HSI data as a combination of background tensor, anomaly tensor, and noise tensor. In detail, the background tensor is solved by the tensor singular value hard thresholding decomposition. The anomaly tensor is solved by a mapping matrix using the corresponding sparse cardinality. Interestingly, the obtained background and anomaly tensors can also be developed for HAD, thus a TGODEC-based anomaly detector is established, called TGODEC-AD. Specifically, the TGODEC-AD method combines the typical RX-AD and R-AD with the above decomposition result of the TGODEC model and constructs different modal operator detectors. Experimental results on multiple real hyperspectral datasets verify the effectiveness of the TGODEC and TGODEC-AD methods. It means that the proposed TGODEC model can effectively characterize the spatial structural features of HSI. As a result, the pure decomposed components can be obtained, contributing to detecting the anomaly target and suppressing the background better in HAD tasks.