Modeling neural network dynamics using iterative image reconstruction algorithms

Image reconstruction problems can be viewed as energy minimization problems and can be mapped onto a Hopfield neural network. For image reconstruction problems the authors describe the Gerchberg-Papoulis iterative method and the priorized discrete Fourier transform (PDFT) algorithm (C.L. Byrne et al., 1983). Both of these can be mapped onto a Hopfield neural network architecture, with the PDFT incorporating an iterative matrix inversion. The equations describing the operation of the Hopfield neural network are formally equivalent to those used in these iterative reconstruction methods, and these iterative reconstruction algorithms are regularized. The PDFT algorithm is a closed form solution to the Gerchberg-Papoulis algorithm when image support information is used. The regularized Gerchberg-Papoulis algorithm can be implemented synchronously, from which it follows that the Hopfield neural network implementation can also converge