Suprathreshold stochastic resonance and noise-enhanced Fisher information in arrays of threshold devices

Abstract

We analyze the parametric estimation that can be performed on a signal buried in noise based on the parsimonious representation provided by a parallel array of threshold devices. The Fisher information contained in the array output about the input parameter is used as the measure of performance in the estimation task. For estimation on a suprathreshold input signal, we establish that enhancement of the Fisher information can be obtained by addition of independent noises to the thresholds in the array. Similar improvement by noise is also shown to be possible for the estimation error of the maximum likelihood estimator. These results extend the applicability of the recently introduced nonlinear phenomenon of suprathreshold stochastic resonance.

Noise-Improved Bayesian Estimation With Arrays of One-Bit Quantizers

“…Since its recent introduction in [22], suprathreshold SR has been shown to be possible in various conditions, with different types of signals and indexes of performance, including Shannon mutual information [3], [22], [23], input-output cross correlation [24], Fisher information [25], or signal-to-noise ratio [26]. Suprathreshold SR has also been applied to arrays of sensory neurons [27], to motion detectors [28], and to cochlear implants [29].…”

Optimal coding of a random stimulus by a population of parallel neuron models

“…We relate recent results 1 on a general model known as the Suprathreshold Stochastic Resonance (SSR) model [2][3][4][5][6][7][8][9][10][11][12][13] to rate coding in sensory neural populations. Information theory is used to demonstrate that the SSR model is equivalent to a large population of sensory neurons that can overcome the effects of noise to produce an accurate rate-code representation of an analog random stimulus.…”

Noise-enhanced nonlinear detector to improve signal detection in non-Gaussian noise

“…This non-standard strategy to design suboptimal detectors based on two-state quantizers benefits from recent studies on the use of stochastic resonance and the constructive role of noise in nonlinear processes [9][10][11][12][13][14]. This paradoxical nonlinear phenomenon, has been intensively studied during the last two decades.…”

“…Recently, another form of stochastic resonance was proposed in [9,10], with parallel arrays of two-state quantizers, under the name of suprathreshold stochastic resonance. This form in [9][10][11][12][13][14] applies to signals of arbitrary amplitude, which do not need to be small and subthreshold, whence the name. Different measures of performance have been studied to quantify the suprathreshold stochastic resonance: general information measures like the input-output Shannon mutual information [9], the input-output correlation coefficient [11], signal-to-noise ratios [11,13], in an estimation context with the Fisher information contained in the array output [12] or in a detection context with a probability of error [14].…”