Linear hyperspectral unmixing (LHU) is a class of important problems in remote sensing. It can be modelled by a linearly constrained convex optimization problem with a coupled objective function. This paper proposes an alternating direction method of multipliers (ADMM) for solving this LHU model. The special structure of the LHU model allows explicit solutions to the subproblems in the ADMM and hence the ADMM is easily implementable. The global convergence of the ADMM is established despite the existence of a coupled term in the objective function. Our numerical experiments with four data sets demonstrated that the proposed ADMM is effective for solving the LHU model.

线性高光谱解混（LHU）是遥感中的一类重要问题。它可以通过具有耦合目标函数的线性约束凸优化问题来建模。本文提出了一种求解该 LHU 模型的交替方向乘数法 (ADMM)。LHU 模型的特殊结构允许显式求解 ADMM 中的子问题，因此 ADMM 易于实现。尽管目标函数中存在耦合项，但 ADMM 的全局收敛性仍然成立。我们对四个数据集的数值实验表明，所提出的 ADMM 对求解 LHU 模型是有效的。