Sequential Sparse Blind Source Separation for Non-Linear Mixtures

Abstract

Linear Blind Source Separation (BSS) has known a tremendous success in fields ranging from biomedical imaging to astrophysics. In this work, we however propose to depart from the usual linear setting and tackle the case in which the sources are mixed by an unknown non-linear function. We propose to use a sequential decomposition of the data enabling its approximation by a linear-by-part function. Beyond separating the sources, the introduced StackedAMCA can further empirically learn in some settings an approximation of the inverse of the unknown non-linear mixing, enabling to reconstruct the sources despite a severely ill- posed problem. The quality of the method is demonstrated experimentally, and a comparison is performed with state-of-the art non-linear BSS algorithms.