Robust image retrieval from noisy inputs using lattice associative memories

Abstract

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 autoassociative 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.

Multivariate Data Retrieval Modified by Random Noise using Lattice Autoassociative Memories with Eroded or Dilated Input Residuals

“…Noise masking [12][13][14] was originally proposed to endow a single LAAM with recall capability for multivariate data degraded by random noise. Furthermore, the noise masking strategy has been recently used to good advantage to increase retrieval performance in max-plus projection autoassociative morphological memories and their fuzzy analogs [15][16][17].…”

“…Based on the theoretical results given by Theorem 3 and Corollary 4 in Section 2 as well as the qualitative comments made in the last paragraph of the same section, the following two subsections present an alternative approach to the noise masking technique developed in earlier papers [12][13][14] and its improvements as described in [15][16][17].…”

“…evaluates the true (clipped value) or false expression (non-clipped value) upon verification of a logical condition. Assuming thatx is a noisy vector obtained with Algorithm I, then the proposed thresholding functions (14) or ( 15) defined component-wise, will produce an erodedẽ or dilated versionõ ofx. where the threshold and domain bound parameters appear explicitly.…”

“…The recall failure of the min AMM for inputs degraded by dilative noise and similarly, the poor performance of the max AMM for inputs corrupted with erosive noise, and consequently their inapplicability to deal with mixed random noise has been exposed repeatedly since their introduction [3,7] and revisited across the most recent theoretical results discovered about them [6,11]. By capitalizing the robustness to either erosive or dilative noise, respectively, of the min-and max-LAAMs, a practical solution to pattern recall from inputs corrupted by mixed random noise using only one of the canonical LAAMs was initiated by masking the noise contained in the corrupted input pattern [12][13][14]. Based on selective pattern indexing, further improvement of the noise masking strategy and its extension to fuzzy type associative morphological memories have been recently reported in [15,16] and [17].…”