Olshausen BA (2003).  Learning Sparse, Overcomplete Representations of Time-Varying Natural Images.  IEEE International Conference on Image Processing.  Sept. 14-17, 2003. Barcelona, Spain.

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.