Do simple cells in primary visual cortex form a tight frame?
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.
Salinas
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Instituto de Fisiología Celular, UNAM, Ciudad Universitaria S&slash;N, 04510 México D.F., México.
Abbott
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LF
D000818:Animals; D002415:Cats; D000882:Haplorhini; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology; D014792:Visual Acuity / Q000502:physiology; D014793:Visual Cortex / Q000502:physiology*; D014794:Visual Fields / Q000502:physiology; D014796:Visual Perception / Q000502:physiology*