Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization
Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization
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DOI：
10.1109/tip.2010.2081678
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发表时间：
2011-04
影响因子：
10.6
通讯作者：
Zuyuan Yang;Guoxu Zhou;S. Xie;Shuxue Ding;Jun-Mei Yang;Jun Zhang
中科院分区：
文献类型：
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作者：
Zuyuan Yang;Guoxu Zhou;S. Xie;Shuxue Ding;Jun-Mei Yang;Jun Zhang
非负矩阵分解(NMF)是一种广泛使用的盲谱分解(SU)方法，其目的是在只知道收集的混合光谱数据的情况下获得端元和相应的分数丰度。值得注意的是，丰度可能是稀疏的(即端元可能是稀疏分布的)，稀疏的NMF往往导致唯一的结果，因此用稀疏约束NMF对于求解SU是直观和有意义的。然而，由于SU中的丰度和一约束，传统的用L0/L1范数衡量的稀疏性不再是有效的约束。利用信号向量的高阶范数，提出了一种新的稀疏性度量(称为S度量)。它具有物理意义。针对SU问题，利用S度量约束，提出了一种基于梯度的稀疏NMF算法(简称NMF-SMC)，该算法自适应地选择学习率，同时估计端元和丰度。在提出的NMF-SMC中，没有纯指数假设，也不需要知道先验丰度的确切稀疏程度。然而，它不需要降维的预处理，在降维过程中可能会丢失一些有用的信息。基于AVIRIS和HYDICE传感器采集的合成混合物和真实世界图像的实验验证了该方法的有效性。
Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only the collected mixing spectral data. It is noted that the abundance may be sparse (i.e., the endmembers may be with sparse distributions) and sparse NMF tends to lead to a unique result, so it is intuitive and meaningful to constrain NMF with sparseness for solving SU. However, due to the abundance sum-to-one constraint in SU, the traditional sparseness measured by L0/L1-norm is not an effective constraint any more. A novel measure (termed as S-measure) of sparseness using higher order norms of the signal vector is proposed in this paper. It features the physical significance. By using the S-measure constraint (SMC), a gradient-based sparse NMF algorithm (termed as NMF-SMC) is proposed for solving the SU problem, where the learning rate is adaptively selected, and the endmembers and abundances are simultaneously estimated. In the proposed NMF-SMC, there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior. Yet, it does not require the preprocessing of dimension reduction in which some useful information may be lost. Experiments based on synthetic mixtures and real-world images collected by AVIRIS and HYDICE sensors are performed to evaluate the validity of the proposed method.