The performance capability of quadratic Hebbian type associative memories (QHAM's) in the presence of interconnection faults is examined, and equations for predicting the probability of direct convergence P(dc) given a fraction of interconnection faults are developed. The interconnection faults considered are the equivalent of open circuit and short circuit synaptic interconnections in electronic implementations. Our results show that a network with open circuit interconnection faults has a higher probability of direct convergence P (dc) than a network with short circuit interconnection faults, when the fraction of failed interconnections p is small and the short circuit signal G is large. Certain values of G are found to have only mild effects on network performance degradation. Network reliability characteristics taking the generalization capability into account are also analyzed. All of these results are compared with those of Hebbian type associative memories (HAM's), which have linear association network models. Our results indicate that QHAM's have much higher network capacity and fault tolerance capability in the presence of interconnection faults. However, the fault tolerance to input errors in QHAM's is much less than that of HAM's.

The performance of Hebbian-type associative memories (HAMs) in the presence of faulty (open- and short-circuit) synaptic interconnections is examined and equations for predicting network reliability are developed. The results show that a network with open-circuit interconnection faults has a higher probability of direct convergence than a network with short-circuit interconnection faults when the fraction of failed interconnections is small and the short-circuit signal is large. The results are extended to the case where network attraction radius is considered. Under certain assumptions, it is found that the expected numbers of neurons with b, b-1, b-2,. . .,1 input error bits in their state update are equal. Because of the capability of error correction, an asynchronous HAM is also found to have a higher probability of direct convergence than a synchronous HAM. Using these results, network reliability and generalization capability can be estimated when both the interconnection faults and the number of error bits in the probe vectors are taken into account.

A statistical method is applied to explore the unique characteristics of a certain class of neural network autoassociative memory with N neurons and first-order synaptic interconnections. The memory matrix is constructed to store M = αN vectors based on the outer-product learning algorithm. We theoretically prove that, by setting all the diagonal terms of the memory matrix to be M and letting the input error ratio ρ = 0, the probability of successful recall Pr steadily decreases as α increases, but as α increases past 1.0, Pr begins to increase slowly. When 0 < ρ ≤ 0.5, the network exhibits strong error-correction capability if α ≤ 0.15 and this capability is shown to rapidly decrease as α increases. The network essentially loses all its error-correction capability at α = 2, regardless of the value of ρ. When 0 < ρ ≤ 0.5, and under the constraint of Pr > 0.99, the tradeoff between the number of stable states and their attraction force is analyzed and the memory capacity is shown to be 0.15N at best.

The performance of Hebbian-type associative memories (HAMs) in the presence of faulty interconnections is examined, and equations for predicting network reliability are developed. Several HAM operating modes, i.e. zero or nonzero autoconnections (ZA or NZA), bipolar or unipolar network inputs, asynchronous or synchronous operation, have been investigated. Networks with NZA and bipolar inputs have the best performance in both capacity and reliability. An equation relating the probability of direct one-step convergence,Pdc, to the percentage of failed connections is derived. For a connection failure rate of up to 50%, this equation can estimatePdcaccurately. The reliability becomes poorer when the network size increases; hence, reducing the percentage of failed connections becomes very important in physical implementations of large networks. Also, as the number of stored vectors increases, the network reliability decreases. Asynchronous-mode and synchronous-mode operation have the samePdcand reliability when there are no error bits in the probe vector, but networks operating in the asynchronous mode have higher Pdcand better reliability when the number of input errors increases. Reliability measures for second-order HAMs are also investigated

Statistical parameters that can be used to estimate the convergence probability of arbitrary-order Hebbian-type neural network associative memories (HAMs) withNneurons andMstored patterns are developed. The principle involves using two figures of merit, ε/η and ηN, to determine the convergence probability for indirect (iterative) convergence and direct (one-step) convergence HAMs. Given η, the probability that a neuron changes to an incorrect bit after one update, the parameter ε/η determines the capability of converging iteratively to at most εNbits away from the stored vector after a stable state is reached, where 0Pic≈1.0 for all HAMs having ε/η>20. If precise convergence to the stored vector is required in one step, the parameter ηNis used to determine the probability of direct convergence,Pdc

A number of adaptive estimators to restore images degraded by signal-dependent film grain noise have been derived. These estimators are characterized by their ability to adapt to the nonstationary properties of the image signal distribution. This adaptability results in restored images with better contrast and noise suppression properties when compared with nonadaptive estimators. Lookup tables were extensively used in order to reduce the computation time. In addition to the optimal Bayesian estimators, two suboptimal estimators were presented. Results of computer simulations conducted to evaluate the performances of the estimators using various image quality measures were also presented.

An algorithm is presented for calculating recognition error when applying pattern vectors to an optimum Bayes' classifier. The pattern vectors are assumed to come from two classes whose populations have Gaussian statistics with unequal covariance matrices and arbitrary a priori probabilities. The quadratic discriminant function associated with a Bayes' classifier is used as a one-dimensional random variable from which the probability of error is calculated, once the distribution of the discriminant function is obtained.

A new criterion for measuring separability of two pattern classes is given that is based on the determination of an averaged minimum distance from the mean feature vectors of two classes to an optimal separating hypersurface determined by Baye's postulate.