Geometric associative memories applied to pattern restoration

Two main research areas in Pattern Recognition are pattern classification and pattern restoration. In the literature, many models have been developed to solve many of the problems related to these areas. Among these models, Associative Memories (AMs) can be highlighted. An AM can be seen as a one-layer Neural Network. Recently, a Geometric Algebra based AM model was developed for pattern classification, the so-called Geometric Associative Memories (GAMs). In general, AMs are very efficient for restoring patterns affected BY either additive or subtractive noise, but in the case of mixed noise their efficiency is very poor. In this work, modified GAMs are used to solve the problem of pattern restoration. This new modification makes use of Conformal Geometric Algebra principles and optimization techniques to completely and directly restore patterns affected by (mixed) noise. Numerical and real examples are presented to test whether the modification can be efficiently used for pattern restoration. The proposal is compared with other reported approaches in the literature. Formal conditions are also given to ensure the correct functioning of the proposal.