We present a two-layer dynamic generative model of the statistical structure of natural image sequences. The second layer of the model is a linear mapping from simple-cell outputs to pixel values, as in most work on natural image statistics. The first layer models the dependencies of the activity levels (amplitudes or variances) of the simple cells, using a multivariate autoregressive model. The second layer shows the emergence of basis vectors that are localized, oriented and have different scales, just like in previous work. But in our new model, the first layer learns connections between the simple cells that are similar to complex cell pooling: connections are strong among cells with similar preferred location, frequency and orientation. In contrast to previous work in which one of the layers needed to be fixed in advance, the dynamic model enables us to estimate both of the layers simultaneously from natural data.
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