Before revision: We introduce groupICA, a novel independent component analysis (ICA ) algorithm which decomposes linearly mixed multivariate observations into independent components that are corrupted (and rendered dependent) by hidden group-wise  confounding.
After revision: We introduce coroICA, confounding-robust independent component analysis (ICA ) algorithm which decomposes linearly mixed multivariate observations into independent components that are corrupted (and rendered dependent) by hidden group-wise confounding.