Heuristics for efficient sparse blind source separation

Sparse Blind Source Separation (sparse BSS) is a key method to analyze multichannel data in fields ranging from medical imaging to astrophysics. However, since it relies on seeking the solution of a non-convex penalized matrix factorization problem, its performances largely depend on the optimization strategy. In this context, Proximal Alternating Linearized Minimization (PALM) has become a standard algorithm which, despite its theoretical grounding, generally provides poor practical separation results. In this work, we first investigate the origins of these limitations, which are shown to take their roots in the sensitivity to both the initialization and the regularization parameter choice. As an alternative, we propose a novel strategy that combines a heuristic approach with PALM. We show its relevance on realistic astrophysical data.