Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires efficient regularization schemes to better distinguish between the sources and yield interpretable solutions. For that purpose, we investigate a semi-supervised source separation approach in which we combine a projected alternating least-square algorithm with a learning-based regularization scheme. In this article, we focus on constraining the mixing matrix to belong to a learned manifold by making use of generative models. Altogether, we show that this allows for an innovative BSS algorithm, with improved accuracy, which provides physically interpretable solutions. The proposed method, coined sGMCA, is tested on realistic hyperspectral astrophysical data in challenging scenarios involving strong noise, highly correlated spectra and unbalanced sources. The results highlight the significant benefit of the learned prior to reduce the leakages between the sources, which allows an overall better disentanglement.

中文翻译：

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具有学习约束的半盲源分离

盲源分离 (BSS) 算法是无监督的方法，通过允许物理上有意义的数据分解，它是高光谱数据分析的基石。BSS 问题不适定，解决方案需要有效的正则化方案来更好地区分源并产生可解释的解决方案。为此，我们研究了一种半监督源分离方法，其中我们将投影交替最小二乘算法与基于学习的正则化方案相结合。在本文中，我们专注于通过使用生成模型将混合矩阵约束为属于学习的流形。总而言之，我们表明这允许一种创新的 BSS 算法，具有更高的准确性，它提供了物理上可解释的解决方案。所提出的方法，创造了 sGMCA，在涉及强噪声、高度相关光谱和不平衡源的具有挑战性的场景中，对真实的高光谱天体物理数据进行了测试。结果突出了在减少源之间的泄漏之前学习的显着好处，这允许整体更好的解开。