Low-rank tensor decomposition based anomaly detection for hyperspectral imagery

Anomaly detection becomes increasingly important in hyper-spectral image analysis, since it can now uncover many material substances which were previously unresolved by multi-spectral sensors. In this paper, we propose a Low-rank Tensor Decomposition based anomaly Detection (LTDD) algorithm for Hyperspectral Imagery. The HSI data cube is first modeled as a dense low-rank tensor plus a sparse tensor. Based on the obtained low-rank tensor, LTDD further decomposes the low-rank tensor using Tucker decomposition to extract the core tensor which is treated as the “support” of the anomaly spectral signatures. LTDD then adopts an unmixing approach to the reconstructed core tensor for anomaly detection. The experiments based on both simulated and real hyperspectral data sets verify the effectiveness of our algorithm.