Distributed Blind Hyperspectral Unmixing via Joint Sparsity and Low-Rank Constrained Non-Negative Matrix Factorization

Hyperspectral unmixing is a crucial processing step in remote sensing image analysis. Its aim is the decomposition of each pixel in a hyperspectral image into a number of materials, the so-called endmembers, and their corresponding abundance fractions. Among the various unmixing approaches that have been suggested in the literature, we are interested here in unsupervised techniques that rely on some form of non-negative Matrix factorization (NMF). NMF-based techniques provide an easy way to simultaneously estimate the endmembers and their corresponding abundances, though they suffer from mediocre performance and high computational complexity due to the nonconvexity of the involved cost function. Improvements in performance have been recently achieved by imposing additional constraints to the NMF optimization problem related to the sparsity of the abundances. Another feature of hyperspectral images that can be exploited is their high spatial correlation, which is translated into the low rank of the involved abundance matrices. Motivated by this, in this paper we propose a novel unmixing method that is based on a simultaneously sparse and low-rank constrained NMF. In addition, prompted by the rapid evolution of multicore processors and graphics processing units, we devise a distributed unmixing scheme that processes in parallel different parts of the image. The proposed distributed unmixing algorithm achieves improved performance and faster convergence than existing state-of-the-art techniques as it is verified by extensive simulations on synthetic and real hyperspectral data.