Extended Associative Memories for Recalling Gray Level Patterns

Abstract

We show how the binary αβ associative memories recently proposed by Yáñez in [1] can be extended to work now in the gray-level case. To get the desired extension we take the operators α and β, foundation of the αβ memories, and propose a more general family of operators among them the original operators α and β are a subset. For this we formulate a set of functional equations, solve this system and find a family of solutions. We show that the α and β originally proposed in [1] are just a particular case of this new family. We give the properties of the new operators. We then use these operators to build the extended memories. We provide the conditions under which the proposed extended memories are able to recall a pattern either from the pattern’s fundamental set or from altered versions of them. We provide real examples with images where the proposed memories show their efficiency.