Wiener filtration versus averaging of evoked responses

The extraction of the evoked potential by the Wiener filtration technique is performed to compare it with classical averaging. It is well known that the Wiener filter supplies the least square error estimate. On the other hand, it is apparent that this error substantially depends on the choice of the lengths of interstimulation intervals. Artificially simulated examples are processed by both techniques, averaging and Wiener filtration, to show that the proper choice of the interstimulating intervals is much more relevant for decreasing the estimate error than in helping us make the decision which of these methods should be used.     

Analysis of visual evoked potentials through Wiener filtering applied to a small number of sweeps

We introduce a method for processing visual evoked potentials, on the basis of a Wiener filter algorithm applied to a small number of consecutive responses. The transfer function of the filter is obtained by taking into account both the average of 99 sweeps (as an estimate of the true signal) and the EEG signal just before the stimulus onset (as an estimate of the noise superimposed on each individual response). The process acts as a sweep-by-sweep filter (in the sense of the mean square error) which considers the possible non-stationarities of the EEG signal during a complete clinical procedure. The average of a small number of consecutive filtered sweeps reveals variations in the morphology of the evoked responses which produce a change in the principal latencies. Applications are foreseen in neurophysiological studies of visual evoked potential responses, and in the clinic, where it is important to evaluate adaptive mechanisms, dynamic changes in single groups of visual evoked potentials and cognitive responses.     

Some notes on the statistical properties of a posteriori Wiener filtering

In this study the authors analyse the asymptotic distribution of estimated a posteriori Wiener filtering of averaged evoked responses and the problem of the existence and convergence of moments of the estimated filter and the filtered signal. The authors conclude that the only justification of a posteriori Wiener filtering lies in the possibility to use it as a vehicle of a priori information.     

An adaptation of the Wiener filter suitable for analyzing images of isolated single particles

The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent (“spectral”) signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.     

Median‐modified Wiener filter provides efficient denoising,preserving spot edge and morphology in 2‐DE image processing

Denoising is a fundamental early stage in 2‐DE image analysis strongly influencing spot detection or pixel‐based methods. A novel nonlinear adaptive spatial filter (median‐modified Wiener filter, MMWF), is here compared with five well‐established denoising techniques (Median, Wiener, Gaussian, and Polynomial‐Savitzky–Golay filters; wavelet denoising) to suggest, by means of fuzzy sets evaluation, the best denoising approach to use in practice. Although median filter and wavelet achieved the best performance in spike and Gaussian denoising respectively, they are unsuitable for contemporary removal of different types of noise, because their best setting is noise‐dependent. Vice versa, MMWF that arrived second in each single denoising category, was evaluated as the best filter for global denoising, being its best setting invariant of the type of noise. In addition, median filter eroded the edge of isolated spots and filled the space between close‐set spots, whereas MMWF because of a novel filter effect (drop‐off‐effect) does not suffer from erosion problem, preserves the morphology of close‐set spots, and avoids spot and spike fuzzyfication, an aberration encountered for Wiener filter. In our tests, MMWF was assessed as the best choice when the goal is to minimize spot edge aberrations while removing spike and Gaussian noise.     

Denoising of Electron Tomographic Reconstructions Using Multiscale Transformations

The visualization of volume maps obtained by electron tomographic reconstruction is severely hampered by noise. As electron tomography is usually applied to individual, nonrepeatable structures, e.g., cell sections or cell organelles, the noise cannot be removed by averaging as is done implicitly in electron crystallography or explicitly in single particle analysis. In this paper, an approach for noise reduction is presented, based on a multiscale transformation, e.g., the wavelet transformation, in conjunction with a nonlinear filtration of the transform coefficients. After a brief introduction to the theoretical background, the effect of this type of noise reduction is demonstrated by test calculations as well as by applications to tomographic reconstructions of ice-embedded specimens. Regarding noise reduction and structure preservation, the method turns out to be superior to conventional filter techniques, such as the median filter or the Wiener filter. Results obtained with the use of different types of multiscale transformations are compared and the choice of suitable filter parameters is discussed.     

Optimal (‘Wiener’) digital filtering of auditory evoked potentials: use of coherence estimates

Auditory evoked potentials (AEPs) to 40 Hz clicks and amplitude-modulated 500 Hz tones in human subjects were digitally filtered using an optimal (‘Wiener’) filter uniquely determined for each AEP. Use of coherence functions to compute coefficients appropriate for filtering grand average AEPs or subsets such as split-half averages is described. Wiener-filtered AEPs correlated better than unfiltered AEPs with split-half replicates and with references AEPs (obtained with long data collection periods). Visual detection thresholds were lower (more sensitive) for the Wiener-filtered AEPs, but not as low as objectively determined thresholds using coherence values.     

Estimation of the noise autocorrelation function in auditory evoked potential applications

This work presents a simple and accurate method to estimate the noise autocorrelation function in auditory evoked potential applications. It basically consists in applying a conventional correlation function estimator over the contaminated evoked potential signal processed by a comb filter. The main feature of the proposed technique is the possibility of obtaining information on large correlation lags without the need of extra time intervals, minimizing the estimation time. A theoretical analysis is provided showing that, under certain but achievable conditions, the correlation function of the processed signal approximates the real noise correlation function. Simulation results and an example with a single-trial evoked potential estimation technique illustrate the expected performance. The proposed method is of special interest to either single or small number of trials evoked potential estimation techniques in anaesthesia monitoring applications.     

MRI denoising using nonlocal neutrosophic set approach of Wiener filtering

In this paper, a new filtering method is presented to remove the Rician noise from magnetic resonance images (MRI) acquired using single coil MRI acquisition system. This filter is based on nonlocal neutrosophic set (NLNS) approach of Wiener filtering. A neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Now, we apply the neutrosophic set into image domain and define some concepts and operators for image denoising. First, the nonlocal mean is applied to the noisy MRI. The resultant image is transformed into NS domain, described using three membership sets: true (T), indeterminacy (I) and false (F). The entropy of the neutrosophic set is defined and employed to measure the indeterminacy. The ω-Wiener filtering operation is used on T and F to decrease the set indeterminacy and to remove the noise. The experiments have been conducted on simulated MR images from Brainweb database and clinical MR images. The results show that the NLNS Wiener filter produces better denoising results in terms of qualitative and quantitative measures compared with other denoising methods, such as classical Wiener filter, the anisotropic diffusion filter, the total variation minimization and the nonlocal means filter. The visual and the diagnostic quality of the denoised image are well preserved.     

Theory and practice of a posteriori “Wiener” filtering of average evoked potentials

In this study a theoretical and practical analysis of the technique of a posteriori Wiener filtering of averaged evoked potentials is presented. It is shown that spectral smoothing plays a central role in obtaining a reliable estimate. Attention is paid to some practical problems that arise when the method is applied in discrete time. In an illustrative case study results are compared to theoretical Wiener filtering, while the influence of slow amplitude modulation has also been investigated. Some of the conflicting results regarding the method that have been reported in several recent papers are discussed. It is concluded, that when the method is applied with prudence, it may lead to an improved estimation of those evoked potentials that can be assumed to be approximately stationary. If the latter assumption is not valid, application of a time-varying filter technique is recommended instead.     

Characterizing and correcting for the dynamic response of a bag-in-box system

A bag-in-box system (BBS) whose volume is monitored by a mechanical spirometer tends to have a slow response if the volume of the box is large, and this may significantly affect its measurement of gas flow. We describe a device for creating reproducible gas flows with which the impulse response of a BBS may be conveniently determined. Two computational techniques for correcting a BBS flow measurement for the effects of the impulse response were investigated: 1) an exponential model method that assumes a second-order model of the BBS dynamics and 2) a Fourier transform-based method of deconvolution known as Wiener filtering. Both correction methods produced a significant increase in the accuracy of BBS flow estimations, with the Wiener filter giving superior results.     

Nonlinear analysis of the human visual evoked response

Using time-domain correlation techniques, the first- and second-order Wiener kernels have been calculated for the system mediating the human visual evoked response. The first-order kernels indicate the linear element is a resonant one, with a natural frequency near 20 Hz, and a memory of approximately 250 ms. The transport delay associated with this element is approximately 56 ms. The second-order kernels indicate a quadratic nonlinear element with a memory less than 20 ms. The analytic form of this element can be approximated by a parabola shifted to the right of the origin. A close correspondance between the spectrum of the first-order kernel and the spectrum of the main diagonal of the second-order kernel suggests the nonlinear element preceeds the linear one. Tests of reproducibility on the first-order kernel and the main diagonal of the second-order kernel suggest they are reliable describing functions for the system mediating the human visual evoked response.     

用稳态视觉诱发电位研究注意的选择机制

众所周知,注意是一种心理活动,是对外界刺激的一种选择,对人的其它认知活动有一定的调节作用。关于注意的选择机制,有两种不同的理论,一种是早期选择机制,另一种是晚期选择机制。稳态视觉诱发电位是视觉通路对外界刺激的一种物理反应,它的产生过程处于认知的早期阶段,如果它能受到注意的调节,这就支持了注意的早期选择机制。在现有的利用闪光稳态诱发电位对注意的研究中,注意的对象是认知任务,而不是闪光。该实验用两种不同频率的闪光分别做诱发源,对在注意与不注意闪光两种情况下(都没有认知任务)的稳态视觉诱发电位进行研究,发现其明显地受注意调节,而且对不同频率光刺激的调节大小不一样。因此,该实验结果支持了注意的早期选择机制。     

A computer program for Wiener filtering of evoked potential data.

We have developed a computer program for Wiener filtering of evoked potential data. The basic algorithm involves computation of the difference berween the power spectrum of the sweep sum and the sum of power spectra of individual sweeps. Power spectra are computed by means of the discrete Fourier transform. The program is now being run on a LSI-11 computer in a neurophysiology research laboratory to analyze somatic evoked potential data from monkeys.     

Parameters of exponentially damped sinusoids in noise and their application to the analysis of visual evoked potentials

The backward prediction and singular value (SV) truncation methods for estimating multiple exponentially damped real sinusoids in noise have been studied. The basic theory and algorithm are outlined, and the effect on the error of computational parameters, such as the sampling window, the sampling rate, the order of the prediction-error filter (PEF) and the truncated point of SV, were studied using simulated data. If the computational parameters are carefully chosen, the estimate of frequency and damping factor of a damped sinusoid is quite accurate (within a certain range of signal to noise (S/N) ratio). We use this method to estimate the parameters of visual evoked potentials (VEP) and then reconstructed them from estimated parameters according to the resonant model. The error between original VEP and the reconstructed waveform is within 5%. This method can be used in the analysis and recognition of various systems.     

A Wiener-type neuronal model in the presence of exponential refractoriness

An instantaneous return process in the presence of random refractoriness for Wiener model of single neuron activity is considered. The case of exponential distributed refractoriness is analyzed and expressions for output distributions and interspike intervals density are obtained in closed form. A computational study is performed to elucidate the role played by the model parameters in affecting the firing probabilities and the interspike distribution.     

A note on the estimation of evoked response

The traditional average evoked response is compared and contrasted with several alternate estimates, derived from frequency domain considerations, for a model of evoked responses superimposed upon a stationary noise series. Further, a means of constructing approximate confidence intervals for the values of an evoked response is indicated. The case of several simultaneously recorded series is also considered.Prepared with the support of the National Science Foundation Grant MCS 76-06117     

Interstitial fluid glucose time-lag correction for real-time continuous glucose monitoring

Time lag between subcutaneous interstitial fluid and plasma glucose decreases the accuracy of real-time continuous glucose monitors. However, inverse filters can be designed to correct time lag and attenuate noise enabling the blood–glucose profile to be reconstructed in real time from continuous measurements of the interstitial-fluid glucose. We designed and tested a Wiener filter using a set of 20 sensor-glucose tracings (～30 h each) with a 1-min sample interval. Delays of 10 ± 2 min (mean ± SD) were introduced into each signal with additive Gaussian white noise (SNR = 40 dB). Performance of the filter was compared to conventional causal and non-causal seventh-order finite-impulse response (FIR) filters. Time lags introduced an error of 5.3 ± 2.7%. The error increased in the presence of noise (to 5.7 ± 2.6%) and attempts to remove the noise with conventional low-pass filtering increased the error still further (to 7.0 ± 3.5%). In contrast, the Wiener filter decreased the error attributed to time delay by ～50% in the presence of noise (from 5.7% to 2.60 ± 1.26%) and by ～75% in the absence of noise (5.3% to 1.3 ± 1%). Introducing time-lag correction without increasing sensitivity to noise can increase CGM accuracy.     

Statistical analysis of the parameters defining the cortical visual evoked potentials in the phases of the sleep-wake cycle

Visual evoked potential parameters (latencies, intervals of latencies and amplitudes) obtained by photic stimulation using a light-emitting diode implanted in the frontal sinus of cats were studied by statistical methods (analysis of variance) during the stages of wakefulness, slow sleep and paradoxical sleep. The results show: a) greater intraindividual homogeneity in all cases with special emphasis on the latencies; b) the greatest homogeneity of responses was found during slow sleep and paradoxical sleep stages; c) in relation to the influences exerted by the sleep-wakefulness cycle on the visual evoked potentials, the parameters most affected were those closely related to the secondary complex. We conclude, that latency, due to its great homogeneity, is the most useful parameter in this kind of experiments and secondly, that it is the secondary complex of the visual evoked potentials that is affected by the endogenous conditions of the subject (in our case the sleep-wakefulness cycle stage).     

Rapid-Rate Paired Associative Stimulation over the Primary Somatosensory Cortex

Rapid-rate paired associative stimulation (rPAS) involves repeat pairing of peripheral nerve stimulation and Transcranial magnetic stimulation (TMS) pulses at a 5 Hz frequency. RPAS over primary motor cortex (M1) operates with spike-timing dependent plasticity such that increases in corticospinal excitability occur when the nerve and TMS pulse temporally coincide in cortex. The present study investigates the effects of rPAS over primary somatosensory cortex (SI) which has not been performed to date. In a series of experiments, rPAS was delivered over SI and M1 at varying timing intervals between the nerve and TMS pulse based on the latency of the N20 somatosensory evoked potential (SEP) component within each participant (intervals for SI-rPAS: N20, N20-2.5 ms, N20 + 2.5 ms, intervals for M1-rPAS: N20, N20+5 ms). Changes in SI physiology were measured via SEPs (N20, P25, N20-P25) and SEP paired-pulse inhibition, and changes in M1 physiology were measured with motor evoked potentials and short-latency afferent inhibition. Measures were obtained before rPAS and at 5, 25 and 45 minutes following stimulation. Results indicate that paired-pulse inhibition and short-latency afferent inhibition were reduced only when the SI-rPAS nerve-TMS timing interval was set to N20-2.5 ms. SI-rPAS over SI also led to remote effects on motor physiology over a wider range of nerve-TMS intervals (N20-2.5 ms – N20+2.5 ms) during which motor evoked potentials were increased. M1-rPAS increased motor evoked potentials and reduced short-latency afferent inhibition as previously reported. These data provide evidence that, similar to M1, rPAS over SI is spike-timing dependent and is capable of exerting changes in SI and M1 physiology.