TY - JOUR T1 - Learning Complex Representations from Spatial Phase Statistics of Natural Scenes JF - bioRxiv DO - 10.1101/112813 SP - 112813 AU - HaDi MaBouDi AU - Hideaki Shimazaki AU - Hamid Soltanian-Zadeh AU - Shun-ichi Amari Y1 - 2017/01/01 UR - http://biorxiv.org/content/early/2017/03/01/112813.abstract N2 - Natural scenes contain higher-order statistical structures that can be encoded in their spatial phase information. Nevertheless, little progress has been made in modeling phase information of images in order to understand efficient representation of image phases in the brain. Based on recent findings of spatial phase structure in natural scenes, we introduce a generative model of the phase information in the visual systems according to the efficient coding hypothesis. In this model, we assume independent priors for the amplitude and phase of the coefficients, and model the phase using a non-uniform distribution, which extends existing models of independent component analysis for complex-valued signals. The parameters of the proposed model are then estimated under the maximum-likelihood principle. Using simulated data, we show that the proposed model outperforms conventional models with a uniform phase prior in blind source separation of complex-valued signals. We then apply the proposed model to natural scenes in the Fourier domain. The learning yields nonlinear features specified by a pair of similar Gabor-like filters in quadratic phase structure. These features predict properties of phase sensitive complex cells in the visual cortex, and indicate that the phase sensitive complex cells are essential for removing redundancy in natural scenes. ER -