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Neural Computation

February 1, 2000, Vol. 12, No. 2, Pages 313-335
(doi: 10.1162/089976600300015817)
© 2000 Massachusetts Institute of Technology
Do Simple Cells in Primary Visual Cortex Form a Tight Frame?
Article PDF (296.54 KB)

Sets of neuronal tuning curves, which describe the responses of neurons as functions of a stimulus, can serve as a basis for approximating other functions of stimulus parameters. In a function-approximating network, synaptic weights determined by a correlation-based Hebbian rule are closely related to the coefficients that result when a function is expanded in an orthogonal basis. Although neuronal tuning curves typically are not orthogonal functions, the relationship between function approximation and correlation-based synaptic weights can be retained if the tuning curves satisfy the conditions of a tight frame. We examine whether the spatial receptive fields of simple cells in cat and monkey primary visual cortex (V1) form a tight frame, allowing them to serve as a basis for constructing more complicated extrastriate receptive fields using correlation-based synaptic weights. Our calculations show that the set of V1 simple cell receptive fields is not tight enough to account for the acuity observed psychophysically.