Associative Memory for Noisy and Structurally Deformed Two-Dimensional Images Using Neural Networks

This paper studies the problem of understanding noisy and structurally deformed two-dimensional images by means of abstractly defined neural works. First, in the framework of systems theory a neural network defined over a Hilbert space is introduced such that any given vectors in the Hilbert space are assigned to locally asymptotically stable fixed points of the network. Then, introducing structural deformation into images a modified neural network is constructed to remove such structural deformation as well as noise. Finally, the modified neural network is used for implementing associative memory of two-dimensional images corrupted by structural deformation as well as noise, and some numerical examples are presented to illustrate the result.