Effective Spectral Unmixing via Robust Representation and Learning-based Sparsity
This work improves hyperspectral image analysis for remote sensing applications, but it is incremental as it builds on existing methods with specific enhancements.
The paper tackles hyperspectral unmixing by addressing outlier channels and large solution spaces through a model combining robust representation and learning-based sparsity, achieving more accurate guidance maps and better results than state-of-the-art methods.
Hyperspectral unmixing (HU) plays a fundamental role in a wide range of hyperspectral applications. It is still challenging due to the common presence of outlier channels and the large solution space. To address the above two issues, we propose a novel model by emphasizing both robust representation and learning-based sparsity. Specifically, we apply the $\ell_{2,1}$-norm to measure the representation error, preventing outlier channels from dominating our objective. In this way, the side effects of outlier channels are greatly relieved. Besides, we observe that the mixed level of each pixel varies over image grids. Based on this observation, we exploit a learning-based sparsity method to simultaneously learn the HU results and a sparse guidance map. Via this guidance map, the sparsity constraint in the $\ell_{p}\!\left(\!0\!<\! p\!\leq\!1\right)$-norm is adaptively imposed according to the learnt mixed level of each pixel. Compared with state-of-the-art methods, our model is better suited to the real situation, thus expected to achieve better HU results. The resulted objective is highly non-convex and non-smooth, and so it is hard to optimize. As a profound theoretical contribution, we propose an efficient algorithm to solve it. Meanwhile, the convergence proof and the computational complexity analysis are systematically provided. Extensive evaluations verify that our method is highly promising for the HU task---it achieves very accurate guidance maps and much better HU results compared with state-of-the-art methods.