School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China.
Sensors (Basel). 2022 Jul 20;22(14):5417. doi: 10.3390/s22145417.
Hyperspectral unmixing (HU) is a technique for estimating a set of pure source signals (end members) and their proportions (abundances) from each pixel of the hyperspectral image. Non-negative matrix factorization (NMF) can decompose the observation matrix into the product of two non-negative matrices simultaneously and can be used in HU. Unfortunately, a limitation of many traditional NMF-based methods, i.e., the non-convexity of the objective function, may lead to a sub-optimal solution. Thus, we put forward a new unmixing method based on NMF under smoothing and sparse constraints to obtain a better solution. First, considering the sparseness of the abundance matrix, a weight sparse regularization is introduced into the NMF model to ensure the sparseness of the abundance matrix. Second, according to the similarity prior of the same feature in the adjacent pixels, a Total Variation regularization is further added to the NMF model to improve the smoothness of the abundance map. Finally, the signatures of each end member are modified smoothly in spectral space. Moreover, it is noticed that discontinuities may emerge due to the removal of noisy bands. Therefore, the spectral data are piecewise smooth in spectral space. Then, in this paper, a piecewise smoothness constraint is further applied to each column of the end-member matrix. Experiments are conducted to evaluate the effectiveness of the proposed method based on two different datasets, including a synthetic dataset and the real-life Cuprite dataset, respectively. Experimental results show that the proposed method outperforms several state-of-the-art HU methods. In the Cuprite hyperspectral dataset, the proposed method's Spectral Angle Distance is 0.1694, compared to the TV-RSNMF method's 0.1703, NMF method's 0.1925, and VCA-FCLS method's 0.1872.
高光谱解混（HU）是一种从高光谱图像的每个像素中估计一组纯源信号（端元）及其比例（丰度）的技术。非负矩阵分解（NMF）可以同时将观测矩阵分解为两个非负矩阵的乘积，并可用于 HU。不幸的是，许多传统基于 NMF 的方法的一个局限性，即目标函数的非凸性，可能导致次优解。因此，我们提出了一种基于 NMF 的新解混方法，该方法在平滑和稀疏约束下，可以获得更好的解。首先，考虑到丰度矩阵的稀疏性，我们在 NMF 模型中引入了权重稀疏正则化项，以确保丰度矩阵的稀疏性。其次，根据相邻像素中相同特征的相似性先验，我们进一步向 NMF 模型中添加了全变差正则化项，以提高丰度图的平滑度。最后，在光谱空间中平滑地修改每个端元的特征。此外，需要注意的是，由于去除了噪声带，可能会出现不连续。因此，光谱数据在光谱空间中是分段平滑的。然后，在本文中，我们进一步对端元矩阵的每一列应用分段平滑约束。实验分别基于两个不同的数据集，包括一个合成数据集和一个真实的 Cuprite 数据集，评估了所提出方法的有效性。实验结果表明，所提出的方法优于几种先进的 HU 方法。在 Cuprite 高光谱数据集中，所提出方法的光谱角距离为 0.1694，而 TV-RSNMF 方法为 0.1703，NMF 方法为 0.1925，VCA-FCLS 方法为 0.1872。
