Subspace Matching Pursuit for Sparse Unmixing of Hyperspectral Data
Subspace Matching Pursuit for Sparse Unmixing of Hyperspectral Data
复制标题
DOI：
10.1109/tgrs.2013.2272076
复制
发表时间：
2014-06
影响因子：
8.2
通讯作者：
Zhenwei Shi;Wei Tang;Zhana Duren;Zhi-guo Jiang
中科院分区：
文献类型：
--
作者：
Zhenwei Shi;Wei Tang;Zhana Duren;Zhi-guo Jiang
稀疏解混假设高光谱图像中的每个混合像素可以表示为光谱库中先验已知的仅几个光谱（端元）的线性组合。然后，它的目的是估计这些端元在现场的分数丰度。然而，由于光谱库通常具有很高的相关性，稀疏分解问题仍然是一个很大的挑战。此外，大多数相关的工作集中在l1凸松弛方法，很少注意到使用同时稀疏表示通过贪婪算法（GAs）（SGA）稀疏解混。SGA具有无需平滑惩罚项、计算复杂度低、可直接得到l0问题的近似解以及充分利用高光谱数据的空间信息等优点。因此，有必要探索使用这种算法进行稀疏解混的潜力。受现有的SGA方法的启发，本文提出了一种新的遗传算法称为子空间匹配追踪（SMP）的高光谱数据稀疏分解。SMP算法利用高光谱图像中的低次混合像元，通过迭代寻找一个子空间来重建高光谱数据。证明了在一定条件下，SMP可以从光谱库中恢复最优端元。此外，SMP可以作为一个字典修剪算法。因此，它可以提升其他稀疏解混算法，使其更准确和时间效率。在合成数据和真实的数据上的实验结果证明了该算法的有效性。
Sparse unmixing assumes that each mixed pixel in the hyperspectral image can be expressed as a linear combination of only a few spectra (endmembers) in a spectral library, known a priori. It then aims at estimating the fractional abundances of these endmembers in the scene. Unfortunately, because of the usually high correlation of the spectral library, the sparse unmixing problem still remains a great challenge. Moreover, most related work focuses on the l1 convex relaxation methods, and little attention has been paid to the use of simultaneous sparse representation via greedy algorithms (GAs) (SGA) for sparse unmixing. SGA has advantages such as that it can get an approximate solution for the l0 problem directly without smoothing the penalty term in a low computational complexity as well as exploit the spatial information of the hyperspectral data. Thus, it is necessary to explore the potential of using such algorithms for sparse unmixing. Inspired by the existing SGA methods, this paper presents a novel GA termed subspace matching pursuit (SMP) for sparse unmixing of hyperspectral data. SMP makes use of the low-degree mixed pixels in the hyperspectral image to iteratively find a subspace to reconstruct the hyperspectral data. It is proved that, under certain conditions, SMP can recover the optimal endmembers from the spectral library. Moreover, SMP can serve as a dictionary pruning algorithm. Thus, it can boost other sparse unmixing algorithms, making them more accurate and time efficient. Experimental results on both synthetic and real data demonstrate the efficacy of the proposed algorithm.