The Dynamics of Image Processing by Feature Maps in the Primary Visual   Cortex
  The operational characteristics of a linear neural network image processing system based on the brain's vision system are investigated. The final stage of the network consists of edge detectors of various orienations arranged in a feature map, corresponding to the primary visual cortex, or V1. The lateral geniculate nucleus is modeled as a preprocessing stage. Excitatory forward and inhibitory backward connections exist between the LGN and V1. By a method of reconstructing the input images in terms of V1 activities, the simulations show that images can be faithfully represented in V1 by the proposed network. The signal-to-noise ratio of the image is improved by the representation, and compression ratios of well over two-hundred are possible. Lateral interacations between V1 neurons sharpen their orientational tuning. We further study the dynamics of the processing, showing that the rate of decrease of the error of the representation is maximized for the receptive fields used, and we develop a Fokker-Planck equation for a more detailed prediction of the error value vs. time. Finally, we show how the eigenvalues of the covariance matrix of the inputs can be employed to predict the rate of error decrease. 
Ted Hesselroth and Klaus Schulten