Joint Reconstruction and Anomaly Detection From Compressive Hyperspectral Images Using Mahalanobis Distance-Regularized Tensor RPCA

Anomaly detection plays an important role in remotely sensed hyperspectral image (HSI) processing. Recently, compressive sensing technology has been widely used in hyperspectral imaging. However, the reconstruction from compressive HSI and detection are commonly completed independently, which will reduce the processing's efficiency and accuracy. In this paper, we propose a framework for hyperspectral compressive sensing with anomaly detection which reconstruct the HSI and detect the anomalies simultaneously. In the proposed method, the HSI is composed of the background and anomaly parts in the tensor robust principal component analysis model. To characterize the low-dimensional structure of the background, a novel tensor nuclear norm is used to constrain the background tensor. As the anomaly part is formed by a few anomalous spectra, the anomaly part is assumed to be a tuber-wise sparse tensor. In addition, to enhance the separation of the background and anomaly, we minimize the sum of Mahalanobis distance of the background pixels. Experiments on four HSIs demonstrate that the proposed method outperforms several state-of-the-art methods on both reconstruction and anomaly detection accuracies.