Regularized Tensor Representative Coefficient Model for Hyperspectral Target Detection

Target detection based on hyperspectral image (HSI) representations has drawn wide attention given its wide variety of features. The matrix-based approach inevitably loses spatial information and fails to explore the intrinsic multimodal structure of an HSI cube. In this letter, we propose a regularized tensor-based model without altering the data structure. We assume that an observed third-order HSI tensor is decomposed into the sum of a total variation (TV)-regularized low-rank background tensor and a sparse (TVLrS) target tensor. The two tensors are represented as the mode-3 product of a third-order tensor, called the tensor representation coefficient (TRC), and a spectra dictionary matrix. Then, the model is coined as TVLrS-TRC. The background TRC has a low-rank property, contributing to the low-rankness characterization in our model. Moreover, as the size of the background TRC term is smaller than the background tensor, characterizing its local smoothness via TV regularization reduces the computational cost compared with that of the background tensor. Extensive experiments on two real hyperspectral datasets demonstrate the advantage of the proposed method compared with the state of the art.