Hyperspectral Anomaly Detection Based on Regularized Tensor Decomposition

International audienceThe tensor-based anomaly detection (AD) model has attracted increasing interest in the hyperspectral image (HSI) community. Since it is powerful in maintaining spatial and spectral structures, an HSI is essentially a third-order tensor. In this article, we propose a novel AD method based on a lowrank background linear mixing model of the scene background. The obtained abundance maps possess more distinctive features than the raw data, which is beneficial for identifying an anomaly from the background. Specifically, the low-rank tensor background is approximated as the mode-3 product of an abundance tensor and endmember matrix. Due to the spatial sparse and smooth natures of abundance maps, the ℓ 1-norm is introduced to enforce sparseness, and the total variation (TV) regularizer is adopted to encourage spatial smoothness. Moreover, the typical great correlation among abundance vectors implies the low-rank structure of abundance maps. Compared with the rigorous lowrank constraint, a soft low-rank regularization is imposed on the background in order to leverage its spatial homogeneity. Its strictness is controlled by scalar parameters. For the anomaly part, the anomaly spectra account for a small part of the whole scene, and therefore, an ℓ 1,1,2-norm is defined to characterize its tube-wise sparsity. Notably, Gaussian noise is integrated into the model to suppress confusion with the anomaly. The experimental results on five real datasets demonstrate the outstanding performance of our proposed method