A model of V1 complex cells based on factorizing amplitude and phase

How does visual cortex form increasingly complex and invariant representations? We address this question starting from our understanding of natural images and V1. Although it is well-known that the relative phases of frequency components in images contain important structure, the standard model of V1 complex cells discards phase information within the receptive field. We propose a model for disentangling invariances and their accompanying transformations based on a complex-valued sparse coding model adapted from Cadieu & Olshausen 2012. This model makes phase information explicit by factorizing images into both phase and amplitude components, with structure represented by amplitude and phase patterns, and local deformations as coordinated phase shifts. The resulting amplitude and phase representation allows us to analyze the higher-order statistics of natural images, and provides a basis for building models of feature selectivity and invariance in V2.