Published on February 16, 2014
Noise-induced amplification of MEA signal based in Stochastic Resonance Francisco Fambrini José Hiroki Saito
Stochastic Resonance • Stochastic resonance (SR) is a phenomenon where a signal that is normally too weak to be detected by a sensor, can be boosted by adding white noise to the signal, which contains a wide spectrum of frequencies. • The added white noise can be enough to be detectable by the sensor, which can then filter it out to effectively detect the original, previously undetectable signal. • Extends to many other systems, whether electromagnetic, physical or biological, and is an area of intense research. R. Benzi, A. Sutera and A. Vulpiani, The mechanism of stochastic resonance, J. Phys. A14, L453-L457 (1981).
What is Stochastic Resonance ? • Stochastic Resonance (SR) is the name of a phenomenon that has been studied by physicists for more than 25 years, because there are circunstances in which a noise or unpredictable fluctuations can be used purposefully or deliberately introduced to obtain a benefit
What is Stochastic Resonance ? • When the random noise in the form of electronic fluctuations corrupts or transmitted electromagnetic interference messages, it imposes limits on the rate at which error-free Communication can be achieved. If everything else is optimal, then Noise is the enemy.
What is Stochastic Resonance ? • In particular, the paradoxical notion of'' good'' noise is a double-edged sword for researchers to SR. • How to use a good noise so as to ensure its operation within a solution with stochastic resonance?
What is Stochastic Resonance ? • Stochastic Resonance (SR) is a term originally used for a specific, and is now widely applied context to describe any phenomenon whose which the presence of noise in a nonlinear system is better for the quality of the output signal of his absence.
What is Stochastic Resonance ? • This idea can be distilled into stating that whenever SR occurs, it must be true that Performance(noise+nonlinearity) > performance(nonlinearity).
What is Stochastic Resonance ? • The term stochastic resonance was first used in the context of noise enhanced signal processing in 1980 by Roberto Benzi, at the International School of Climatology, as a name for the mechanism suggested to be behind the periodic behavior of the Earth's ice ages. The same idea was independently proposed. Stochastic resonance has been used in accordance with the ISI-Web of Science database from over 2,300 publications Fig. 1.
Fig. 1 Frequency of stochastic resonance papers by year—between 1981 and 2007—according to the ISI database.
"What is Stochastic Resonance ? • About 20% of papers in SR also include a reference in the title, abstract or keywords with the neuron or neural words, illustrating the great interest in studying a positive role for randomness in neural function.
What is Stochastic Resonance ? • Stochastic resonance is often described as a phenomenon. This is mainly due to its historic past, once since coining the term in 1980, virtually all research only considered systems where the input SR was a combination of a periodic input signal single frequency and broadband noise.
Stochastic resonance as ‘‘noise benefits’’ • The term stochastic resonance is now used so frequently in the much wider sense of being the occurrence of any kind of noise-enhanced signal processing, that we believe this common usage has, by ‘‘weight of numbers’’, led to are definition. Indeed, electrical engineer Bart Kosko, who made pioneering developments in fuzzy logic and neural networks, concisely defines SR in his popular science book Noise as meaning ‘‘noise benefit’’. Kosko also states the caveat that the noise interferes with a ‘‘signal of interest’’, and we concur that SR can be defined as a ‘‘noise benefit in a signal-processing system’’, or alternatively ‘‘noise-enhanced signal processing’’.
Stochastic resonance as ‘‘noise benefits’’ • We emphasize here is the fact that only occurs within the context SR increase the signal, since this is the feature that differentiates it from make the list of phenomena that could be described as operating some form of noise, and still may not be all defined in terms of an improved signal.
Biomedical Applications of SR • A different form of indirect evidence for SR existing naturally in biology is successful biomedical applications. A particularly notable example is the use of electrically generated subthreshold stimuli in biomedical prosthetics to improve human balance control and somato sensation. This work led to James J. Collins winning a estigious MacArthur Fellowship in October 2003.
What is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology “ Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations—e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being “suboptimal”. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the “neural code”. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain.” Mark D. McDonnell1 and Derek Abbott, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2660436/
Symmetrical double-sided potential well Stochastic Resonance: from climate to biology Roberto Benzi, Dipartimento di Fisica and INFN, Universit`a di Roma ,2008.
Detection of weak signals P. Hänggi, Stochastic resonance in biology - How noise can enhance detection of weak signals and help improve biological information processing, ChemPhysChem 3, 285-290 (2002).
Signal-noise-ratio (SNR) Three power spectra of spike trains recorded at near optimal noise intensity using a neuron model (Fitzhugh-Nagumo). Stimulated at 55 Hz, the signal features (sharp peaks at about 55 Hz) are clearly visible. It is obvious that their amplitude changes with noise intensity with the maximum amplitude obtained at the optimal value of noise. The lower panel also shows clearly that noise larger than optimum raises the noise floor and reduces the relative amplitude of the signal feature. Mechanoreceptors and stochastic resonance,Dr. Lon A. Wilkens, Biology and Center for Neurodynamics, University of Missouri-St. Louis
Convencional photo spectroscopy
noise is added in each pixel of image Dmitry V. Dylov, Jason W. Fleischer, 2010: Nonlinear self-filtering of noise images via dynamical stochastic resonance, Nature Photonics, Vol.: Advance online publication, DOI: 10.1038/nphoton.2010.31
Photoacoustic spectroscopy - 2
SR in signal analysis • A related phenomenon is dithering applied to analog signals before analog-to-digital conversion. Stochastic resonance can be used to measure transmittance amplitudes below an instrument's detection limit. If Gaussian noise is added to a subthreshold (i.e., immeasurable) signal, then it can be brought into a detectable region. After detection, the noise is removed. A fourfold improvement in the detection limit can be obtained.
Photoacoustic signals: photospectrometry with SR This work is based in this paper: Huiyu Song · Xueguang Shao · Qingde Su, 2001 “A study on the detection of weak photoacoustic signals by stochastic resonance”, Fresenius J Anal Chem, 370 :1087– 1090
“A study on the detection of weak photoacoustic signals” A simulated signal was used to test the performance of adjusting μ. In the simulated signal, A ×Sign(t) of Input(t) was s imulated from the Gaussian equation. A =0.05 · D × Noise(t) was chosen randomly from a uniform distribution on the interval (0.0,1.0). The length of Input(t) was 2000 points Ordinate S and abscissa X were arbitrary units because they were simulated signals. Equation (1) was adopted as the non-linear system μ was adjusted with other conditions unchangeable to obtain the value which output the optimum SNR. The program was written in C++ and implemented on an IBMP166/32 M computer. PA spectrum of real sample. The PA spectrometer was constructed in our laboratory without a lock-in amplifier. Light from a 500 W xenon lamp was converted into monochromatic light by means of a CT-30F monochromator and the modulated light was then incident on a CH-353 chopper. The acoustic wave generated after illumination of the sample by light was detected by means of a microphone (ERM-10). The output signal of the microphone was fed to a preamplifier (Model-115). The data from the sample were collected on an A/ D converter and processed by means of a computer. • Erythrosin was used as the sample for the PA signal. Erythrosin spectra were normalized against carbon black to take into account spectral variations resulting from the light source and the spectrometer. The spectral range was 450–650 nm.
Convencional amplification in MEA systems • Operational Amplifier: non-inverter and inverter But... SR need nonlinear device or system: the input-output relationship must be nonlinear !
Dead zone: non-linear region
Weak signal + noise in op amp
Multielectrode Array aplications of SR • Can we perform MEA signal amplification using SR ?
Diode white noise generation The first stage is noise generation, where the constant power output is produced. We can to generate noise with the zener breakdown phenomenon that´s occur when a zener diode is run in the reverse breakdown region of operation. This usually occurs when approximately -1mA of current is passed through the diode. At this current level the zener diode enters reverse breakdown and the current through it drops rapidly while the voltage across it remains relatively constant. This voltage level is termed zener voltage and is represented by VZ. The I-V plot showing this phenomenon is shown in Figure. The noise generated while operating a zener diode in this region is based on the avalanche breakdown that occurs in the pn junction.
Electronic white noise generator • A Noise generator is a circuit that produces electrical noise (random signal). Two NPN bipolar transistors (BJT) are tied together at their bases and connected to the same power supply. One of the BJTs is connected to the powersupply at its collector terminal and tied to ground at the emitter. The other BJT is connected to the power supply at its emitter terminal and the collector terminal is floating. This essentially creates a pn junction all the same creates a pn junction all the same as zener diode. The next step in the generation process was to make sure that we were operating the transistors (pn junction) in the reverse breakdown region.
Complete first stage: noise gen
Optimal intensity of the noise • The optimal intensity of the noise must be adjusted as the nature of the signal to be detected changes. Intensity of noise x Signal noise ratio Austrian Journal of Statistics, Vol. 32 (2003), No. 1&2, 49-70
Photo of the prototype
Senoidal pure signal
Attenuated sinusoidal signal
Noise + sinusoidal signal - 1
Noise + sinusoidal signal - 2
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