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

2021 ◽  
Vol 379 (2198) ◽  
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)’.

Different fast excitations on the improvement of stochastic resonance in bounded noise excited system

2020 ◽  
Vol 34 (26) ◽  
pp. 2050238
Author(s):  
Huayu Liu ◽  
Jianhua Yang ◽  
Houguang Liu ◽  
Shuai Shi
Keyword(s):  
Stochastic Resonance ◽  
Circuit Simulation ◽  
Bistable System ◽  
Key Factors ◽  
Vibrational Resonance ◽  
Bounded Noise ◽  
High Frequency Signal ◽  
Excited System ◽  
Improvement Effect ◽  
Fast Excitation

Stochastic resonance is significant for signal detection. In this paper, a method to improve the stochastic resonance performance in a bistable system excited by bounded noise is studied. Specifically, we add a high-frequency signal to the system as an auxiliary excitation to induce vibrational resonance and focus on the influence of the auxiliary excitation waveform on the improvement effect. We investigate the stochastic resonance performance improved by a fast excitation in different waveforms through numerical simulations. The results show that, the improvement effect of the stochastic resonance depends on the waveform of the fast excitation closely. The symmetry property and constant component of the fast excitation are two key factors. Further, we accomplish the circuit simulation by constructing a circuit to generate bounded noise and the circuit of the bistable system.

QUANTIFYING STOCHASTIC RESONANCE IN A SINGLE THRESHOLD DETECTOR FOR RANDOM APERIODIC SIGNALS

2004 ◽  
Vol 04 (02) ◽  
pp. L247-L265 ◽  
Author(s):  
ARUNEEMA DAS ◽  
N. G. STOCKS ◽  
A. NIKITIN ◽  
E. L. HINES
Keyword(s):  
Stochastic Resonance ◽  
Cross Correlation ◽  
Signal To Noise Ratio ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Surprising Result ◽  
Threshold Detector ◽  
Gaussian Form ◽  
Aperiodic Signal

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.

Saddle-Node Bifurcation and Vibrational Resonance in a Fractional System with an Asymmetric Bistable Potential

2015 ◽  
Vol 25 (02) ◽  
pp. 1550023 ◽  
Author(s):  
J. H. Yang ◽  
Miguel A. F. Sanjuán ◽  
F. Tian ◽  
H. F. Yang
Keyword(s):  
Potential Function ◽  
Fractional Order ◽  
Nonlinear Dynamical Systems ◽  
Technical Problem ◽  
Vibrational Resonance ◽  
High Frequency Signal ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Bistable Potential ◽  
Fractional System

We investigate the saddle-node bifurcation and vibrational resonance in a fractional system that has an asymmetric bistable potential. Due to the asymmetric nature of the potential function, the response and its amplitude closely depend on the potential well where the motion takes place. And consequently for numerical simulations, the initial condition is a key and important factor. To overcome this technical problem, a method is proposed to calculate the bifurcation and response amplitude numerically. The numerical results are in good agreement with the analytical predictions, indicating the validity of the numerical and theoretical analysis. The results show that the fractional-order of the fractional system induces one saddle-node bifurcation, while the asymmetric parameter associated to the asymmetric nature of the potential function induces two saddle-node bifurcations. When the asymmetric parameter vanishes, the saddle-node bifurcation turns into a pitchfork bifurcation. There are three kinds of vibrational resonance existing in the system. The first one is induced by the high-frequency signal. The second one is induced by the fractional-order. The third one is induced by the asymmetric parameter. We believe that the method and the results shown in this paper might be helpful for the analysis of the response problem of nonlinear dynamical systems.

Vibrational resonance in a discrete neuronal model with time delay

2014 ◽  
Vol 28 (16) ◽  
pp. 1450103 ◽  
Author(s):  
Canjun Wang ◽  
Keli Yang ◽  
Shixian Qu
Keyword(s):  
Time Delay ◽  
Input Signal ◽  
High Frequency ◽  
Phase Synchronization ◽  
Low Frequency ◽  
Neuronal Model ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
High Frequency Signal ◽  
Neuron System

The effects of time delay on the vibrational resonance (VR) in a discrete neuron system with a low-frequency signal and a high-frequency signal are investigated by numerical simulations. The results show that there exists a delay time that optimizes the phase synchronization between the low-frequency input signal and the output signal. VR is induced by the time delay. Furthermore, the time delay can improve the response to a low-frequency input signal. Therefore, the time delay plays a constructive role in the transmission of a low-frequency signal by inducing and enhancing VR.

MULTIPLICATIVE STOCHASTIC PERTURBATIONS OF ONE-DIMENSIONAL MAPS

2013 ◽  
Vol 13 (02) ◽  
pp. 1250020 ◽  
Author(s):  
YUKIKO IWATA
Keyword(s):  
Markov Process ◽  
Probability Measure ◽  
Noise Level ◽  
Random Perturbation ◽  
Invariant Probability Measure ◽  
Random Perturbations ◽  
Stochastic Perturbations ◽  
One Dimensional ◽  
One Dimensional Maps

We consider random perturbations of some one-dimensional map S : [0, 1] → [0, 1] such that [Formula: see text] parametrized by 0 < ε < 1, where {Cn} is an i.i.d. sequence. We prove that this random perturbation is small with respect to the noise level 0 < ε < 1 and give a class of one-dimensional maps for which there always exists a smooth invariant probability measure for the Markov process {Xn}n≥0.

Enhancing the Weak Signal With Arbitrary High-Frequency by Vibrational Resonance in Fractional-Order Duffing Oscillators

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
J. H. Yang ◽  
Miguel A. F. Sanjuán ◽  
H. G. Liu
Keyword(s):  
Fractional Order ◽  
High Frequency ◽  
Low Frequency ◽  
Original System ◽  
Scale Transformation ◽  
Weak Signal ◽  
Vibrational Resonance ◽  
High Frequency Signal ◽  
System A ◽  
Auxiliary Signal

When the traditional vibrational resonance (VR) occurs in a nonlinear system, a weak character signal is enhanced by an appropriate high-frequency auxiliary signal. Here, for the harmonic character signal case, the frequency of the character signal is usually smaller than 1 rad/s. The frequency of the auxiliary signal is dozens of times of the frequency of the character signal. Moreover, in the real world, the characteristic information is usually indicated by a weak signal with a frequency in the range from several to thousands rad/s. For this case, the weak high-frequency signal cannot be enhanced by the traditional mechanism of VR, and as such, the application of VR in the engineering field could be restricted. In this work, by introducing a scale transformation, we transform high-frequency excitations in the original system to low-frequency excitations in a rescaled system. Then, we make VR to occur at the low frequency in the rescaled system, as usual. Meanwhile, the VR also occurs at the frequency of the character signal in the original system. As a result, the weak character signal with arbitrary high-frequency can be enhanced. To make the rescaled system in a general form, the VR is investigated in fractional-order Duffing oscillators. The form of the potential function, the fractional order, and the reduction scale are important factors for the strength of VR.

An improved adaptive stochastic resonance method for improving the efficiency of bearing faults diagnosis

2017 ◽  
Vol 232 (13) ◽  
pp. 2352-2368 ◽  
Author(s):  
Dawen Huang ◽  
Jianhua Yang ◽  
Jingling Zhang ◽  
Houguang Liu
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Signal To Noise Ratio ◽  
Fault Simulation ◽  
Resonance Method ◽  
Bistable System ◽  
Scale Transformation ◽  
High Frequency Signal ◽  
Bearing Fault ◽  
Feature Information

The general scale transformation (GST) method is used in the bistable system to deal with the weak high-frequency signal submerged into the strong noisy background. Then, an adaptive stochastic resonance (ASR) method with the GST is put forward and realized by the quantum particle swarm optimization (QPSO) algorithm. Through the bearing fault simulation signal, the ASR method with the GST is compared with the normalized scale transformation (NST) stochastic resonance (SR). The results show that the efficiency of the GST method is higher than the NST in recognizing bearing fault feature information. In order to simulate the actual engineering environment, both the adaptive GST and the NST methods are implemented to deal with the same experimental signal, respectively. The signal-to-noise ratio (SNR) of the output is obviously improved by the GST method. Specifically, the efficiency is improved greatly to extract the weak high-frequency bearing fault feature information. Moreover, under different noise intensities, although the SNR is decreased versus the increase of the noise intensity, the ASR method with the GST is still better than the traditional NST SR. The proposed GST method and the related results might have referenced value in the problem of weak high-frequency feature extraction in engineering fields.

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