Hyperspectral Unmixing Using Sparsity-Constrained Deep Nonnegative Matrix Factorization With Total Variation
Hyperspectral unmixing is an important processing step for many hyperspectral applications, mainly including: 1) estimation of pure spectral signatures (endmembers) and 2) estimation of the abundance of each endmember in each pixel of the image. In recent years, nonnegative matrix factorization (NMF) has been highly attractive for this purpose due to the nonnegativity constraint that is often imposed in the abundance estimation step. However, most of the existing NMF-based methods only consider the information in a single layer while neglecting the hierarchical features with hidden information. To alleviate such limitation, in this paper, we propose a new sparsity-constrained deep NMF with total variation (SDNMF-TV) technique for hyperspectral unmixing. First, by adopting the concept of deep learning, the NMF algorithm is extended to deep NMF model. The proposed model consists of pretraining stage and fine-tuning stage, where the former pretrains all factors layer by layer and the latter is used to reduce the total reconstruction error. Second, in order to exploit adequately the spectral and spatial information included in the original hyperspectral image, we enforce two constraints on the abundance matrix. Specifically, the  $L_{1/2}$  constraint is adopted, since the distribution of each endmember is sparse in the 2-D space. The TV regularizer is further introduced to promote piecewise smoothness in abundance maps. For the optimization of the proposed model, multiplicative update rules are derived using the gradient descent method. The effectiveness and superiority of the SDNMF-TV algorithm are demonstrated by comparing with other unmixing methods on both synthetic and real data sets.