A new two-level associative memory for efficient pattern restoration

Pattern reconstruction or pattern restoration in the presence of noise is a main problem in pattern recognition. An essential feature of the noise acting on a pattern is its local nature. If a pattern is split into enough sub-patterns, a few of them will be less or more affected by noise, others will remain intact. In this paper, we propose a simple but effective methodology that exploits this fact for the efficient restoration of a pattern. A pattern is restored if enough of its sub-patterns are also restored. Since several patterns can share the same sub-patterns, the final decision is accomplished by means of a voting mechanism. Before deciding if a sub-pattern belongs to a pattern, sub-pattern restoration in the presence of noise is done by an associative memory. Numerical and real examples are given to show the effectiveness of the proposal. Formal conditions under which the proposal guaranties perfect restoration of a pattern from an unaltered or and altered version of it are also given.