基于图拉普拉斯正则化的柯西非负矩阵分解高光谱解混

Cauchy Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Graph Laplacian Regularization

基于欧氏距离标准的非负矩阵分解(NMF)在面对含有噪声和异常像元污染的高光谱图像时,容易造成解混的失败。为了抑制噪声或异常像元的影响,采用基于柯西损失函数的NMF模型以提高解混的鲁棒性。由于对异常值的抑制可能会破坏高光谱图像内在的丰度结构,因此为保证原始高光谱内部数据不被破坏,将图拉普拉斯约束引入模型中。同时,为提高丰度矩阵的稀疏性,提高解混性能,引入重加权稀疏约束项,提出基于图拉普拉斯正则化的柯西非负矩阵(CNMF-GLR)分解的算法。考虑到图拉普拉斯约束对邻域选择的需求,使用局部邻域加权的方法,通过矩形窗结构来确定局部邻域。在模拟数据集和真实数据集上使用相同初始化条件与其他经典算法进行比较,结果表明,所提算法具有更好的鲁棒性和解混性能。

Nonnegative matrix decomposition(NMF)based on Euclidean distance standard is easy to cause unmixing failure in hyperspectral images with noise and abnormal pixel pollution.In order to suppress the influence of noise or abnormal pixels,the NMF model based on Cauchy loss function is adopted to improve the robustness of unmixing.Because the suppression of outliers may destroy the intrinsic abundance structure of hyperspectral images.Therefore,in order to ensure that the original hyperspectral internal data is not destroyed,the graph Laplace constraint is introduced into the model.At the same time,in order to improve the sparsity of abundance matrix and improve the performance of unmixing,a reweighted sparse constraint term is introduced,and a decomposition algorithm of Cauchy nonnegative matrix based on graph Laplacian regularization(CNMFGLR)is proposed.Considering the requirement of Laplacian constraint on neighborhood selection,this paper uses local neighborhood weighting method to determine local neighborhood by rectangular window structure.By comparing with other classical algorithms with the same initialization conditions on simulated and real data sets,the proposed algorithm is proved to have better robustness and unmixing performance.