Low-rank and sparse tensor recovery for hyperspectral anomaly detection

Anomaly is generally defined as an object that strays away from the background clutter. As for hyperspectral anomaly detection, most of the previous methods fail to fully take advantage of the knowledge in both spatial and spectral domain. In this paper, we propose a novel method based on tensor recovery in which spatial structures and spectral characters are reasonably considered to separate the hypercube into a low-rank background and sparse anomalies. Since background is highly consistent not only in spectral domain, but also in spatial domain, we impose low-rank constraints on three unfolding matrix of the hypercube respectively to capture the global structure together. To better describe the local irregularities with low probability, a general l₁ norm constraint and an extra sparse regularization are imposed on pixels in the spectral mode alone, for that we consider each spectrum as an entirety. Extensive experiments on two real datasets show outstanding anomaly detection performance of the proposed method in comparison with the state-of-the-art methods.