Paper Special Issue on Nonlinear Theory and Its Applications

Image Associative Memory by Recurrent Neural Subnetworks W ladys law S k arbek y3 and Andrzej Cichocki y33 , Members SUMMARY Gray scale images are represented by recurrent neural subnetworks which together with a competition layer create an associative memory. The single recurrent subnetwork N i implements a stochastic nonlinear fractal operator F i , constructed for the given image f i. W e show that under realistic assumptions F has a unique attractor which is located in the vicinity of the original image. Therefore one subnetwork represents one original image. The associative recall is implemented in two stages. Firstly, the competition layer nds the most invariant subnetwork for the given input noisy image g. Next, the selected recurrent subnetwork in few (5-10) global iterations produces high quality approximation of the original image. The degree of invariance for the subnetwork N i on the input g is measured by a norm kg0F i (g)k. W e h a v e experimentally veried that associative recall for images of natural scenes with pixel values in [0; 255] is successful even when Gaussian noise has the standard deviation as large as 500. Moreover, the norm, computed only on 10% of pixels chosen randomly from images still successfuly recalls a close approximation of original image. Comparing to Amari-Hopeld associative memory, our solution has no spurious states, is less sensitive to noise, and its network complexity is signicantly lower. However, for each new stored image a new subnetwork must be added.