#### SPARSE CODING OF TIMEVARYING NATURAL IMAGES

Bruno A. Olshausen

baolshausen@ucdavis.edu

We show how the principle of sparse coding may be
applied to learn the forms of structure occurring in
timevarying natural images. A sequence of images is
described as a linear superposition of spacetime func
tions, each of which is convolved with a timevarying
coefficient signal. When a sparse, independent repre
sentation is sought over the coefficients, the basis func
tions that emerge are spacetime inseparable functions
that resemble the motionselective receptive fields of
cortical simple cells. Interestingly, the coefficients form
a spikelike representation of moving images, and thus
suggest an interpretation of spiking activity in the brain
in terms of sparse coding in time.