Some statistical aspects of digital Wiener filtering and detection of prescribed frequency components in time averaging of biological signals

A statistical analysis of digital a posteriori Wiener filtering as applied to time averaging techniques for biological signals is presented. The authors show that when ap.w.f. is applied to the average signal hardly any effect can be expected, where as when applied to the individual responses, ap.w.f. improves the signal to noise ratio. The applied analysis leads to a simple test to check whether a prescribed frequency component is present.     

Filtering noise for synchronised activity in multi-trial electrophysiology data using Wiener and Kalman filters

Novel approaches to effectively reduce noise in data recorded from multi-trial physiology experiments have been investigated using two-dimensional filtering methods, adaptive Wiener filtering and reduced update Kalman filtering. Test data based on signal and noise model consisting of different conditions of signal components mixed with noise have been considered with filtering effects evaluated using analysis of frequency coherence and of time-dependent coherence. Various situations that may affect the filtering results have been explored and reveal that Wiener and Kalman filtering can considerably improve the coherence values between two channels of multi-trial data and suppress uncorrelated components. We have extended our approach to experimental data: multi-electrode array (MEA) local field potential (LFPs) recordings from the inferotemporal cortex of sheep and LFP vs. electromyogram (LFP-EMG) recording data during resting tremor in Parkinson’s disease patients. Finally general procedures for implementation of these filtering techniques are described.     

Dynamics of brain rhythmic and evoked potentials

A package of methods and an experimental set-up for the analysis of dynamics of electrical signals from the brain. The methods described and discussed in this study allow detailed and multipurpose analysis of brain potentials both in the time and frequency domains. Special emphasis is given to a new computer-method introduced in this study: A posteriori selective averaging. The selective averaging method is compared with Wiener Filter Estimation of Evoked Potentials.     

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.     

Additional comments on the use of Wiener filtering for the estimation of evoked potentials

The problem of average potentials filtration in the case of periodic stimulation is discussed in the paper. Some considerations proving the correctness of Wiener filtering processes suggested by Doyle are presented here. The basic assumtion of the proof is an approximation of the noise power density by means of a step function.     

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.     

General methodology for nonlinear modeling of neural systems with Poisson point-process inputs

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process inputs. It shows that only the Wiener kernels can be estimated via cross-correlation, but must be defined as zero along the diagonals. The Volterra kernels can be estimated far more accurately (and from shorter data-records) by use of the Laguerre expansion technique adapted to point-process inputs, and they are independent of the mean rate of stimulation (unlike their P-W counterparts that depend on it). The Volterra kernels can also be estimated for broadband point-process inputs that are not Poisson. Useful applications of this modeling approach include cases where we seek to determine (model) the transfer characteristics between one neuronal axon (a point-process 'input') and another axon (a point-process 'output') or some other measure of neuronal activity (a continuous 'output', such as population activity) with which a causal link exists.     

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.     

Cellular traction force recovery: An optimal filtering approach in two-dimensional Fourier space

Quantitative estimation of cellular traction has significant physiological and clinical implications. As an inverse problem, traction force recovery is essentially susceptible to noise in the measured displacement data. For traditional procedure of Fourier transform traction cytometry (FTTC), noise amplification is accompanied in the force reconstruction and small tractions cannot be recovered from the displacement field with low signal-noise ratio (SNR). To improve the FTTC process, we develop an optimal filtering scheme to suppress the noise in the force reconstruction procedure. In the framework of the Wiener filtering theory, four filtering parameters are introduced in two-dimensional Fourier space and their analytical expressions are derived in terms of the minimum-mean-squared-error (MMSE) optimization criterion. The optimal filtering approach is validated with simulations and experimental data associated with the adhesion of single cardiac myocyte to elastic substrate. The results indicate that the proposed method can highly enhance SNR of the recovered forces to reveal tiny tractions in cell-substrate interaction.     

A new algorithm for the identification of multiple input Wiener systems

Multiple-input Wiener systems consist of two or more linear dynamic elements, whose outputs are transformed by a multiple-input static non-linearity. Korenberg (1985) demonstrated that the linear elements of these systems can be estimated using either a first order input-ouput cross-covariance or a slice of the second, or higher, order input-output cross-covariance function. Korenberg's work used a multiple input LNL structure, in which the output of the static nonlinearity was then filtered by a linear dynamic system. In this paper we show that by restricting our study to the slightly simpler Wiener structure, it is possible to improve the linear subsystem estimates obtained from the measured cross-covariance functions. Three algorithms, which taken together can identify any multiple-input Wiener system, have been developed. We present the theory underlying these algorithms and detail their implementation. Simulation results are then presented which demonstrate that the algorithms are robust in the presence of output noise, and provide good estimates of the system dynamics under a wide set of conditions.     

Denoising of surface EMG with a modified Wiener filtering approach

The correlation dimension D₂ yields good results in several biomedical fields. Nonetheless, no clinical application to electromyography has been developed yet. One reason is the high electromagnetic noise typical of clinical environments. This noise is characterized by sharp spectral lines of variable intensity and frequency. The filtering techniques commonly implemented in electromyographs can efficiently deal with this kind of noise. They allow a safe estimate of linear quantities like the root mean square (r.m.s.) or the median frequency (MF). Their performance is not as good for nonlinear purposes. The filters may modify the nonlinear properties of the signal, leading to unacceptable estimates of D₂. We consider a simple procedure based on a modified Wiener filter. Its performance is compared with that from a bandpass followed by multiple notch filters. Our procedure leads to a gain in precision and accuracy when estimating D₂. The two filtering approaches are also compared with respect to a biomedical application proposed by others. Using data from 12 healthy subjects, the modified Wiener procedure raises the percentage of successes in that application from 17% to 83%. New experimental data suggest D₂ carries information not carried by r.m.s. or MF.     

Mathematical methods for the acquisition of changes in vecps

Procedures such as principal component analysis, autocorrelation and cross-correlation, Fourier analysis, Wiener filtering, which have been used so far for the mathematical analysis of VECP mainly serve purpose of quantization and frequency analysis of signals and the evaluation of their intraindividual and interindividual variability. Although some of the above methods are also employed for the differentiation of VECPs, it seems that methods of primarily comparative character are better suited for the classification of different signal forms. This paper reports on results obtained by multivariate analysis of variance.     

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.     

Preventing errors when estimating single channel properties from the analysis of current fluctuations.

The conductance, number, and mean open time of ion channels can be estimated from fluctuations in membrane current. To examine potential errors associated with fluctuation analysis, we simulated ensemble currents and estimated single channel properties. The number (N) and amplitude (i) of the underlying single channels were estimated using nonstationary fluctuation analysis, while mean open time was estimated using covariance and spectral analysis. Both excessive filtering and the analysis of segments of current that were too brief led to underestimates of i and overestimates of N. Setting the low-pass cut-off frequency of the filter to greater than five times the inverse of the effective mean channel open time (burst duration) and analyzing segments of current that were at least 80 times the effective mean channel open time reduced the errors to < 2%. With excessive filtering, Butterworth filtering gave up to 10% less error in estimating i and N than Bessel filtering. Estimates of mean open time obtained from the time constant of decay of the covariance, tau obs, at low open probabilities (Po) were much less sensitive to filtering than estimates of i and N. Extrapolating plots of tau obs versus mean current to the ordinate provided a method to estimate mean open time from data obtained at higher Po, where tau obs no longer represents mean open time. Bessel filtering gave the least error when estimating tau obs from the decay of the covariance function, and Butterworth filtering gave the least error when estimating tau obs from spectral density functions.     

Sepia officinalis hemocyanin: A refined 3D structure from field emission gun cryoelectron microscopy

The extracellular respiratory pigment of the cuttlefish Sepia officinalis was observed by cryoelectron microscopy with conventional LaB(6) and field emission gun electron sources at 100 and 200 kV, respectively. Each image series was used to compute one 3D reconstruction volume with correction of the contrast transfer function by Wiener filtering. A strong boosting of the contrast was corrected by band-pass filtering of the final volumes, and a qualitative gain in resolution was observed when using the field emission gun electron microscope. In this volume, a strong signal is present down to 1/18 A(-1) and some meaningful information is obtained down to 1/12.5 A(-1). The complex is composed of five pairs of polypeptide chains and resembles a hollow cylinder with five wall oblique units and five inner arches. Three types of wall-wall connections termed pillar P1 to P3 are visible in this volume and the four functional units present in the arches are each linked to the wall by two arch-wall connections. The dispositions of the functional units in the arches of Sepia and Octopus hemocyanins share no common feature.     

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.     

Effects of EMG processing on biomechanical models of muscle joint systems: sensitivity of trunk muscle moments, spinal forces, and stability

Biomechanical models are in use to estimate parameters such as contact forces and stability at various joints. In one class of these models, surface electromyography (EMG) is used to address the problem of mechanical indeterminacy such that individual muscle activation patterns are accounted for. Unfortunately, because of the stochastical properties of EMG signals, EMG based estimates of muscle force suffer from substantial estimation errors. Recent studies have shown that improvements in muscle force estimation can be achieved through adequate EMG processing, specifically whitening and high-pass (HP) filtering of the signals. The aim of this paper is to determine the effect of such processing on outcomes of a biomechanical model of the lumbosacral joint and surrounding musculature. Goodness of fit of estimated muscle moments to net moments and also estimated joint stability significantly increased with increasing cut-off frequencies in HP filtering, whereas no effect on joint contact forces was found. Whitening resulted in moment estimations comparable to those obtained from optimal HP filtering with cut-off frequencies over 250 Hz. Moreover, compared to HP filtering, whitening led to a further increase in estimated joint-stability. Based on theoretical models and on our experimental results, we hypothesize that the processing leads to an increase in pick-up area. This then would explain the improvements from a better balance between deep and superficial motor unit contributions to the signal.     

Feeding and Swimming Behavior in Grazing Microzooplankton1,2

ABSTRACT A random-walk model of food-searching behavior is considered for the microzooplankton. It is suggested that in still waters a random walk of the conventional sort, modeled by a Wiener process, is less efficient than a Levy walk (a random walk whose excursions follow a Levy distribution) with Levy parameter less than two. For Levy parameter less than one, however, little advantage is gained by further reduction. In turbulent water, on the other hand, dispersion due to a random walk is dominated by the turbulent diffusion of the medium so that the Levy parameter appears to be less important. The effect of chemosensory responses is considered. It is suggested that these are most useful in still water, whereas in turbulent water their value would be less, and a non-specific filtering behavior might be more plausible.     

Estimation of signal and noise spectra by special averaging techniques with application to a posteriori “Wiener” filtering

This paper deals with the problem of separating the spectra of signal and noise in ensembles where the signal can be considered as an invariant component and the noise as a stationary additive background. Several methods are discussed and compared on the basis of a statistical analysis of the first two moments of the estimators for signal and noise spectra. As a consequence a procedure is proposed which provides a flexible compromise between estimation accuracy and computational effort. The application of this procedure to a posteriori Wiener filtering is compared with a more common, but time consuming, technique.