## Abstract

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}. We 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 finds 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 ∥_{g} - ℱ_{i}(g)∥. We have experimentally verified that associative recall for images of natural scenes with pixel values in [0,255] is successful even when Gaussian noise has the standard deviation σ 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-Hopfield associative memory, our solution has no spurious states, is less sensitive to noise, and its network complexity is significantly lower. However, for each new stored image a new subnetwork must be added.

Original language | English |
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Pages (from-to) | 1638-1644 |

Number of pages | 7 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E79-A |

Issue number | 10 |

Publication status | Published - 1996 |

Externally published | Yes |

## Keywords

- Associative memory
- Fractals
- Image compression
- Recurrent neural networks