Previously, we have shown that the receptive field properties of simple-cells
in area V1 may be accounted for in terms of a strategy for producing a
sparse distribution of output activity in response to natural images (Nature,
381:607-609). Here, in addition to describing this work in a more expansive
fashion, we examine the neurobiological implications of sparse coding.
Of particular interest is the case when the code is overcomplete---i.e.,
when the number of code elements is greater than the effective dimensionality
of the input space. Because the basis functions overlap (i.e., are non-orthogonal
and not linearly independent of each other) sparsifying the code will recruit
only those basis functions necessary for representing a given input, and
so the input-output function will deviate from being purely linear. Interestingly,
these deviations from linearity provide a potential explanation for the
weak forms of non-linearity observed in the response properties of cortical
simple cells. Further predictions of the model and proposed experimental
tests are discussed.