Many unmixing methods hold the assumption that endmembers correspond to major land covers, but not true for some unmixing tasks where observed minor object signals corresponding to some special types of endmembers are relatively weak. When there exist weak signals that have low intensity potentially caused by subtle mixing abundance fractions regarding the endmembers of minor objects, the traditional unmixing techniques may fail. This article pioneers weak signal scenarios in hyperspectral unmixing using an efficient method called HyperWeak. In particular, HyperWeak involves a sparse nonnegative matrix factorization (NMF) model that contains two main parts, where the unsupervised part estimates the endmember and abundance matrices, and the supervised part ensures the minimal degradation of prior knowledge. To enhance the robustness of the HyperWeak model, this article considers a reweighted sparsity constraint to boost the sparseness of the abundance matrix. For effectively solving optimization problems, a Nesterov’s optimal gradient method (OGM) is used in this article. Experiments conducted on synthetic and real hyperspectral images indicate that HyperWeak can improve the unmixing performances of hyperspectral data in weak signal situations.

中文翻译：

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高光谱数据中的弱信号分析：一种有效的分解视角

许多分解方法都假设端元对应于主要土地覆盖，但对于某些分解任务而言并非如此，因为观察到的与某些特殊类型的端元相对应的次要目标信号相对较弱。当存在可能由与次要天体端元的细微混合丰度分数有关的低强度弱信号时，传统的解混合技术可能会失败。本文使用称为 HyperWeak 的有效方法开创了高光谱分解中的弱信号场景。特别是，HyperWeak 涉及一个稀疏非负矩阵分解 (NMF) 模型，该模型包含两个主要部分，其中无监督部分估计端元和丰度矩阵，监督部分确保先验知识的最小退化。为了增强 HyperWeak 模型的鲁棒性，本文考虑重新加权稀疏约束来提高丰度矩阵的稀疏性。为了有效解决优化问题，本文使用了 Nesterov 的最优梯度法 (OGM)。在合成和真实高光谱图像上进行的实验表明，HyperWeak 可以提高弱信号情况下高光谱数据的分解性能。