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Olshausen BA, Field DJ (1996). Emergence of simple-cell receptive field
properties by learning a sparse code for natural images. *Nature, 381*:
607-609. (ps.gz
| pdf)

The spatial receptive fields of simple cells in mammalian striate cortex
have been reasonably well described physiologically and can be characterized
as being localized, oriented, and bandpass (selective to structure at different
spatial scales), comparable to the basis functions of wavelet transforms.
One approach to understanding such response properties of visual neurons
has been to consider their relationship to the statistical structure of
natural images in terms of efficient coding. Along these lines, a number
of studies have undertaken to train unsupervised learning algorithms on
natural images in the hope of developing receptive fields with similar
properties but none has succeeded in producing a full set that spans the
image space and contains all three of the above properties. Here, we investigate
the proposal that a coding strategy which maximizes sparseness is sufficient
to account for these properties. We show that a learning algorithm that
attempts to find sparse linear codes for natural scenes will develop a
complete family of localized, oriented, bandpass receptive fields, similar
to those found in the striate cortex. The resulting sparse image code provides
a more efficient representation for later stages of processing because
it possesses a higher degree of statistical independence among its outputs.