基于端元和丰度属性的NMF算法改进

发布时间：2018-03-21 20:15

本文选题：高光谱图像　切入点：非负矩阵分解　出处：《大连海事大学》2017年硕士论文　论文类型：学位论文

【摘要】：非负矩阵分解(Non-negative matrix factorization,NMF)算法是一种盲线性光谱解混技术中的一个重要研究分支。然而,原始的NMF算法直接应用在高光谱解混时,会导致局部最小解,而且收敛速度慢,在此基础上发展了很多的改进算法。论文基于结合端元体积最小化的改进算法MDC-NMF算法,考虑了端元和丰度的属性,提出了两种对目标函数进行约束的改进的非负矩阵分解算法。一方面,利用光谱信息散度来衡量像元之间的相似性,进而将图像局部不变性加入到非负矩阵分解算法中,同时引入端元体积最小化约束促使单形体收敛到真实端元位置,提出了结合流型正则化和最小距离作为约束条件的非负矩阵分解算法 MMDC-NMF。另一方面考虑了图像中像元结构的特点,将稀疏约束加入到非负矩阵分解算法中,对丰度矩阵进行约束,同时加入端元距离约束,对端元矩阵进行约束,提出了结合稀疏和最小距离作为约束条件的非负矩阵分解算法SMDC-NMF。论文通过对上述改进后的目标函数的构造及迭代规则进行推导,分别获得端元矩阵和丰度矩阵的优化策略,并在模拟高光谱图像和真实高光谱图像上设计实现。模拟数据和真实数据的实验结果表明,所提出的两种方法都取得了好于MDC-NMF的算法的结果,并且MMDC-NMF比SMDC-NMF适合于稀疏度较低的高光谱图像解混,而SMDC-NMF在稀疏度较高的图像上效果明显。
[Abstract]:Non-negative matrix factorization (NMF) algorithm is an important branch of blind linear spectral demultiplexing. However, when the original NMF algorithm is directly applied to hyperspectral demultiplexing, it will lead to local minimum solution and slow convergence rate. On this basis, many improved algorithms are developed. In this paper, the properties of endmembers and abundance are considered based on the improved MDC-NMF algorithm, which combines with the minimization of endmember volume. Two improved nonnegative matrix decomposition algorithms are proposed to constrain the objective function. On the one hand, the spectral information divergence is used to measure the similarity between pixels, and then the local invariance of the image is added to the non-negative matrix decomposition algorithm. At the same time, the end element volume minimization constraint is introduced to make the body converge to the real end element position. A non-negative matrix decomposition algorithm MMDC-NMF, which combines flow pattern regularization and minimum distance as constraint condition, is proposed. On the other hand, considering the characteristics of pixel structure in images, sparse constraints are added to the non-negative matrix decomposition algorithm. The abundance matrix is constrained, the endmember distance constraint is added, and the endmember matrix is constrained. A nonnegative matrix decomposition algorithm, SMDC-NMF, which combines sparse and minimum distance as constraint condition, is proposed. By deducing the construction and iterative rules of the above improved objective function, the optimization strategies of endmember matrix and abundance matrix are obtained, respectively. The experimental results of the simulated and real hyperspectral images show that the proposed two methods are better than the MDC-NMF algorithm. Moreover, MMDC-NMF is more suitable than SMDC-NMF for demultiplexing of hyperspectral images with lower sparsity, while SMDC-NMF is more effective in images with higher sparsity.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP751

【参考文献】