高光谱图像Pareto优化稀疏解混

高光谱解混是学术界的一个难题，稀疏高光谱解混指的是利用已知光谱库进行解混，旨在从先验光谱库中找到一些可以表征图像的数个纯光谱向量作为高光谱图像的端元，并利用这些端元求解相应的端元丰度，这是一个NP难的组合优化问题。目前多通过将L0范数凸松弛为L1范数进行稀疏解混，但该方法得到的仅仅是近似解。文中提出了一种基于Pareto优化的稀疏解混算法（ParetoSU），将稀疏解混问题转化为一个两目标优化问题，其中一个优化目标是建模误差，另一个目标是端元稀疏度。ParetoSU直接解决稀疏解混中的组合优化问题，不需要对L0范数进行近似。最后利用仿真数据验证了该解混算法的有效性。

Sparse unmixing of hyperspectral images based on Pareto optimization

Hyperpectral unmixing is a difficult problem in academia. Sparse hyperspectral unmixing uses priori spectral library, aiming at finding several pure spectral signatures to express hyperspectral images and computing corresponding abundance fractions. This is NP-hard to solve. Convex relaxation for L0 norm as L1 norm is a common approach to solve the sparse unmixing problem, but only approximation results can be achieved. A Pareto optimization based sparse unmixing algorithm was proposed(ParetoSU). ParetoSU firstly transformed sparse unmixing to a bi-objective optimization problem. One of the two objectives was the modelling error and the other one was the sparsity of endmembers. ParetoSU can solve the sparse unmixing problem without any approximation of L0 norm. At last, synthetic data were used to test the performance of ParetoSU.