IEEE Trans Image Process. 2016 Apr;25(4):1516-29. doi: 10.1109/TIP.2016.2523345. Epub 2016 Jan 28.
Spectral unmixing aims at estimating the proportions (abundances) of pure spectrums (endmembers) in each mixed pixel of hyperspectral data. Recently, a semi-supervised approach, which takes the spectral library as prior knowledge, has been attracting much attention in unmixing. In this paper, we propose a new semi-supervised unmixing model, termed framelet-based sparse unmixing (FSU), which promotes the abundance sparsity in framelet domain and discriminates the approximation and detail components of hyperspectral data after framelet decomposition. Due to the advantages of the framelet representations, e.g., images have good sparse approximations in framelet domain, and most of the additive noises are included in the detail coefficients, the FSU model has a better antinoise capability, and accordingly leads to more desirable unmixing performance. The existence and uniqueness of the minimizer of the FSU model are then discussed, and the split Bregman algorithm and its convergence property are presented to obtain the minimal solution. Experimental results on both simulated data and real data demonstrate that the FSU model generally performs better than the compared methods.
光谱分解旨在估计高光谱数据中每个混合像素中纯光谱（端元）的比例（丰度）。最近，一种利用光谱库作为先验知识的半监督方法在分解中引起了广泛关注。在本文中，我们提出了一种新的半监督分解模型，称为基于框架的稀疏分解（FSU），该模型促进了框架域中的丰度稀疏性，并区分了框架分解后高光谱数据的近似分量和细节分量。由于框架表示的优点，例如，图像在框架域中有良好的稀疏近似，并且大部分加性噪声包含在细节系数中，因此 FSU 模型具有更好的抗噪能力，从而得到更好的分解性能。然后讨论了 FSU 模型的最小值的存在性和唯一性，并提出了分裂布格曼算法及其收敛性质以获得最小解。在模拟数据和真实数据上的实验结果表明，FSU 模型通常比比较方法表现更好。
