Postnonlinear Overcomplete Blind Source Separation Using Sparse Sources

Abstract. We present an approach for blindly decomposing an observed random vector x into f(As) where f is a diagonal function i.e. f = f1 × . . . × fm with one-dimensional functions fi and A an m × n matrix. This postnonlinear model is allowed to be overcomplete, which means that less observations than sources (m < n) are given. In contrast to Independent Component Analysis (ICA) we do not assume the sources s to be independent but to be sparse in the sense that at each time instant they have at most m−1 non-zero components (Sparse Component Analysis or SCA). Identifiability of the model is shown, and an algorithm for model and source recovery is proposed. It first detects the postnonlinearities in each component, and then identifies the now linearized model using previous results. Blind source separation (BSS) based on ICA is a rapidly growing field (see for instance [1,2] and references therein), but most algorithms deal only with the case of at least as many observation...

• Type: Conference
• Year: 2004
• Where: ICA
• Authors: Fabian J. Theis, Shun-ichi Amari
• Keywords: Component Analysis, ICA 2004, Model, Observed Random Vector