Distribution theory and transform analysis: an introduction to generalized functions, with applications
Signal processing with alpha-stable distributions and applications
Signal processing with alpha-stable distributions and applications
Large Margin Classification Using the Perceptron Algorithm
Machine Learning - The Eleventh Annual Conference on computational Learning Theory
Design of detectors based on stochastic resonance
Signal Processing
Stochastic resonance in noisy threshold neurons
Neural Networks - 2003 Special issue: Advances in neural networks research IJCNN'03
2005 Special Issue: Stochastic resonance in noisy spiking retinal and sensory neuron models
Neural Networks - 2005 Special issue: IJCNN 2005
Noise-enhanced nonlinear detector to improve signal detection in non-Gaussian noise
Signal Processing - Special section: Distributed source coding
Quantizer noise benefits in nonlinear signal detection with alpha-stable channel noise
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Optimal noise benefits in Neyman-Pearson and inequality-constrained statistical signal detection
IEEE Transactions on Signal Processing
Neural signal-detection noise benefits based on error probability
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Noise-enhanced performance for an optimal Bayesian estimator
IEEE Transactions on Signal Processing
VLSI implementations of threshold logic-a comprehensive survey
IEEE Transactions on Neural Networks
Adaptive stochastic resonance in noisy neurons based on mutual information
IEEE Transactions on Neural Networks
Stochastic Resonance in Continuous and Spiking Neuron Models With Levy Noise
IEEE Transactions on Neural Networks
Noise-enhanced clustering and competitive learning algorithms
Neural Networks
Hi-index | 0.00 |
Five new theorems and a stochastic learning algorithm show that noise can benefit threshold neural signal detection by reducing the probability of detection error. The first theorem gives a necessary and sufficient condition for such a noise benefit when a threshold neuron performs discrete binary signal detection in the presence of additive scale-family noise. The theorem allows the user to find the optimal noise probability density for several closed-form noise types that include generalized Gaussian noise. The second theorem gives a noise-benefit condition for more general threshold signal detection when the signals have continuous probability densities. The third and fourth theorems reduce this noise benefit to a weighted-derivative comparison of signal probability densities at the detection threshold when the signal densities are continuously differentiable and when the noise is symmetric and comes from a scale family. The fifth theorem shows how collective noise benefits can occur in a parallel array of threshold neurons even when an individual threshold neuron does not itself produce a noise benefit. The stochastic gradient-ascent learning algorithm can find the optimal noise value for noise probability densities that do not have a closed form.