Hyperspectral Anomaly Detection With Total Variation Regularized Low Rank Tensor Decomposition and Collaborative Representation
Shou Feng, Dan Wu, Rui Feng, Chunhui Zhao
Abstract
Nowadays, many anomaly detection (AD) methods still have shortcomings in using the spatial information of hyperspectral images (HSIs), which leads to the inability to separate the background and anomalies well. In this letter, a hyperspectral AD (HAD) approach with total variation regularized low-rank tensor decomposition and collaborative representation (LRTDCRD) is proposed. First, the total variation regularized low-rank tensor decomposition (LRTD) model is adopted to separate an HSI into the background data part and the mixed information part. By virtue of exploiting the global and the piecewise smooth structure of an HSI, the low-rank background data obtained by the LRTD model can be very pure. Then, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l_{2},_{1}}$ </tex-math></inline-formula> norm followed by the domain transform recursive filter (DTRF) is built to detect anomalies from the mixed information part. Finally, the collaborative representation-based detector (CRD) is used to extract anomalous information embedding in the low-rank data part. As the low-rank component still contains the information of some anomalies after LRTD, this procedure can be used as a support and supplement for the final detection. Using CRD to detect anomalies in low-rank data can not only ensure the stability of the whole algorithm, but also detect anomalies in low-rank data. The final detection map can be obtained by fusing the initial results of the low-rank data and the mixed information parts. Experimental results on three datasets express that the proposed LRTDCRD exceeds eight state-of-the-art anomaly methods used for comparison.