Sparsely Connected Autoassociative Fuzzy Implicative Memories for the Reconstruction of Large Gray-Scale Images

Autoassociative fuzzy implicative memories (AFIMs) are models that exhibit optimal absolute storage capacity and an excellent tolerance with respect to incomplete or eroded patterns. Thus, they can be effectively used for the reconstruction of gray-scale images. In practice, however, applications of AFIMs are confined to images of small size due to computational limitations. This paper introduces a class of sparsely connected AFIMs (SCAFIMs) that circumvent this computational overhead and, therefore, can be used for the reconstruction of large images. We show that SCAFIMs exhibit optimal absolute storage capacity and tolerance with respect to incomplete or eroded patterns. Furthermore, we compare the performance of SCAFIMs with their corresponding fully connected AFIM both theoretically and by means of computational experiments.