Effective Spectral Unmixing via Robust Representation and Learning-based Sparsity

Hyperspectral unmixing (HU) plays a fundamental role in a wide range of hyperspectral applications. However, HU is still highly challenging due to the large solution space and the common presence of outlier channels. In this work, we propose a novel model by emphasizing both robust representation and learning-based sparsity. To relieve the side effects of badly degraded channels, a $\ell_{2,1}$-norm based robust loss is employed. Besides, the learning-based sparsity method is exploited by simultaneously learning the HU results and a sparse guidance map. Through this guidance map, the individually mixed level of each pixel is described and respected by imposing an adaptive sparsity constraint according to the mixed level of each pixel. Compared with the state-of-the-art method, such implementation is better suited to the real situation, thus expected to achieve better HU performances. The resulted objective is highly non-convex and non-smooth, and so it is hard to deal with. As a profound theoretical contribution, we propose an efficient algorithm to solve it. Meanwhile, the convergence proofs and the computational complexity analysis are systematically and theoretically provided. Extensive evaluations demonstrate that our method is highly promising for the HU task---it achieves very accurate guidance maps and extraordinarily better HU performances compared with the state-of-the-art methods.