Sparsity and Independence: Balancing Two Objectives in Optimization for Source Separation with Application to fMRI Analysis.

•We provide a mathematical framework for blind source separation that enables direct control over the relative influence of independence and sparsity.•Apply this framework to the development of an effective ICA algorithm that can jointly exploit independence and sparsity.•We study the effect of the relative influence of independence and sparsity on both the algorithm’s separation accuracy and reproducibility using simulated functional magnetic resonance imaging (fMRI) data.•Based on our observations using simulated fMRI data, we provide guidance on how to balance these two objectives in real world applications where the ground truth is not available.