Hyperspectral Anomaly Detection Based on Tensor Ring Decomposition With Factors TV Regularization

Abstract

Anomaly detection in the hyperspectral image (HSI) has gradually become a hot topic in remote sensing. Recently, some tensor-based methods have been proposed to improve detection performance by exploiting the characteristic of HSI data existing in the inherent multi-dimensional. However, the existing tensor-based methods may only partially use the prior properties in both spatial and spectral dimensions. In this paper, we proposed a novel tensor ring (TR) decomposition with factors TV regularization model for hyperspectral anomaly detection. First, raw HSI data is decomposed into background and anomaly tensors. The tensor ring decomposition is adopted to exploit the low-rank property of the background existing in both spatial and spectral dimensions. Then, the total variation (TV) regularization is designed on the three dimensions of the background tensor to explore the piecewise smoothness of the background existing in both spatial and spectral dimensions. Further, this TV regularization is transferred to each factor tensor by exploiting the relationship between the background tensor and each factor tensor. Next, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> norm regularization is designed on the anomaly tensor to exploit the group sparsity of anomaly pixels. Finally, the alternating direction method of multipliers (ADMM) scheme is adopted to update the involved variables. Experimental results validated on several real hyperspectral datasets demonstrate the effectiveness of the proposed algorithm.