I show how to adapt an overcomplete dictionary of space-time functions so
as to represent time-varying natural images with maximum sparsity. The
basis functions are considered as part of a probabilistic model of image
sequences, with a sparse prior imposed over the coefficients. Learning
is accomplished by maximizing the log-likelihood of the model, using natural
movies as training data. The basis functions that emerge are space-time
inseparable functions that resemble the motion-selective receptive fields
of simple-cells in mammalian visual cortex. When the coefficients are
computed via matching-pursuit in space and time, one obtains a punctate,
spike-like representation of continuous time-varying images. It is
suggested that such a coding scheme may be at work in the visual cortex.
Olshausen BA (2003). Learning Sparse, Overcomplete Representations
of Time-Varying Natural Images. IEEE International Conference on Image
Processing. Sept. 14-17, 2003. Barcelona, Spain.