Stochastic resonance of a threshold detector: image visualization and explanation

We explore stochastic resonance (SR) effects in a single comparator (threshold detector) driven by either a Gaussian or exponentially distributed aperiodic signal. The behaviour of different performance measures, namely the cross-correlation coefficient (CCC), signal-to-noise ratio (SNR) and mutual information, I, has been investigated. The signals were added to Gaussian noise before being passed through the threshold detector. For the two signals tested, we observe the perhaps surprising result that the SNR never displays SR. However, SR is displayed by both the CCC and I for Gaussian signals. For exponential signals SR is not displayed by any of the measures. By generating signals whose probability distributions have the generalized Gaussian form Ae-|βx|n it is possible to demonstrate that SR ceases to occur if n<1.7. We conclude that SR is only observable in threshold based systems for certain types of aperiodic signal. Specifically, SR is not expected to occur for signals whose probability density functions have long, slowly decaying, tails. We discuss the implication of these results for the role of SR in biological sensory systems.

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On some applications of vibrational resonance on noisy image perception: the role of the perturbation parameters

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2020.0240 ◽

2021 ◽

Vol 379 (2198) ◽

Cited By ~ 1

Author(s):

S. Morfu ◽

B. I. Usama ◽

P. Marquié

Keyword(s):

Stochastic Resonance ◽

Noise Level ◽

Random Perturbation ◽

Nonlinear Resonance ◽

Image Size ◽

Image Perception ◽

Vibrational Resonance ◽

High Frequency Signal ◽

Threshold Detector ◽

Perturbation Parameters

In this paper, we first propose a brief overview of nonlinear resonance applications in the context of image processing. Next, we introduce a threshold detector based on these resonance properties to investigate the perception of subthreshold noisy images. By considering a random perturbation, we revisit the well-known stochastic resonance (SR) detector whose best performances are achieved when the noise intensity is tuned to an optimal value. We then introduce a vibrational resonance detector by replacing the noisy perturbation with a spatial high-frequency signal. To enhance the image perception through this detector, it is shown that the noise level of the input images must be lower than the optimal noise value of the SR-based detector. Under these conditions, considering the same noise level for both detectors, we establish that the vibrational resonance (VR)-based detector significantly outperforms the SR-based detector in terms of image perception. Moreover, we show that whatever the perturbation amplitude, the best perception through the VR detector is ensured when the perturbation frequency exceeds the image size. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

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