In recent years, sparse unmixing has attracted significant attention, as it can effectively avoid the bottleneck problems associated with the absence of pure pixels and the estimation of the number of endmembers in hyperspectral scenes. The joint-sparsity model has outperformed the single sparse unmixing method. However, the joint-sparsity model might cause some aliasing artifacts for the pixels on the boundaries of different constituent endmembers. To address this shortcoming, researchers have developed many unmixing algorithms based on low-rank representation, which makes good use of the global structure of data. In addition, the high mutual coherence of spectral libraries strongly affects the applicability of sparse unmixing. In this study, adopting combined constraints imposing sparsity and low rankness, a novel algorithm called nonconvex joint-sparsity and low-rank unmixing with dictionary pruning is developed In particular, we impose sparsity on the abundance matrix using the $\ell _{2,p}$ mixed norm, and we also employ the weighted Schatten $p$-norm instead of the convex nuclear norm as an approximation for the rank. The key parameter $p$ is set between 0.4 and 0.6, and a good quality sparse solution is generated. The effectiveness of the proposed algorithm is demonstrated on both simulated and real hyperspectral datasets.

中文翻译：

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通过具有字典修剪的非凸稀疏和低秩约束进行高光谱解混

近年来，稀疏解混引起了极大的关注，因为它可以有效避免与纯像素缺失和高光谱场景中端元数量估计相关的瓶颈问题。联合稀疏模型​​优于单一稀疏解混合方法。然而，联合稀疏模型​​可能会导致不同组成端元边界上的像素出现一些混叠伪影。针对这一不足，研究人员开发了许多基于低秩表示的解混算法，很好地利用了数据的全局结构。此外，谱库的高度相互相干性强烈影响稀疏解混的适用性。在本研究中，采用施加稀疏性和低秩的组合约束，$\ell _{2,p}$ 混合范数，我们还使用加权 Schatten $p$-norm 而不是凸核范数作为秩的近似值。关键参数$p$设置在 0.4 和 0.6 之间，并生成一个质量好的稀疏解。在模拟和真实的高光谱数据集上都证明了所提出算法的有效性。