Sparse Blind Source Separation (BSS) has become a well established tool for a wide range of applications - for instance, in astrophysics and remote sensing. Classical sparse BSS methods, such as the Proximal Alternating Linearized Minimization (PALM) algorithm, nevertheless often suffer from a difficult hyperparameter choice, which undermines their results. To bypass this pitfall, we propose in this work to build on the thriving field of algorithm unfolding/unrolling. Unrolling PALM enables to leverage the data-driven knowledge stemming from realistic simulations or ground-truth data by learning both PALM hyperparameters and variables. In contrast to most existing unrolled algorithms, which assume a fixed known dictionary during the training and testing phases, this article further emphasizes on the ability to deal with variable mixing matrices (a.k.a. dictionaries). The proposed Learned PALM (LPALM) algorithm thus enables to perform semi-blind source separation, which is key to increase the generalization of the learnt model in real-world applications. We illustrate the relevance of LPALM in astrophysical multispectral imaging: the algorithm not only needs up to $10^4-10^5$ times fewer iterations than PALM, but also improves the separation quality, while avoiding the cumbersome hyperparameter and initialization choice of PALM. We further show that LPALM outperforms other unrolled source separation methods in the semi-blind setting.

本研究提出 Learned PALM 算法，通过算法展开/展开来解决常规稀疏盲源分离算法的超参数选择困难的问题，并能够处理变量混合矩阵，从而实现半盲源分离。在黑洞成像等领域中，这种算法比PALM算法拥有更高的分离质量和更少的迭代次数，并优于其他半盲源分离方法。

基于PALM的稀疏半盲源分离算法