Drumetz Lucas, Meyer Travis R, Chanussot Jocelyn, Bertozzi Andrea L, Jutten Christian
IEEE Trans Image Process. 2019 Jul;28(7):3435-3450. doi: 10.1109/TIP.2019.2897254. Epub 2019 Feb 4.
Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually mixtures of the contributions of several materials. The spectral unmixing problem aims at recovering the spectra of the pure materials of the scene (endmembers), along with their proportions (abundances) in each pixel. In order to deal with the intra-class variability of the materials and the induced spectral variability of the endmembers, several spectra per material, constituting endmember bundles, can be considered. However, the usual abundance estimation techniques do not take advantage of the particular structure of these bundles, organized into groups of spectra. In this paper, we propose to use group sparsity by introducing mixed norms in the abundance estimation optimization problem. In particular, we propose a new penalty, which simultaneously enforces group and within-group sparsity, to the cost of being nonconvex. All the proposed penalties are compatible with the abundance sum-to-one constraint, which is not the case with traditional sparse regression. We show on simulated and real datasets that well-chosen penalties can significantly improve the unmixing performance compared to classical sparse regression techniques or to the naive bundle approach.
高光谱图像比传统成像技术提供了更多的信息，能够精确识别观测场景中的材料，但由于空间分辨率有限，观测结果通常是几种材料贡献的混合。光谱解混问题旨在恢复场景中纯材料（端元）的光谱，以及它们在每个像素中的比例（丰度）。为了处理材料的类内变异性以及由此引起的端元光谱变异性，可以考虑每种材料的多个光谱，构成端元束。然而，通常的丰度估计技术没有利用这些束的特殊结构，这些束是按光谱组组织的。在本文中，我们建议在丰度估计优化问题中引入混合范数来使用组稀疏性。特别是，我们提出了一种新的惩罚项，它在非凸代价的情况下同时强制组稀疏性和组内稀疏性。所有提出的惩罚项都与丰度总和为一的约束兼容，而传统的稀疏回归则不满足这一约束。我们在模拟和真实数据集上表明，与经典的稀疏回归技术或简单的束方法相比，精心选择的惩罚项可以显著提高解混性能。
