Manifold Regularized Sparse NMF for Hyperspectral Unmixing

Hyperspectral unmixing is one of the most important techniques in analyzing hyperspectral images, which decomposes a mixed pixel into a collection of constituent materials weighted by their proportions. Recently, many sparse nonnegative matrix factorization (NMF) algorithms have achieved advanced performance for hyperspectral unmixing because they overcome the difficulty of absence of pure pixels and sufficiently utilize the sparse characteristic of the data. However, most existing sparse NMF algorithms for hyperspectral unmixing only consider the Euclidean structure of the hyperspectral data space. In fact, hyperspectral data are more likely to lie on a low-dimensional submanifold embedded in the high-dimensional ambient space. Thus, it is necessary to consider the intrinsic manifold structure for hyperspectral unmixing. In order to exploit the latent manifold structure of the data during the decomposition, manifold regularization is incorporated into sparsity-constrained NMF for unmixing in this paper. Since the additional manifold regularization term can keep the close link between the original image and the material abundance maps, the proposed approach leads to a more desired unmixing performance. The experimental results on synthetic and real hyperspectral data both illustrate the superiority of the proposed method compared with other state-of-the-art approaches.