Deep Low-Rank and Piecewise-Smooth Constraint Tensor Model for Hyperspectral Anomaly Detection

Low-rank tensor decomposition and autoencoder (AE) have recently attracted much attention in the hyperspectral anomaly detection field. Although the low-rank tensor decomposition model is self-explainable, a low-rank prior may only partially match real data. In contrast, AE can automatically learn the discriminative features between anomaly and background, whereas AE is not self-explainable. To overcome these problems, a deep low-rank and piecewise-smooth constraint tensor model is proposed for hyperspectral anomaly detection in this paper, which makes full use of the low-rank and piecewise-smooth properties of the background tensor in model-driven tensor-based methods and combines the advantage of data-driven AE methods at the same time. Specifically, the background is reconstructed through the AE network, and the tensor nuclear norm and total variation regularization are designed on the network output to make it self-explainable to exploit the low-rank and piecewise-smooth properties of the background in the three dimensions. At the same time, an alternating direction method of multipliers (ADMM) based approach is given to solve the proposed model, making the low-rank and piecewise-smooth background tensor estimation process and the network training process into two sub-problems. Then, the background can be approximately reconstructed under the constraint of latent priors, while the anomaly is reconstructed with significant reconstruction errors. Finally, the reconstruction errors indicate the anomalous degree. Experimental results validated on several real hyperspectral datasets demonstrate the effectiveness of the proposed algorithm.