Weighted Sparsity Constraint Tensor Factorization for Hyperspectral Unmixing

Recently, the unmixing methods based on non-negative tensor factorization (NTF) have received a lot of attention. Many NTF-based methods combine total variation (TV) regularization, aiming at maintaining the smoothness of the abundance maps to improve the performance of unmixing. However, the existing TV regularization ignores the sparsity sharing on the spatial difference images among different bands. To tackle this issue, a weighted total variation regularizer on the spatial difference maps of abundances is proposed in this paper, which uses the $L_{2,1}$ norm to explore the sparse structure in abundances along the spectral dimension. In addition, the $L_{1/2}$ norm is used to enhance the spatial sparsity of abundances. The proposed method can not only enhance the sparsity in abundances, but also keep the spatial similarity characteristics of data. Compared with the existing popular methods, the proposed method has superior performance on both synthetic data and real data.