Since lattice algebra based associative memories can store any number k of associated vector pairs (x, y), where x is a real n-dimensional vector and y is a real m-dimensional vector, we propose a basic redundancy mechanism to endow with retrieval capability the dual canonical min-W and max-M lattice associative memories for inputs corrupted by random noise. To achieve our goal, given a finite set of exemplar vectors, redundant patterns are added in order to enlarge the original fixed point set of the original exemplars. The redundant patterns are masked versions designed to be spatially correlated with each exemplar x in a given learning data set. An illustrative example with noisy color images are given to measure the retrieval capability performance of the proposed redundancy technique as considered for lattice associative memories.
Lattice associative memories also known as morphological associative memories are fully connected feedforward
neural networks with no hidden layers, whose computation at each node is carried out with lattice algebra
operations. These networks are a relatively recent development in the field of associative memories that has
proven to be an alternative way to work with sets of pattern pairs for which the storage and retrieval stages use
minimax algebra. Different associative memory models have been proposed to cope with the problem of pattern
recall under input degradations, such as occlusions or random noise, where input patterns can be composed
of binary or real valued entries. In comparison to these and other artificial neural network memories, lattice
algebra based memories display better performance for storage and recall capability; however, the computational
techniques devised to achieve that purpose require additional processing or provide partial success when inputs
are presented with undetermined noise levels. Robust retrieval capability of an associative memory model is
usually expressed by a high percentage of perfect recalls from non-perfect input. The procedure described here
uses noise masking defined by simple lattice operations together with appropriate metrics, such as the normalized
mean squared error or signal to noise ratio, to boost the recall performance of either the min or max lattice auto-associative
memories. Using a single lattice associative memory, illustrative examples are given that demonstrate
the enhanced retrieval of correct gray-scale image associations from inputs corrupted with random noise.
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