Kernel PCA Based Estimation of the Mixing Matrix in Linear Instantaneous Mixtures of Sparse Sources

Source sparsity based methods have become a common approach to blind source separation (BSS) problems, especially in the underdetermined case (more sources than sensors). If the sources are not sparse in the time-domain, in most cases, they can be mapped to a transformed domain (e.g., wavelets, time-frequency, Fourier) in which this assumption is verified. In this paper, we are solely interested in the estimation of the mixing matrix. As observed by Zibulevski and coauthors, the data represented in the scatter plot of the observations tend to cluster along the mixing matrix columns. Each column can be seen as one of the principal components of the data in a higher (possibly infinite) dimension space, and these components can be estimated with a kernel principal component analysis (KPCA) based approach. The theoretical framework is derived, and excellent performance is observed both on synthetic and audio signals