Generalized Morphological Component Analysis for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is an active research topic in the remote-sensing community. It aims at modeling mixed pixels using a collection of pure constituent materials (endmembers) weighted by their corresponding fractional abundances. Among existing unmixing schemes, nonnegative matrix factorization (NMF) has drawn significant attention due to its unsupervised nature, as well as its capacity to obtain both endmembers and fractional abundances simultaneously. In this article, we present a new blind unmixing method based on the generalized morphological component analysis (GMCA) framework, in which an additional constraint is introduced into the standard NMF model to represent the sparsity and morphological diversity of the abundance maps associated with each endmember. More specifically, we take into account the fact that different ground categories in a hyperspectral scene generally exhibit various spatial distributions and morphological characteristics. As a result, when providing a specific dictionary basis for these categories, their corresponding abundance maps (referred to as sources) can be sparsely represented. In addition, due to the low correlation between different sources, their sparse representations will not share the same most significant coefficients. With this observation in mind, we can further promote source discrimination and separation in the unmixing process. Moreover, in order to obtain a stable solution of the involved optimization problem, we adopt an alternate iterative constrained algorithm with a threshold descent strategy. Our experiments, carried out on both synthetic and real hyperspectral scenes, reveal that our newly developed GMCA-based unmixing method obtains very promising results with fast convergence speed and requiring significantly less parameter tuning. This confirms the advantage of the proposed spatial morphological component approach for HU purposes.