A sparse and spectral smooth regularized low-rank tensor decomposition method for hyperspectral target detection

In recent years, hyperspectral target detection methods have been widely used in military or civilian fields. Many high-performance hyperspectral target detection methods have been proposed, and tensor decomposition-based methods have attracted the attention of researchers. However, the non-uniqueness of tensor rank and the interference of noise will reduce the effect of target detection. In order to solve these problems, a sparse and spectral smooth regularized low-rank tensor decomposition method for hyperspectral target detection is proposed in this paper. The proposed method adds the low-rank regularization to the factor matrix of the tensor decomposition framework, which can reduce the adverse effect of information redundancy on the detection effect of the algorithm. Furthermore, the spectral smooth regularization is added to the spectral factor matrix to suppress noise and the sparse regularization is added to the core tensor to solve the problems of non-uniqueness of the Tucker tensor decomposition, which can improve the effect of target detection. On this basis, it simplifies the calculation process and reduces the complexity of the algorithm by using the conjugate gradient algorithm and the tensor Kronecker product. In this paper, the algorithm is tested on four real hyperspectral data sets and compared with six state-of-the-art algorithms. The experimental results show that targets detected by the proposed method are more obvious and the background is more pure.