FaSUn: Fast Semi-Supervised Unmixing Using Alternating Direction Method of Multipliers.

This paper proposes a semi-supervised unmixing technique using the alternating direction method of multipliers (ADMM). Firstly, we introduce a nonconvex optimization approach for semi-supervised unmixing, assuming that the endmembers are convex combinations of the endmembers provided by a spectral library. Subsequently, we present an ADMM algorithm to solve this nonconvex problem by decomposing it into convex subproblems using a cyclic descent scheme. Unlike sparse unmixing methods, the proposed minimization problem is nonconvex. We offer a GPU-accelerated implementation using PyTorch, which results in an efficient unmixing technique. We compare the proposed algorithm with state-of-the-art (SOTA) unmixing techniques to validate our approach. Experimental results confirm the superiority of FaSUn over the SOTA for two synthetic datasets and the Cuprite dataset. For those interested, we provide an open-source PyTorch implementation available at: https://github.com/BehnoodRasti/FaSUn.