一种自适应鲁棒最小体积高光谱解混算法

对高光谱图像解混的目的在于从低空间分辨率的高光谱图像中找到端元与对应的丰度.本文根据解混算法中的最小体积准则，提出了一种自适应鲁棒最小体积高光谱解混算法（Robust minimum volume based algorithm with automatically estimating regularization parameters for hyperspectral unmixing，RMVHU）.本算法通过引入负数惩罚正则项，替换了同类算法中的丰度非负性约束（Non-negativity constraint，ANC），使算法对图像中的噪声与异常值具有更强的鲁棒性；采用循环最小化方法，将非凸优化问题分解为凸优化子问题，然后应用交替方向乘子法解决随着像素点个数增大带来的求解困难问题；对于正则项系数，本算法提出了一种自适应调整策略，提高了算法的收敛性，并且通过定性分析，说明了该调整方法的合理性.将算法应用于合成数据与实际数据，实验结果表明，与同类算法相比，本文提出的算法能够取得更为优秀的效果.

A Robust Minimum Volume Based Algorithm with Automatically Estimating Regularization Parameters for Hyperspectral Unmixing

Hyperspectral unmixing aims at finding hidden endmembers and their corresponding abundances from hyperspectral images with low spatial resolution. Based on the well-known minimum volume (MV) rule in geometrical based approaches, a robust minimum volume based algorithm with automatically estimating regularization parameters for hyperspectral unmixing (RMVHU) is proposed. In this algorithm, the ANC constraint is replaced with a negative number punished regularizer which may lead to a more robust result to outliers and noise. A cyclic minimization algorithm is used to split the nonconvex RMVHU problem into convex subproblems, and ADMM is referred to sovle the large scale optimization problem with the increasing number of pixels in the image. To improve the convergence of the algorithm, a strategy to estimate the regularization parameters of the regularizer automatically is proposed. Compared with some existing geometrical based methods, experimental results show the superiority of the RMVHU algorithm on both synthetic datasets and real datasets.