Learning nonlinear statistical regularities in natural images by modeling the outer product of image intensities

It is well known that there exist nonlinear statistical regularities in natural images. Existing approaches for capturing such regularities always model the image intensities by assuming a parameterized distribution for the intensities and learn the parameters. In the letter, we propose to model the outer product of image intensities by assuming a gaussian distribution for it. A two-layer structure is presented, where the first layer is nonlinear and the second layer is linear. Trained on natural images, the first-layer bases resemble the receptive fields of simple cells in the primary visual cortex (V1), while the second-layer units exhibit some properties of the complex cells in V1, including phase invariance and masking effect. The model can be seen as an approximation of the covariance model proposed in Karklin and Lewicki (2009) but has more robust and efficient learning algorithms.