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Sparse coding with an overcomplete basis set: a strategy employed by V1 (1997)
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| Venue: | Vision Research |
| Citations: | 943 - 9 self |
BibTeX
@ARTICLE{Olshausen97sparsecoding,
author = {Bruno A. Olshausen and David J. Fieldt},
title = {Sparse coding with an overcomplete basis set: a strategy employed by V1},
journal = {Vision Research},
year = {1997},
volume = {37},
pages = {3311--3325}
}
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Abstract
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 ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. 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 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. These deviations from linearity provide a potential explanation for the weak forms of non-linearity observed in the response properties of cortical simple cells, and they further make predictions about the expected interactions among units in
Keyphrases
overcomplete basis basis function neurobiological implication wavelet transforms code element expected interaction output activity sparse distribution response property potential explanation simple cell input-output function natural image spatial receptive field receptive field property ban as weak form effective dimensionality particular interest input space expansive fashion cortical simple cell mammalian striate cortex
