Enhancing Blind Source Separation with Dissociative Principal Component Analysis

Principal component analysis (PCA) and its sparse variants (sPCA) are widely used as a precursor to independent component analysis (ICA) for blind source separation (BSS). However, sPCA typically relies on a deflation strategy that extracts components sequentially and imposes orthogonality between them. When the underlying sources overlap, this discards the cross component structure that ICA depends on, degrading separation. This paper proposes dissociative PCA (DPCA), which estimates components jointly rather than by deflation. DPCA introduces left and right dissociation matrices into the SVD based decomposition to explicitly model the interdependencies among principal components (PCs) and loading vectors (LVs), while sparsity constraints maintain interpretability. We develop three algorithms called DPCA1a, DPCA1b, and DPCA2, using adaptive soft thresholding with gradient and coordinate descent, together with a secondary firm thresholding step that preserves sparsity and suppresses background noise in the recovered loading vectors. The method is evaluated on four settings, namely simulated fMRI source retrieval, foreground and background separation, image reconstruction, and image inpainting, where it recovers source structure more reliably than classical sPCA based pipelines, with the largest gains under significant spatial overlap. DPCA reduces to ordinary PCA when the sparsity parameter is zero. A MATLAB implementation of the proposed algorithms is publicly available at https://github.com/usmankhalid06/DPCA.