Effect Of Noise Correlation Research Articles

The effect of noise correlations in populations of diversely tuned neurons

AbstractThe amount of information encoded by networks of neurons critically depends on the correlation structure of their activity. Neurons with similar stimulus preferences tend to have higher noise correlations than others. In homogeneous populations of neurons this limited range correlation structure is highly detrimental to the accuracy of a population code. Therefore, reduced spike count correlations under attention, after adaptation or after learning have been interpreted as evidence for a more efficient population code. Here we analyze the role of limited range correlations in more realistic, heterogeneous population models. We use Fisher information and maximum likelihood decoding to show that reduced correlations do not necessarily improve encoding accuracy. In fact, in populations with more than a few hundred neurons, increasing the level of limited range correlations can substantially improve encoding accuracy. We found that this improvement results from a decrease in noise entropy that is associated with increasing correlations if the marginal distributions are unchanged. Surprisingly, for constant noise entropy and in the limit of large populations the encoding accuracy is independent of both structure and magnitude of noise correlations.

Eigenvalue distributions for a class of covariance matrices with application to Bienenstock-Cooper-Munro neurons under noisy conditions

We analyze the effects of noise correlations in the input to, or among, Bienenstock-Cooper-Munro neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input lateral geniculate nucleus neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.

The Temporal Winner-Take-All Readout

How can the central nervous system make accurate decisions about external stimuli at short times on the basis of the noisy responses of nerve cell populations? It has been suggested that spike time latency is the source of fast decisions. Here, we propose a simple and fast readout mechanism, the temporal Winner-Take-All (tWTA), and undertake a study of its accuracy. The tWTA is studied in the framework of a statistical model for the dynamic response of a nerve cell population to an external stimulus. Each cell is characterized by a preferred stimulus, a unique value of the external stimulus for which it responds fastest. The tWTA estimate for the stimulus is the preferred stimulus of the cell that fired the first spike in the entire population. We then pose the questions: How accurate is the tWTA readout? What are the parameters that govern this accuracy? What are the effects of noise correlations and baseline firing? We find that tWTA sensitivity to the stimulus grows algebraically fast with the number of cells in the population, N, in contrast to the logarithmic slow scaling of the conventional rate-WTA sensitivity with N. Noise correlations in first-spike times of different cells can limit the accuracy of the tWTA readout, even in the limit of large N, similar to the effect that has been observed in population coding theory. We show that baseline firing also has a detrimental effect on tWTA accuracy. We suggest a generalization of the tWTA, the n-tWTA, which estimates the stimulus by the identity of the group of cells firing the first n spikes and show how this simple generalization can overcome the detrimental effect of baseline firing. Thus, the tWTA can provide fast and accurate responses discriminating between a small number of alternatives. High accuracy in estimation of a continuous stimulus can be obtained using the n-tWTA.

The Effect of Noise Correlation in Amplify-and-Forward Relay Networks

In wireless relay networks, noise at the relays can be correlated possibly due to common interference or noise propagation from preceding hops. A parallel relay network with noise correlation is considered in this network. For the relay strategy of amplify and forward (AF), the optimal rate maximizing relay gains when correlation knowledge is available at the relays are determined. Interestingly, it is shown that, on average, noise correlation is beneficial regardless of whether the relays know the noise covariance matrix. However, the knowledge of correlation can greatly improve the performance. Typically, the performance improvement from correlation knowledge increases with the relay power and the number of relays. With perfect correlation knowledge the system is capable of canceling interference if the number of interferers is less than the number of relays. For a two-hop multiple-access parallel network, closed-form expressions for the maximum sum rate and the optimal relay strategy are determined. Relay optimization for networks with three hops is also considered. Based on the result of two-hop network with noise correlation, an iterative algorithm is proposed for solving the relay optimization problem for three-hop networks.

WE-D-332-05: Propagation of Correlated Noise in CT Reconstruction

Purpose: The ability to estimate noise in complex CTimages has great utility, but filtered backprojection reconstruction results in nonlocal, nonstationary random noise in an image. The variance propagation method proposed by Chesler has been used recently, but it was derived for the continuum and does not account for effects of noise correlations when used in discrete systems. Several alternative approaches have been developed for making accurate noise maps for a CTimage.Method and Materials: Numerical data were prepared with MATLAB software, using both parallel and fan beam CT geometries. Variances were calculated by repeated simulations, as well as two implementations of Chesler's method for propagating uncorrelated noise. The propagation of correlated noise was implemented by operating on subsets of widely separated projection rays, combining efficiency and accuracy. The dependence of variance distribution on kernel bandwidth and scanner geometry was measured. Results: The correlated‐noise algorithm was in excellent agreement with repeated simulation calculations. For parallel geometries, noise distribution had a common shape for all reconstruction kernels, with differing scale factors. The two uncorrelated noise algorithms provided the correct spatial form of the noise, but required empirical scaling factors. In fan beam geometry, the distribution of the noise was kernel dependent, and uncorrelated noise algorithms had discrepancies on the order of 10–20%. Conclusion: Several methods for noise estimation were examined. The approximate Chesler method is fast (same time as one reconstruction) and can be scaled for parallel beam geometries, but is subject to errors for fan beam geometries. Variance calculations from multiple simulations are unbiased but have errors whose standard deviations decrease as the inverse square root of the number of reconstructions. The correlated‐noise algorithm achieves exact results in a time of 30–40 reconstructions.

Interspike interval statistics of a leaky integrate-and-fire neuron driven by Gaussian noise with large correlation times

We analytically investigate the interspike interval (ISI) density, the Fano factor, and the coefficient of variation of a leaky integrate-and-fire neuron model driven by exponentially correlated Gaussian noise with a large correlation time tau . We find a burstinglike behavior of the spike train, which is revealed by a dominant peak of the ISI density at small intraburst intervals and a slow power-law decay of long interburst intervals. The large, power-law distributed ISIs give rise to a coefficient of variation which diverges as square root [tau] . This leads to the paradoxical effect that ISI correlations, as expressed by the serial correlation coefficient, vanish for large correlation times. This is in contrast to findings of previous works on a simpler neuron model where the effect of noise correlations appeared in higher-order statistical measures.

Effects of Noise Correlations on Information Encoding and Decoding

Response variability is often correlated across populations of neurons, and these noise correlations may play a role in information coding. In previous studies, this possibility has been examined from the encoding and decoding perspectives. Here we used d prime and related information measures to examine how studies of noise correlations from these two perspectives are related. We found that for a pair of neurons, the effect of noise correlations on information decoding can be zero when the effect of noise correlations on the information encoded obtains its largest positive or negative values. Furthermore, there can be no effect of noise correlations on the information encoded when it has an effect on information decoding. We also measured the effect of noise correlations on information encoding and decoding in simultaneously recorded neurons in the supplementary motor area to see how well d prime accounted for the information actually present in the neural responses and to see how noise correlations affected encoding and decoding in real data. These analyses showed that d prime provides an accurate measure of information encoding and decoding in our population of neurons. We also found that the effect of noise correlations on information encoding was somewhat larger than the effect of noise correlations on information decoding, but both were relatively small. Finally, as predicted theoretically, the effects of correlations were slightly greater for larger ensembles (3-8 neurons) than for pairs of neurons.

Effect of noise correlation in channels of a digital X-ray detector—converter on evaluation of detection quantum efficiency

Effect of noise correlation in channels of a digital X-ray detector—converter on evaluation of detection quantum efficiency

Bit-error probabilities for 2- and 4-DPSK in general Nakagami fading channels with correlated Gaussian noise

Exact bit-error probability (BEP) expressions are derived for 2- and 4-ary differential phase shift keying (2- and 4-DPSK) with post-detection equal gain combining (EGC) in arbitrarily correlated slow Nakagami fading channels. Unlike previous work, the effect of noise correlation between adjacent symbol intervals is considered and shown explicitly in the BEP expressions. The characteristic function method is used to give a BEP expression in a general form for 2- and 4-DPSK. Furthermore, closed-form BEP expressions are derived for 2-DPSK with coloured noise, and for 4-DPSK with white noise and integer fading parameter m. The theoretical result is demonstrated by analysing two antenna configurations, giving some interesting findings.

Coding to improve SNR in magnetic recording

The magnetic recording channel is often equalised to the PR4 partial response. Viterbi detection is used to detect the recorded data, but suffers a loss owing to the effects of noise correlation. The use of coding on the PR4 magnetic recording channel to reduce the effects of noise correlation is proposed. This is shown to achieve a gain in effective SNR over an uncoded channel. Parity codes are shown to be one method of achieving this. The read data is decoded with a soft decision Viterbi detector. The performance of the method is verified through simulations.

Tracking technique for manoeuvring target with correlated measurement noises and unknown parameters

The problem of tracking a manoeuvring target with sequentially correlated measurement noise is considered in the paper. Using Singer's method to model the manoeuvring target, the correlated measurement noise can be decorrelated by reformulating the measurement equation such that the conventional Kalman filter can be directly applied in this tracking problem. An analytical error analysis for this processing is derived. If some of the parameters are unknown, the conventional innovation correlation method can usually be employed to estimate these parameters adaptively. This method assumes that the measurement noise is white. If the measurement noise is sequentially correlated, this technique is not valid and the parameters can not be estimated with sufficient accuracy to obtain the desired tracking performance. By considering the effect of noise correlation, a modified computationally efficient method known as a multiple-level estimator is presented to improve the performance in estimating the unknown parameters in the presence of correlated measurement noise. >

Tracking a manoeuvring target with correlated measurement noises by manoeuvre detection method

The tracking problem for a manoeuvring target with correlated measurement noises is considered in this letter. A modified manoeuvre detection method with the decorrelation process is employed for tracking the manoeuvring target. From computer simulation, it can be seen that the system performance can be improved significantly if the effect of noise-correlation is considered.

A differentially coherent receiver for minimum shift keying signal

The author extends to the case of minimum-shift-keying (MSK) modulation the differentially coherent reception theory established for phase-shift-keying modulation. A novel differentially coherent detector for MSK is thus derived. The receiver filter is equivalent to the cascade of a matched filter and an equalizer in order to suppress inherent intersymbol interference. It is shown that performance can be improved when the delay between signals, multiplied by the differential detector, is increased from one to M bit time intervals. This decreases the effect of noise correlation and, thus, the bit error probability. The bit error probability of the proposed receiver is calculated. It is found that almost all potential improvement due to the delay M is obtained with M=3. >

Local methods for constructing stationary distribution functions of systems of stochastic differential Langevin-type equations: Noise influence on simple bifurcation

The influence is considered of two additive correlated noise effects on a two-dimensional quadratic-nonlinear system describing the behavior of two hydrodynamic modes. Using the method of Gaussian approximation, local characteristics of the distribution function are calculated, which are used to construct the global distribution function with the aid of the method of fraction-rational approximations. It is shown that for a system at whose bifurcation point the asymptotic stability is lost, in an expanded space of parameters (bifurcation parameter in the absence of noise plus noise parameters) there appears an instability zone within which the stationary distribution function does not exist. The effect of noise correlation on the stationary characteristics of the system is studied.

Effect of noise correlation on detectability of disk signals in medical imaging.

Pixel signal-to-noise ratio is one accepted measure of image quality for predicting observer performance in medical imaging. We have found, however, that images with equal pixel signal-to-noise ratio (SNRp) but different correlation properties give quite different observer-performance measures for a simple detection experiment. The SNR at the output of an ideal detector with the ability to prewhiten the noise is also a poor predictor of human performance for disk signals in high-pass noise. We have found constant observer efficiencies for humans relative to the performance of a nonprewhitening detector for this task.

The Effects of Noise Correlation and Power Imbalance on Terrestrial and Satellite DPSK Channels

New results are given for the bit error probability for binary DPSK modulation over both terrestrial and satellite channels taking into account noise correlation and power imbalance. The new expressions are remarkably simpler than their previously published counterparts. For the terrestrial channel, the results are in closed form in terms of tabulated functions and, for the hard-limiting satellite channel, both in terms of integrals readily evaluated by quadrature and in terms of infinite series. Using the results, it is shown that the error rate does not depend on the noise correlation (down-link in the satellite case) so long as the a priori symbol probabilities are equal, thereby solving an open problem posed by Lee, French, and Hong. Also, the satellite case in which each of the up-link and down-link channels contains nonzero noise correlations is briefly treated.

The Effect of Noise Correlation on Binary Differentially Coherent PSK Communication Systems

Several authors have calculated the probability of error in binary differentially coherent phase-shift-keyed (DCPSK) communication systems. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,2,3,4</sup> All of these calculations make the assumption that the sample values of the noise at the sampling instants in adjacent time slots are statistically independent random variables. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> Because the noise is band-limited this assumption is not strictly true. The purpose of this note is to justify the assumption for most cases of interest and to point out where the assumption introduces some discrepancy.

Effect of Noise Correlation on Binaural-Signal Detection

This is an extension of a study of the effect of the interaural correlation for a masking noise upon the masked threshold for a 500-cps tone as reported in 1961 by Robinson and Jeffress. At that time, comparisons were made between thresholds obtained under both homophasic and antiphasic conditions. However, the variability associated with the threshold measurements (obtained by the constant method) was such as to obscure possible differences between the two antiphasic conditions or between the two homophasic. The present study employs a method derived from the theory of signal detection to obtain a more stable measure of the effects of interaural-noise correlation. Performance was measured in a two-interval forced-choice experiment. The signal levels required for a predetermined value of d′ were obtained for the various conditions from functions relating d′ toE/No. Such signal levels, when plotted as masking level differences (MLD's) relative to the homophasic condition at the 1.0 value of the noise correlation, permit comparisons with similar data obtained by a threshold procedure. The results show, as did the results of the earlier study, a very rapid increase in masking as the correlation is reduced from unity for the antiphasic conditions and a gradual decrease in masking for the homophasic conditions with the same shift in correlation. In addition, the functions relating d′ to E/No show large differences in slope between the antiphasic and homophasic conditions.

Effect of Noise Correlation on the Masked Threshold for Tone

This is a repetition and an extension of a study of the effect of the interaural correlation for a masking noise upon the masked threshold for a 500-cps tone, reported in 1953 by Jeffress, Blodgett, and Deatherage. We failed at that time to realize that an uncorrelated noise can produce a masking level difference (MLD), and used the homophasic condition, at each value of the correlation, as the reference level for computing MLD's. In the present study the results are presented as signal-to-noise ratios based on the effective level of the noise. They show, as the results of the earlier study did, a very rapid increase in masking as the correlation is reduced from unity. The change is not, however, as rapid as that associated with the reduction of the autocorrelation for the critical band of noise when a time delay is introduced into the noise channel to one ear. The paper will discuss some of the implications of this fact for hearing theory.