S. Morfu

Stochastic Resonance Another Way to Retrieve Subthreshold Digital Data

A new type of electronic receiver based on stochastic resonance properties is proposed to retrieve subthreshold modulated (or not) digital signals. In order to check the receiver performances, we investigated different kinds of modulations. Considering both uniform and Gaussian white noise, a total restoration of the emitted data is achieved for an unmodulated or amplitude modulated (AM) signals, while an almost total restoration is reached using a frequency shift keying (FSK) modulation. These experimental results confirm the great interest of stochastic resonance in the signal transmission field.

Nonlinear Systems for Image Processing

I Introduction 79II Mechanical Analogy 83A Overdamped Case 84B Inertial Systems 90III Inertial Systems 95A Image Processing 95B Electronic Implementation 103IV Reaction-Diffusion Systems 108A One-Dimensional Lattice 108B Noise Filtering of a One-Dimensional Signal 111C Two-Dimensional Filtering: Image Processing 119V Conclusion 133VI Outlooks 134A Outlooks on Microelectronic Implementation 134B Future Processing Applications 135Acknowledgments 141Appendix A 142Appendix B 143Appendix C 144Appendix D 145References 146

A NONLINEAR OSCILLATORS NETWORK DEVOTED TO IMAGE PROCESSING

A contrast enhancement and image inverting tool using a lattice of uncoupled nonlinear oscillators is proposed. We show theoretically and numerically that the gray scale picture contrast is strongly enhanced even if this one is initially very small. An image inversion can be also obtained in real time with the same Cellular Nonlinear Network (CNN) without reconfiguration of the network. A possible electronic implementation of this CNN is finally discussed.

Analog simulation of neural information propagation using an electrical FitzHugh–Nagumo lattice

A nonlinear electrical lattice modelling neural information propagation is presented. It is shown that our system is an analog simulator of the FitzHugh–Nagumo equations, and hence supports pulse propagation with the appropriate properties.

Revisiting the asymmetric binary channel: joint noise-enhanced detection and information transmission through threshold devices

In this paper we revisit the asymmetric binary channel from the double point of view of detection theory and information theory. We first evaluate the capacity of the asymmetric binary channel as a function of the probabilities of false alarm and of detection, thus allowing a noise distribution independent analysis. This sets the a priori probabilities of the hypotheses and couples the two points of view. We then study the simple realization of the asymmetric binary channel using a threshold device. We particularly revisit noise-enhanced processing for subthreshold signals using the aforementioned parametrization of the capacity, and we report a somewhat paradoxical effect: using the channel at its capacity precludes in general an optimal detection.

DIGITAL INFORMATION RECEIVER BASED ON STOCHASTIC RESONANCE

An electronic receiver based on stochastic resonance is presented to rescue subthreshold modulated digital data. In real experiment, it is shown that a complete data restoration is achieved for both uniform and Gaussian white noise.

NOISE-ENHANCED PROPAGATION IN A DISSIPATIVE CHAIN OF TRIGGERS

We study the influence of spatiotemporal noise on the propagation of square waves in an electrical dissipative chain of triggers. By numerical simulation, we show that noise plays an active role in improving signal transmission. Using the Signal to Noise Ratio at each cell, we estimate the propagation length. It appears that there is an optimum amount of noise that maximizes this length. This specific case of stochastic resonance shows that noise enhances propagation.

PROPAGATION FAILURE INDUCED BY COUPLING INHOMOGENEITIES IN A NONLINEAR DIFFUSIVE MEDIUM

Kink propagation failure induced by coupling inhomogeneities in a Nagumo lattice is investigated. Considering the case of weak couplings, we define analytically and numerically the coupling conditions leading to the pinning of the kink.

Noise induced breather generation in a sine–Gordon chain

We consider a sine–Gordon chain driven sinusoidally at one end. In the absence of noise, there exists a well known critical value of the amplitude beyond which breather modes can be generated via the phenomenon of supratransmission. We consider values of the driving amplitude below the critical amplitude such that no breather propagates in the medium. We show that noise induces breather generation with a given probability depending on the noise intensity. We also propose a bifurcation diagram which extends the supratransmission effect to a more realistic signal, namely a noisy sinusoidal excitation. We finally discuss some promising signal processing applications that can be developed by taking into account the contribution of noise in the media sharing this supratransmission phenomenon.

EXPERIMENTS ON AN ELECTRICAL NONLINEAR OSCILLATORS NETWORK

We have recently proposed a Cellular Nonlinear Network (CNN) based on nonlinear oscillator properties to perform image processing tasks. We present here the electronic implementation of the elementary cell of this CNN. We experimentally verify the main property of the CNN, that is the possibility to enhance a weak difference of initial condition between two specific cells of the CNN at a given time. For this optimal time, a contrast enhancement of a weak contrasted gray scale is possible.