Redundancy reduction has been proposed as a principle underlying the self-organization of neural representations at the early stages of sensory processing . In particular, principal component analysis (PCA), symmetric whitening (SWH) and independent component analysis (ICA) have been studied as parsimonious redundancy reduction models. When applied to data sets of natural image patches second-order decorrelation methods such as PCA and SWH do not yield localized, oriented, and bandpass filter shapes. These striking properties of V1 simple cell receptive fields, however, can be derived with ICA because of its additional minimization of higher-order correlations. While this finding is intriguing, the structure of the higher-order correlations encountered in ICA is not well understood and their use for sensory coding remains elusive.