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Hyperspectral unmixing aims to separate pure materials and their corresponding proportions that constitute the mixed pixels of hyperspectral imagery (HSI). Recently, the matrix-vector nonnegative tensor factorization (MV-NTF) has attracted wide attention in this field due to its natural third-tensor representation of HSI. However, the NTF-based unmixing approaches are limited to the nonunique solution and long computational time. To solve these problems, we consider the low-rank and sparse priors of each abundance map simultaneously and propose a new unmixing model adopting a weighted nuclear norm and an <inline-formula><tex-math notation="LaTeX">$L_{1/2}$</tex-math></inline-formula> norm under the MV-NTF framework. Instead of using low-rank matrix decomposition of MV-NTF, this model imposes the low-rank property on the whole abundance map, which avoids determining the rank of the abundance map in advance. Observing that each abundance map is different, we build an adaptive update mechanism to treat each low-rank and sparse constraint differently in the model. Furthermore, a new multiplicative iterative algorithm is designed to solve the proposed model. Specially, the algorithm designed for this tensor model is simplified by using the equivalence relation with nonnegative matrix factorization. Experiments demonstrate that the proposed method is effective in improving both the unmixing effect and the solving speed.

Efficient Weighted-Adaptive Sparse Constrained Nonnegative Tensor Factorization for Hyperspectral Unmixing