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Optimal noise-aided signal transmission through populations of neurons.

Metabolic considerations and neurophysiological measurements indicate that biological neural systems prefer information transmission via many parallel low intensity channels, compared to few high intensity ones [S. B. Laughlin et al., Nature Neurosci. 1, 36 (1998)]. Furthermore, cortical neurons are exposed to a considerable amount of synaptic background activity, which increases the neurons' conductance and leads to a fluctuating membrane potential that, on average, is close to the threshold [A. Destexhe and D. Paré, J. Neurophysiol. 81, 1531 (1999)]. Recent studies have shown that noise can improve the transmission of subthreshold signals in populations of neurons, e.g., if their response is pooled. In general, the optimal noise level depends on the stimulus distribution and on the number of neurons in the population. In this contribution we show that for a large enough number of neurons the latter dependency becomes weak, such that the optimal noise level becomes almost independent of the number of neurons in the population. First we investigate a binary threshold model of neurons. We derive an analytic expression for the optimal noise level at each single neuron, which-for a large enough population size-depends only on quantities that are locally available to a single neuron. Using numerical simulations, we then verify the weak dependence of the optimal noise level on population size in a more realistic framework using leaky integrate-and-fire as well as Hodgkin-Huxley-type model neurons. Next we construct a cost function, where quality of information transmission is traded against its metabolic costs. Again we find that-for subthreshold signals-there is an optimal noise level which maximizes this cost. This noise level, however, is almost independent of the number of neurons, even for small population sizes, as numerical simulations using the Hodgkin-Huxley model show. Since the dependence of the optimal noise level on population size is weak for large enough populations, local neural adaptation is sufficient to adjust the level of noise to its optimal value.

Animals↗

Discriminating additive from dynamical noise for chaotic time series.

We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only for one variable of the system, while the noise corrupting the second variable is still Gaussian distributed independent of distribution of dynamical noise. Based on these results and using scaling properties of the correlation entropy, we propose a simple method of discriminating additive from dynamical noise. This approach is also useful for estimation of noise level for chaotic time series. We show that the proposed method works well in a wide range of noise levels, providing that one kind of noise predominates and we analyze the variable of the system for which the contamination follows Cauchy-like distribution in the presence of dynamical noise.

Journal Article↗

Resonant-pattern formation induced by additive noise in periodically forced reaction-diffusion systems.

We report frequency-locked resonant patterns induced by additive noise in periodically forced reaction-diffusion Brusselator model. In the regime of 2:1 frequency-locking and homogeneous oscillation, the introduction of additive noise, which is colored in time and white in space, generates and sustains resonant patterns of hexagons, stripes, and labyrinths which oscillate at half of the forcing frequency. Both the noise strength and the correlation time control the pattern formation. The system transits from homogeneous to hexagons, stripes, and to labyrinths successively as the noise strength is adjusted. Good frequency-locked patterns are only sustained by the colored noise and a finite time correlation is necessary. At the limit of white noise with zero temporal correlation, irregular patterns which are only nearly resonant come out as the noise strength is adjusted. The phenomenon induced by colored noise in the forced reaction-diffusion system is demonstrated to correspond to noise-induced Turing instability in the corresponding forced complex Ginzburg-Landau equation.

Journal Article↗

Interpreting anomalously low voltage noise in two-channel measurement systems.

In this work we 1) analyze and give a theoretical explanation for the anomalously low cross-spectral density of voltage fluctuations that is observed when two thermal noise sources with matched intensities are coupled to the inputs of two-channel phase modulation (PM) or amplitude modulation (AM) noise measurement systems (NMS), 2) empirically evaluate spectral resolutions of different types of measurement systems, and 3) discuss noise measurement techniques involving cross-correlation signal processing. Our work shows that the statistical uncertainty, which sets the ultimate spectral resolution in the thermal noise limited regime, is approximately the same for both systems. However, in practical terms, the non-stationary nature of the noise, the temporal separation of calibration and measurement, and the difficulty of reproducing the calibrations for two measurements make it extremely difficult to resolve noise that is more than 10 dB below the noise floor in a single channel NMS. In a two-channel NMS, however, the calibrations of the two channels are carried out simultaneously, and one can take full advantage of a large number of averages and make reproducible noise measurements with resolution 10 dB below the noise floor of a single channel NMS.

Journal Article↗

A fuzzy impulse noise detection and reduction method.

Removing or reducing impulse noise is a very active research area in image processing. In this paper we describe a new algorithm that is especially developed for reducing all kinds of impulse noise: fuzzy impulse noise detection and reduction method (FIDRM). It can also be applied to images having a mixture of impulse noise and other types of noise. The result is an image quasi without (or with very little) impulse noise so that other filters can be used afterwards. This nonlinear filtering technique contains two separated steps: an impulse noise detection step and a reduction step that preserves edge sharpness. Based on the concept of fuzzy gradient values, our detection method constructs a fuzzy set impulse noise. This fuzzy set is represented by a membership function that will be used by the filtering method, which is a fuzzy averaging of neighboring pixels. Experimental results show that FIDRM provides a significant improvement on other existing filters. FIDRM is not only very fast, but also very effective for reducing little as well as very high impulse noise.

Algorithms↗

A switching median filter with boundary discriminative noise detection for extremely corrupted images.

A novel switching median filter incorporating with a powerful impulse noise detection method, called the boundary discriminative noise detection (BDND), is proposed in this paper for effectively denoising extremely corrupted images. To determine whether the current pixel is corrupted, the proposed BDND algorithm first classifies the pixels of a localized window, centering on the current pixel, into three groups--lower intensity impulse noise, uncorrupted pixels, and higher intensity impulse noise. The center pixel will then be considered as "uncorrupted," provided that it belongs to the "uncorrupted" pixel group, or "corrupted." For that, two boundaries that discriminate these three groups require to be accurately determined for yielding a very high noise detection accuracy--in our case, achieving zero miss-detection rate while maintaining a fairly low false-alarm rate, even up to 70% noise corruption. Four noise models are considered for performance evaluation. Extensive simulation results conducted on both monochrome and color images under a wide range (from 10% to 90%) of noise corruption clearly show that our proposed switching median filter substantially outperforms all existing median-based filters, in terms of suppressing impulse noise while preserving image details, and yet, the proposed BDND is algorithmically simple, suitable for real-time implementation and application.

Algorithms↗

Muscle noise and interference behavior in pacemakers: a comparative study.

Inhibition of VVI pacemakers by muscle noise, though known since 1972, has attracted increased interest in recent years. More sensitive dual chamber atrial synchronized pacemakers have proved to be more susceptible to interference and will further enhance the effort at improving pacemaker resistance to interference of all kinds. To study the reaction of 16 pacemakers of 10 different manufacturers with respect to muscle noise, we stored a noisy episode on a 16-second endless loop tape. Each pacemaker was subjected to an identical muscle noise signal, with amplitude varied to reach the response threshold. The results are: The range of muscle noise thresholds consists of more than one decade, varying from 0.4 mV to 4.6 mV. Only 4 of 16 pacemakers remained unaffected if a noise signal of 3 mV maximum is assumed. In 11 out of 16 pacemakers, the threshold amplitude for muscle noise is lower than that for intracardiac electrographic signals which can be explained by a sensitizing mechanism caused by noise. Five pacemakers were so sensitive that even a sensitivity setting of 4 mV would not reject muscle noise. Filtering muscle noise, 50-Hz signals, and intracardiac electrograms with a 12 dB filter of variable upper cut-off frequency revealed that heart signals are always attenuated more than interference signals.

Electricity↗

White noise analysis of pace-maker-response interactions and non-linearities in slowly adapting crayfish stretch receptor.

Input-output relations were investigated in the slowly adapting stretch receptor organ of crayfish using a Gaussian white noise length input with a 0.03-12.5 Hz band width and the resulting action potential output. The noise input was presented to the de-efferented receptor in situ, at three mean elongations and at four different amplitudes. The three mean elongations were set within the normal range in vivo, two at the extremes close to the minimum and maximum physiological lengths and the other in the mid-range. With white noise inputs there is a finite probability that the system will be tested in all possible conditions within the chosen band width because white noise has the advantage that it contains, with a finite probability, all possible stimulus wave forms at random. The analysis indicated similarities between the effects of the input variables, namely white noise amplitude and mean elongation. With low input variables the activity was periodic. With larger inputs, impulse rates were higher and irregular. The average length trajectories leading to a spike (i.e. the average stimulus) were either biphasic with high inputs or multiphasic and periodic with lower input variables. The frequency of periodicity increased with mean elongation. Although for a given length and noise amplitude a variety of individual length trajectories preceded spikes, the final biphasic shortening-lengthening average stimulus sequence before a spike was similar in all cases irrespective of the input variables. The number of possible trajectories decreased with increments in the input variables. The standard deviation of length values for each average stimulus was computed and displayed as a function of time relative to the spike. It was first constant, and decreased gradually to a minimum value at the spike reference. Standard deviation values were lower for higher white noise amplitudes and mean elongation. Simple, short-lasting stimulus wave forms in the white noise were isolated and the corresponding responses were computed. Responses were periodic at low input variables and aperiodic with larger inputs and also asymmetric, being larger and briefer for lengthenings than for shortenings. Asymmetries augmented with input increments. Investigation of the interactions between the pace-maker and the white noise effects showed that lengthenings were more effective when they occurred just after a spike while the effectiveness of shortenings was greater just before a spike.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗

Membrane current noise in toad retinal rods exposed to low external calcium.

Outer segment membrane current of single rod photoreceptors from toad retina was recorded with a suction electrode, and extracellular calcium concentration was manipulated by transferring the recorded cell from one pool of saline to another or by locally perfusing the outer segment. The large increase in dark current that resulted from exposure to low-calcium saline was accompanied by an increase in dark noise in the band 1-800 Hz. This noise was suppressed by bright light, and its power spectrum could be described by a single Lorentzian equation with average corner frequency of 40.1 +/- 9.5 Hz (mean +/- S.D., n = 11). In low-calcium saline, saturating flash responses were often followed by a transient increase in the dark current lasting 30-100 s. During this rebound period of increased dark current, increased dark noise similar to that described in 2 was observed. The power spectrum of this noise was also fitted by a single Lorentzian equation, with corner frequency averaging 29.7 +/- 6.6 Hz (mean +/- S.D., n = 27). To examine the possible role of intracellular voltage fluctuations in generating the noise, suction electrodes were filled with calcium-free saline and recordings were made from outer segments of rods attached to pieces of retina. In this recording configuration, the electrical coupling among the rods in the piece should attenuate voltage fluctuations associated with the post-light rebound period of increased dark current. In this situation, the rebound increase in dark current was still observed, but the noise was reduced or absent. Using the same recording configuration, isolated rods showed pronounced noise during the rebound. The result in 4 suggests that the noise resulted from fluctuations in intracellular voltage, not directly from fluctuations in the light-sensitive channels. In this view, the corner frequency of the noise power spectrum probably reflects the membrane time constant of the isolated rod.

Action Potentials↗

Noise factor analysis for cDNA microarrays.

A microarray-image model is used that takes into account many factors, including spot morphology, signal strength, background fluorescent noise, and shape and surface degradation. The model yields synthetic images whose appearance and quality reflect that of real microarray images. The model is used to link noise factors to the fidelity of signal extraction with respect to a standard image-extraction algorithm. Of particular interest is the identification of the noise factors and their interactions that significantly degrade the ability to accurately detect the true gene-expression signal. This study uses statistical criteria in conjunction with the simulation of various noise conditions to better understand the noise influence on signal extraction for cDNA microarray images. It proposes a paradigm that is implemented in software. It specifically considers certain kinds of noise in the noise model and sets these at certain levels; however, one can choose other types of noise or use different noise levels. In sum, it develops a statistical package that can work in conjunction with the existing image simulation toolbox.

Algorithms↗

Half-scan fan-beam computed tomography with improved noise and resolution properties.

Half-scan strategy can be used for reducing scanning time and radiation dose delivered to the patient in fan-beam computed tomography (CT). In helical CT, the data weighting/interpolation functions are often devised based upon half-scan configurations. The half-scan fan-beam filtered backprojection (FFBP) algorithm is generally used for image reconstruction from half-scan data. It can, however, be susceptible to sample aliasing and data noise for configurations with short focal lengths and/or large fan-angles, leading to nonuniform resolution and noise properties in reconstructed images. Uniform resolution and noise properties are generally desired because they may lead to an increased utility of reconstructed images in estimation and/or detection/classification tasks. In this work, we propose an algorithm for reconstruction of images with uniform noise and resolution properties in half-scan CT. In an attempt to evaluate the image-noise properties, we derive analytic expressions for image variances obtained by use of the half-scan algorithms. We also perform numerical studies to assess quantitatively the resolution and noise properties of the algorithms. The results in these studies confirm that the proposed algorithm yields images with more uniform spatial resolution and with lower and more uniform noise levels than does the half-scan FFBP algorithm. Empirical results obtained in noise studies also verify the validity of the derived expressions for image variances. The proposed algorithm would be particularly useful for image reconstruction from data acquired by use of configurations with short focal lengths and large field of measurement, which may be encountered in compact micro-CT and radiation therapeutic CT applications. The analytic results of the image-noise properties can be used for image-quality assessment in detection/classification tasks by use of model-observers.

Algorithms↗

Noise in flat-panel displays with subpixel structure.

Subpixel structures found in medical monochrome active-matrix liquid crystal displays (AMLCDs) affect noise estimates measured with conventional methods. In this work, we discuss methods that identify sources of noise and permit the comparison of luminance noise estimates across technologies independent of pixel design and device technology. We used a three-million pixel AMLCD with a pixel structure consisting of three color stripes, each in a two-domain, in-plane switching mode. Images of uniform fields displayed on the AMLCD were acquired using a low-noise, high-resolution CCD camera. The camera noise and flat-field response were characterized using a uniform light source constructed for this purpose. We show results in terms of spatial luminance noise and noise power spectrum for high-resolution images and for the same images processed with a pixel-aligned aperture. We find that the pixel-aligned aperture eliminates almost all the noise found in the high-resolution images, suggesting that most of the luminance noise in AMLCDs comes from the subpixel structure and less-than-100% aperture ratio, rather than from interpixel variations.

Computer Terminals↗

Studies of performance of antiscatter grids in digital radiography: effect on signal-to-noise ratio.

We developed a theoretical model which describes the improvement of signal-to-noise ratio (SNR) by a grid in digital radiography. The model takes into account the effects of spatial variations in the scatter-to-primary ratio and in the large-area contrast over an image with structured background on quantum noise, and the effects of noise in the imaging system such as electronic noise and digitization noise. Based on the theoretical model, we analyzed the effects of these factors on the SNR when a grid is employed. We performed experimental measurements to evaluate the improvement in the SNR by a grid when quantum noise is the dominant noise source. It was found that the measured SNR improvement factor due to quantum noise agreed closely with that determined from the measured transmission values of a grid, as predicted from our theoretical model. In order to evaluate the relative performance of grids with various geometric design parameters for digital radiographic systems, we employed Monte Carlo calculations and determined the transmission values of a number of grids under various scatter conditions. The calculated SNR improvement factor, due to quantum noise, correlated well with the measured improvement of the SNR by the grids. Our model predicts that the SNR improvement factor depends strongly on the local contrast ratio and also on the scatter-to-primary ratio. The SNR improvement factor is higher in the underpenetrated regions than in the well-penetrated regions of an image.

Models, Theoretical↗

Noise power spectra of images from digital mammography detectors.

Noise characterization through estimation of the noise power spectrum (NPS) is a central component of the evaluation of digital x-ray systems. We begin with a brief review of the fundamentals of NPS theory and measurement, derive explicit expressions for calculation of the one- and two-dimensional (1D and 2D) NPS, and discuss some of the considerations and tradeoffs when these concepts are applied to digital systems. Measurements of the NPS of two detectors for digital mammography are presented to illustrate some of the implications of the choices available. For both systems, two-dimensional noise power spectra obtained over a range of input fluence exhibit pronounced asymmetry between the orthogonal frequency dimensions. The 2D spectra of both systems also demonstrate dominant structures both on and off the primary frequency axes indicative of periodic noise components. Although the two systems share many common noise characteristics, there are significant differences, including markedly different dark-noise magnitudes, differences in NPS shape as a function of both spatial frequency and exposure, and differences in the natures of the residual fixed pattern noise following flat fielding corrections. For low x-ray exposures, quantum noise-limited operation may be possible only at low spatial frequency. Depending on the method of obtaining the 1D NPS (i.e., synthetic slit scanning or slice extraction from the 2D NPS), on-axis periodic structures can be misleadingly smoothed or missed entirely. Our measurements indicate that for these systems, 1D spectra useful for the purpose of detective quantum efficiency calculation may be obtained from thin cuts through the central portion of the calculated 2D NPS. On the other hand, low-frequency spectral values do not converge to an asymptotic value with increasing slit length when 1D spectra are generated using the scanned synthetic slit method. Aliasing can contribute significantly to the digital NPS, especially near the Nyquist frequency. Calculation of the theoretical presampling NPS and explicit inclusion of aliased noise power shows good agreement with measured values.

Biophysics↗

Spectral models of additive and modulation noise in speech and phonatory excitation signals.

The article presents spectral models of additive and modulation noise in speech. The purpose is to learn about the causes of noise in the spectra of normal and disordered voices and to gauge whether the spectral properties of the perturbations of the phonatory excitation signal can be inferred from the spectral properties of the speech signal. The approach to modeling consists of deducing the Fourier series of the perturbed speech, assuming that the Fourier series of the noise and of the clean monocycle-periodic excitation are known. The models explain published data, take into account the effects of supraglottal tremor, demonstrate the modulation distortion owing to vocal tract filtering, establish conditions under which noise cues of different speech signals may be compared, and predict the impossibility of inferring the spectral properties of the frequency modulating noise from the spectral properties of the frequency modulation noise (e.g., phonatory jitter and frequency tremor). The general conclusion is that only phonatory frequency modulation noise is spectrally relevant. Other types of noise in speech are either epiphenomenal, or their spectral effects are masked by the spectral effects of frequency modulation noise.

Fourier Analysis↗

Speech-reception threshold in noise with one and two hearing aids.

The binaural free-field speech-reception threshold (SRT) in 70-dBA noise was measured with conversational sentences for 24 hearing-impaired subjects without hearing aids, with a hearing aid left, right, and left plus right, respectively. The sentences were always presented in front of the listener and the interfering noise, with a spectrum equal to the long-term average spectrum of the sentences, was presented either frontally, from the right, or from the left side. For subjects with only moderate hearing loss, PTA (average air-conduction hearing level at 500, 1000, and 2000 Hz) less than 50 dB, the SRT in 70-dBA noise in both ears is determined by the signal-to-noise ratio even if only one hearing aid is used. For larger hearing losses the SRT appears to be partly determined by the absolute threshold. In conditions with a high noise level relative to the absolute threshold, in which case for both ears the SRT is determined by the signal-to-noise ratio, a second hearing aid, just as a monaural hearing aid, generally does not improve the SRT. However, in the case of a high hearing level, or a low noise level, in which a monaural hearing aid is profitable, the use of two hearing aids is even more profitable. In a separate experiment, acoustic head shadow was measured at the entrance of the ear canal and at the microphone location of a hearing aid. It appeared that, for a lateral noise source and speech frontal, the microphone position of behind-the-ear hearing aids has a negative effect on the signal-to-noise ratio of 2-3 dB.

Adult↗

Spectral and level effects in noise-on-tone suppression.

The effective internal level of a 1-kHz tone at 50 dB SPL was estimated by measuring the forward masking produced on a 10-ms signal tone of the same frequency. Noise containing a spectral notch was then added to the masker tone, and its influence on the effective level of the tone was measured with a variety of noise levels, notch widths, and notch shapes. In experiment 1, the masker tone was centered in the spectral notch, itself centered in a 2-kHz band of noise. As the spectrum level in the noise passbands increased from 6 dB/Hz to 36 dB/Hz, signal threshold decreased, indicating a decrease in masking by the masker tone. This "unmasking" effect of the noise was attributed to suppression of the masker tone by the components in the noise. Unmasking was greatest with the narrowest spectral notch (250 Hz), and decreased to zero as the notch widened to 1500 Hz. Compared to its level when presented alone, the effective internal level of the masker tone could be reduced by up to 30 dB (250-Hz notch, 36 dB/Hz). The relative suppressive strength of individual noise components was estimated in experiment 2, in which the 1-kHz masker tone was located at one edge of a spectral notch, rather than in the center. Noise spectrum level was fixed at 16 dB/Hz. As notch width decreased to zero, on either the high-frequency or low-frequency side of the masker tone, its effective internal level was again reduced by approximately 30 dB. In a tentative analysis, the first derivative of the smoothed threshold function was taken, to provide an estimate of the relative contributions to suppression at 1 kHz of noise components between 250 and 1740 Hz.(ABSTRACT TRUNCATED AT 250 WORDS)

Auditory Threshold↗

Edge effects on frequency discrimination of tones presented in low- and high-pass noise backgrounds.

Previous research has indicated that frequency discrimination performance is poorer for tones presented near the sharp spectral edge of a low-pass noise than for tones presented near the edge of a high-pass noise, or for tones in the same low-pass noise with high-pass noise added [Emmerich et al., J. Acoust. Soc. Am. 80, 1668-1672 (1986)]. The present study extends these findings in order to investigate how the steepness of the spectral edges of low- and high-pass maskers influences the discriminability of tones presented near these edges. Frequency discrimination was measured in each of three high- and low-pass noise backgrounds (which differed in the steepness of their filter skirts). The following results were obtained: (1) In the low-pass noise background, frequency discrimination performance improved as the filter skirt became more gradual; (2) in the high-pass noise background, performance first improved and then became poorer as the filter skirt became shallower; and (3) performance in low-pass noise was poorer than that in high-pass noise for the two steepest slopes employed (96 and 72 dB/oct) but not for the shallower slope (36 dB/oct). Results are discussed in the context of lateral suppression and edge pitch effects, and of a trade-off between possible edge effects and masking.

Acoustic Stimulation↗