一种基于最小距离和稀疏图正则约束的非负矩阵解混算法

A Nonnegative Matrix Unmixing Algorithm Based on Minimum Distance and Sparse Graph Regularity

摘要: 针对非负矩阵解混模型存在容易陷入局部极小值、受噪声影响较大以及混合像元中存在“异物同谱”端元的情况下解混精度较低等问题，为此，本文提出了一种基于最小距离和稀疏图正则约束的非负矩阵分解算法(DLGNMF)。该算法将空间信息与光谱信息相结合，在目标函数中引入单形体距离最小化约束作为端元的约束条件，弥补解混过程中高光谱数据空间几何特性的缺失，将稀疏约束和图正则化约束作为丰度的约束条件，保证了高光谱图像中端元分布的全局稀疏性与局部相似性，更好的改善了非负矩阵模型存在的问题，提高了解混的精度。

Abstract: Aiming at the problems of non-negative matrix unmixing model, such as easy to fall into the local minimum, being greatly affected by noise, and low unmixing accuracy in the case of “foreign matter having the same spectrum” end elements in mixed pixels, etc., in this paper, a non-negative matrix factorization algorithm (DLGNMF) based on minimum distance and regular constraints of sparse graphs is proposed. The algorithm combines spatial information with spectral information. In the objective function, the constraint of minimizing the distance of a single body is introduced as the constraint condition of the end-member. The sparsity constraint and graph regularization constraint are taken as the constraints of abundance, which ensure the global sparsity and local similarity of the end-member distribution in the hyperspectral image, solve the problems of non-negative matrix model and improve the accuracy of solution unmixing.