重加权稀疏非负矩阵分解的高光谱解混

Reweighted sparse nonnegative matrix decomposition for hyperspectral unmixing

近年来基于非负矩阵分解(Nonnegative Matrix Factorization,NMF)的高光谱图像解混方法引起了大家的广泛关注。但是由于NMF问题的非凸性,该方法并不能保证解的唯一性,容易陷入局部极小。为了缩小NMF问题的解空间,提高解混精度,提出了一种新的丰度重加权稀疏NMF(ARSNMF)的解混方法。首先,考虑到丰度矩阵的稀疏性,稀疏约束被添加到NMF模型中。接着,考虑到问题计算复杂、不易于优化,将其转化为重加权稀疏约束的形式,既实现了的稀疏效果,又解决了范数难以求解的问题。为提高算法收敛速度,采用交替方向乘子算法(ADMM)对模型进行优化,将目标函数拆分成几个子问题进行独立求解。基于仿真数据和真实数据的仿真实验验证了该解混算法的有效性。

In recent years,Nonnegative Matrix Factorization(NMF)methods for hyperspectral image unmixing have attracted widespread attention.However,due to the non-convexity of NMF problem,it cannot guarantee the uniqueness of the solution,and it is easy to fall into local minima.In order to reduce the solution space of NMF problem and improve the unmixing accuracy,a new method of reweighted sparse NMF(ARSNMF)was proposed.Firstly,considering the sparsity of abundance matrix,the sparse constraint was added to the NMF model.Then,considering that the calculation of the problem was complex and not easy to be optimized,it was converted into a form of reweighted sparse constraint,which not only achieved the sparse effect,but also solved the problem that was difficult to solve.In order to improve the convergence speed of the algorithm,the Alternating Direction Method of Multipliers(ADMM)was used to optimize the model,and the objective function was divided into several sub-problems for independent solution.Experiments based on simulation data and real data verify the effectiveness of the proposed algorithm.