Learning complex representations from spatial phase statistics of natural scenes

Natural scenes exhibit higher-order statistical structures encapsulated within their spatial phase information, contributing significantly to visual perception and neural coding. Despite this potential, comprehending the brain's adept representation of phase information and developing computational models to capture these processes remain areas of limited advancement. To address this gap and facilitate the capture of spatial phase patterns within the efficient coding hypothesis framework, we introduce a novel generative model for the representation of the phase images of visual scenes. We propose that images can be deconstructed into complex-valued features and independent source signals while integrating their non-uniform phase distributions. Expanding upon existing bilinear generative models, we provide a gradient-based optimization algorithm for estimating model parameters, firmly rooted in the principles of maximum-likelihood. Additionally, we introduce a technique to decorrelate the elements of each complex source signal. Through extensive simulations, we showcase the model's superiority in blind source separation of complex-valued signals compared to conventional models. The application of our model to amplitude-shuffled natural scenes, which preserves spatial phase statistics but loses amplitude information, uncovers learned complex features reminiscent of the receptive fields of visual cortex simple cells, characterized by distinct pairs of Gabor-like filter profiles. These findings emphasize the model's capacity to enhance goodness-of-fit beyond the limitations of models of natural scenes with uniform phase assumptions, shedding new light on how spatial phase patterns are encoded. Our findings highlight the significance of structured phase information within natural signals, further strengthening the proposition that phase-sensitive cells in the visual cortex play a fundamental role in reducing redundancy in the phase information of natural scenes.