The Multilinear ICA Decompositionwith Applications to NSS Modeling

We refine the classical independent component analysis (ICA) decomposition using a multilinear expansion of the probability density function of the source statistics. In particular, to model the source statistics of natural image textures, we introduce a specific non-linear system that allows us to elegantly capture the statistical dependences between the responses of the multilinear ICA (MICA) filters. The resulting multilinear probability density is analytically tractable and does not require Monte Carlo simulations to estimate the model parameters. We demonstrate the success of the MICA model on natural textures and discuss applications to non-stationarity detection and natural scene statistics (NSS) modeling.