A Tensor-Based Hyperspectral Anomaly Detection Method Under Prior Physical Constraints

Efficient and precise modeling of the background to accurately identify anomalies is the cornerstone to hyperspectral anomaly detection. Hyperspectral image (HSI) can be regarded as 3-D cube data, which contains both spatial and spectral information. The data are converted into 2-D matrices for processing in most existing method, which loses a large amount of structural information. In addition, it is difficult to construct a model with strong representation ability without enough prior knowledge constraints, and the modeling of the background is easily polluted by anomalies. This article introduces a tensor-based hyperspectral anomaly detection method that takes into account prior physical constraints as a solution to the aforementioned problems. The proposed method uses a tensor representation of the image, which preserves its geometrical properties and adheres to fundamental physical principles. After separating them from the image tensor, the background and anomaly tensors are treated separately. For the background tensor, we introduce segmented smoothness constraints in both spatial and spectral dimensions by applying linear total variation (TV) norm regularization. This can improve resistance to complicated backgrounds and lessen the introduction of extra noise when the background is restored. A low-rank constraint based on image eigenvalues is intended to generate a more realistic background model in its spatial dimension, making the method more sensitive to tiny anomalies. For the anomaly tensor, there is sparsity in its spectral dimension, and the background is effectively separated from the anomaly by l(1) -norm constraints. Eventually, the anomaly detection map is decided by the anomaly tensor computed iteratively. Comprehensive experiments on several genuine and simulated datasets show that the proposed method performs significantly better at anomaly detection than the state-of-the-art methods.