Reweighted sparsity regularized deep nonnegative matrix factorization with total variation toward hyperspectral unmixing

Hyperspectral unmixing, as a crucial preprocessing step for many hyperspectral applications, refers to the process of decomposing an image into a set of endmembers and corresponding abundance matrices. Nonnegative Matrix Factorization (NMF) has been widely utilized in hyperspectral unmixing because of its simplicity and effectiveness, whereas traditional NMF exits the local minimum problem. Various modified NMFs have been proposed to address such problem. Deep NMF has shown good performance in feature extraction using a multilayer NMF model. A novel deep NMF algorithm called reweighted sparsity regularized deep NMF with total variation (RSDNMF-TV) is proposed in this study by integrating the total variation and reweighted sparsity with deep layers. First, the deep NMF is obtained by extending the traditional single-layer NMF to the multilayer with pretraining and fine-tuning stages. The former stage pretrains all factors layer by layer, and the latter reduces the decomposition error. Second, a weighted sparse regularizer is integrated into the deep NMF model by sparing the abundance matrix, and its weights are adaptively updated in accordance with the abundance matrix. Finally, the total variation is introduced to improve the piecewise smoothness of abundance maps. In this study, gradient descent method is implemented for the multiplicative update. The experimental results obtained on simulated and real data sets confirm the effectiveness of the proposed method. For real data sets, we utilized the well-known AVIRIS Cuprite and GF-5 data sets. Six other algorithms, namely, total variation regularized reweighted sparse NMF, spatial group sparsity regularized NMF, minimum-volume CNMF, L1/2 sparsity CNMF, multilayer NMF, and VCA-FCLS, were used for comparison. The results on the three hyperspectral datasets show that the proposed unmixing method can outperform other algorithms. In summary, the proposed algorithm achieves improved performance with strong robustness and denoising ability, especially on images with low signal-to-noise ratio. However, RSDNMF-TV has several limitations, which are summarized as follows: (1) the deep NMF has higher computational complexity compared with the traditional NMF. (2) The proposed method only utilizes the prior knowledge of abundance and ignores the constraints on endmembers, such as spectral variability. (3) Parameter β is relevant to image's spatial autocorrelation, and the adaptive selection of the parameter remains challenging. Future work will focus on solving these problems. © 2020, Science Press. All right reserved.