Learning Complex Representations from Spatial Phase Statistics of Natural Scenes

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, and understanding efficient representation of the image phases in the brain. In order to capture spatial phase structure under the efficient coding hypothesis, here we introduce a generative model of natural scenes by assuming independent source signals in a complex domain and non-uniform phase priors for the complex signals. Parameters of the proposed model are then estimated under the maximum-likelihood principle. This approach extends existing methods of independent component analysis for complex-valued signals to the one that utilizes phase information. Using simulated data, we demonstrate 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. Real and imaginary parts of the learned complex features exhibit a pair of Gabor-like filters in quadratic phase structure with a similar shape. The proposed model significantly improved the goodness-of-the-fit from the model with a uniform phase prior, indicating that the structured spatial phases are important for removing redundancy in natural scenes. These results predict the presence of phase sensitive complex cells in the visual cortex.