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PubMed2006

Regularization operators for natural images based on nonlinear perception models.

Image restoration requires some a priori knowledge of the solution. Some of the conventional regularization techniques are based on the estimation of the power spectrum density. Simple statistical models for spectral estimation just take into account second-order relations between the pixels of the image. However, natural images exhibit additional features, such as particular relationships between local Fourier or wavelet transform coefficients. Biological visual systems have evolved to capture these relations. We propose the use of this biological behavior to build regularization operators as an alternative to simple statistical models. The results suggest that if the penalty operator takes these additional features in natural images into account, it will be more robust and the choice of the regularization parameter is less critical.

Algorithms↗

PubMed2005

Maximum-likelihood estimator for dual phase extraction in holographic moire.

A maximum-likelihood (ML) method based on spectral estimation theory for the extraction of dual phase distributions in holographic moire in the presence of nonsinusoidal waveforms, noise, and the miscalibration of piezoelectric (PZT) devices is proposed. The extraction of these phases requires incorporating two PZTs into the moire setup. ML estimators are asymptotically efficient for sufficient data samples. The approach presented uses a direct stochastic algorithm called probabilistic global search Lausanne for minimizing the ML function.

Journal Article↗

PubMed1992

Spectral and temporal weights in spectral-shape discrimination.

The COSS analysis [B. G. Berg, J. Acoust. Soc. Am. 86, 1743-1746 (1989)] was used to estimate spectral and temporal weights of a three-component, amplitude-modulated stimulus in a spectral-shape discrimination task. In all experiments, the task of the observer was to detect an increment in the level of the center component. A spectral-temporal weight quantifies the relative influence of a spectral component on the decisions of an observer during a specified segment of the total stimulus duration. In the first two experiments, the signal was added to all three temporal segments of the center component. The ideal weights for each component should be the same across temporal segments. Spectral-temporal weights were obtained for four conditions with different stimulus durations. In general, the estimated weights for each component were not equal at different temporal segments. In the third experiment, the signal was added to only one of three segments of the center component. Ideally, weight patterns should have changed when the temporal position of the signal segment was altered. Two stimulus durations, 300 and 15 ms, were used. For the 300-ms condition, the signal was added to only the end segment, and for all three observers the weight patterns are different from that obtained in experiment 1 with the signal added to all segments. For the 15-ms conditions, altering the signal position changed the estimated weights for only one observer.

Adult↗

PubMed1989

Covariance density estimation for autoregressive spectral modelling of point processes.

The use of autoregressive modelling has acquired great importance in time series analysis and in principle it may also be applicable in the spectral analysis of point processes with similar advantages over the nonparametric approach. Most of the methods used for autoregressive spectral analysis require positive semidefinite estimates for the covariance function, while current methods for the estimation of the covariance density function of a point process given a realization over the interval [0, T] do not guarantee a positive semidefinite estimate. This paper discusses methods for the estimation of the covariance density and conditional intensity function of point processes and present alternative computational efficient estimation algorithms leading always to positive semidefinite estimates, therefore adequate for autoregressive spectral analysis. Autoregressive spectral modelling of point processes from Yule-Walker type equations and Levinson recursion combined with the minimum AIC or CAT principle is illustrated with neurobiological data.

Animals↗

PubMed2004

Can electrophysiological assessments of brain function be useful to the intensive care physician in daily clinical practice?

Changes in electroencephalogram parameters and auditory event-related potentials, induced by interruption to propofol sedation in intensive care patients, provide a number of electrophysiological measures that can be used to assess neurological function accurately. Studies of electroencephalogram parameters suggest that power spectral estimation, as root mean square power, is more useful and precise than spectral edge frequency 95% in evaluating the functional integrity of the brain. When such parameters are used to evaluate neurological function, in particular the N100 and mismatch negativity components, a precise assessment of a patient's readiness to awaken from a pharmacologically induced coma (such as sedation) can be obtained. In terms of ease of use, however, it is more difficult to establish whether N100 or mismatch negativity is superior.

Electroencephalography↗

PubMed1976

The temporal and periodic organization of REM eye movements in mental retardation.

Time trends and periodic cycles in REM sleep eye movements were examined in 6 functional and 6 mongoloid adolescent retardates. Both groups of subjects showed approximately equal percentages of linear trends, quadratic trends, linear and quadratic trends, and absence of trend. The eye movement time-series were subject to an orthogonal spectral analysis. In both groups of subjects, peak spectral estimates generally occurred at 10.6- or 21.3-min periods. Following this, the eye movements of the longest REM periods (and one long period of pre-sleep wakefulness) were subject to a least-squares spectral analysis. This analysis yielded estimates ranging from 22 to 44 min. Eye movements lacked the ultradian organization previously reported for eye movements of normal subjects. These results imply that the ultradian organization of REM sleep and the ultradian organization of eye movements may be independent.

Adolescent↗

PubMed1994

Autoregressive spectral array for graphical display of EEG data.

A graphical display of the frequency content of background electroencephalogram (EEG) activity is obtained by calculating the spectral estimates using autocorrelation autoregressive method and the classical Fourier transform method. Display of spectral content of consecutive data segments is made using hidden-line suppression technique so as to get a spectral array. The autoregressive spectral array (ASA) is found to be sensitive to baseline drift. Following baseline correction the autoregressive technique is found to be superior to the Fourier method of compressed spectral array (CSA) in detecting the transitions in the frequencies of the signal. The smoothed ASA gives a better picture of transitions and changes in the background activity. The ASA can be made to adapt to specific changes of dominant frequencies while eliminating unnecessary peaks in the spectrum. The utility of the ASA for background EEG analysis is discussed.

Computer Graphics↗

PubMed2003

A method for estimating the CTF in electron microscopy based on ARMA models and parameter adjustment.

In this work, a powerful parametric spectral estimation technique, 2D-auto regressive moving average modeling (ARMA), has been applied to contrast transfer function (CTF) detection in electron microscopy. Parametric techniques such as auto regressive (AR) and ARMA models allow a more exact determination of the CTF than traditional methods based only on the Fourier transform of the complete image or parts of it and performing some average (periodogram averaging). Previous works revealed that AR models can be used to improve CTF estimation and the detection of its zeros. ARMA models reduce the model order and the computing time, and more interestingly, achieve increased accuracy. ARMA models are generated from electron microscopy (EM) images, and then a stepwise search algorithm is used to fit all the parameters of a theoretical CTF model in the ARMA model previously calculated. Furthermore, this adjustment is truly two-dimensional, allowing astigmatic images to be properly treated. Finally, an individual CTF can be assigned to every point of the micrograph, by means of an interpolation at the functional level, provided that a CTF has been estimated in each one of a set of local areas. The user need only know a few a priori parameters of the experimental conditions of his micrographs, for turning this technique into an automatic and very powerful tool for CTF determination, prior to CTF correction in 3D-EM. The programs developed for the above tasks have been integrated into the X-Windows-based Microscopy Image Processing Package (Xmipp) software package, and are fully accessible at www.biocomp.cnb.uam.es.

Algorithms↗

PubMed1997

Heart rate variability spectral indices for haemodynamic classification of haemodialysis patients.

The usefulness of spectral indices extracted from the heart rate variability (HRV) in discriminating between hypotension-prone and hypotension-resistant haemodialysis patients was investigated. In 30 patients, classified as hypotension resistant (stable group) or hypotension prone (unstable group), beat-to-beat heart period was measured during haemodialysis sessions terminated without collapses. HRV was analysed in the frequency domain combining classic autoregressive spectral estimation with two eigen decomposition-based techniques: the reduced rank approximation (RRA) of the autocorrelation matrix and the Pisarenko harmonic decomposition (PHD). Five spectral indices were obtained: the ratio between the powers in the LF and HF bands (LF/HF), the same ratio calculated after application of RRA (LF/HFRRA), the frequency of the main oscillatory component of HRV estimated through PHD with a decomposition order equal to 1 (F1) and equal to 2 (F2) and the difference between the frequencies of the two oscillatory components resolved in the latter cas (Fd). The performances of these indices in discriminating between the two groups of patients were evaluated estimating the misclassification probability (Pm) of a Bayesian quadratic classifier. The HRV spectral pattern was markedly different: in the stable patients power was mainly in the low-frequency band, whereas in the unstable group it was mainly in the high-frequency band. The frequency of the main oscillatory component was significantly greater in the unstable group than in the stable one. Spectral indices displayed good discrimination power, increasing with the length of the dialysis interval. Best performances were achieved by LF/HFRRA both over short dialysis periods (Pm approximately 12% over 20 min intervals) and over longer periods (Pm = 3.3% over 160 min); similar results were obtained with Fd over short periods and LF/HF over long periods. Spectral HRV indices demonstrate, therefore, a diagnostic value in discriminating between hypotension-resistant and hypotension-prone patients.

Bayes Theorem↗

PubMed2001

Distinguishing subtypes of temporal lobe epilepsy with background hippocampal activity.

PURPOSE: Two subtypes of temporal lobe epilepsy (TLE) can be defined through clinical observations and analysis of hippocampal tissue resected during surgical procedures for intractable TLE: (a) mesial temporal sclerosis (MTS), which is characterized by extensive changes to the hippocampus and good surgical outcome; and (b) paradoxical temporal lobe epilepsy (PTLE), which is characterized by minimal cell loss and comparatively poorer surgical outcome. Patients in both subtypes have seizures that appear to begin in the medial temporal lobe, but documented differences in substrate and outcome between these subtypes has defined a need to distinguish MTS and PTLE patients before surgery. This report describes a retrospective study to investigate the feasibility of doing so during intracranial monitoring. METHODS: Background EEG epochs, 5 min in duration, were recorded from the anterior hippocampus in 14 (10 MTS and four PTLE) patients with consistent localization of seizure onset to medial temporal structures. The power spectral density (PSD) of the EEG epochs was calculated by a Fourier spectral estimator, and the total signal power and power of the delta, theta, alpha, beta, and gamma frequency bands were submitted to group-to-group comparison. RESULTS: Spectral peaks were observed in the delta band in all PSD estimates and in the theta band in nine of 14 (seven MTS, two PTLE) estimates. The MTS and PTLE subtypes could be distinguished by the total signal power and delta band power. These power measurements were greater in the PTLE subtype. CONCLUSIONS: Both delta and theta spectral components are present in hippocampal background EEGs recorded from patients with TLE. The results indicate that group differences exist in spectral measures of background hippocampal signals recorded from MTS and PTLE subtypes. This suggests both that substrate differences in cellular composition and connectivity are reflected in hippocampal background EEGs and that spectral measurements of these signals may hold promise for tests to identify the group membership of individual patients.

Adult↗

PubMed2002

Doppler angle estimation using AR modeling.

The transit time spectrum broadening effect has long been explored for Doppler angle estimation. Given acoustic beam geometry, the Doppler angle can be derived based on the mean Doppler frequency and the Doppler bandwidth. Spectral estimators based on the fast Fourier transform (FFT) are typically used. One problem with this approach is that a long data acquisition time is required to achieve adequate spectral resolution, with typically 32-128 flow samples being needed. This makes the method unsuitable for real-time two-dimensional Doppler imaging. This paper proposes using an autoregressive (AR) model to obtain the Doppler spectrum using a small number (e.g., eight) of flow samples. The flow samples are properly selected, then extrapolated to ensure adequate spectral resolution. Because only a small number of samples are used, the data acquisition time is significantly reduced and real-time, two-dimensional Doppler angle estimation becomes feasible. The approach was evaluated using both simulated and experimental data. Flows with various degrees of velocity gradient were simulated, with the Doppler angle ranging from 20 degrees to 75 degrees. The results indicate that the AR method generally provided accurate Doppler bandwidth estimates. In addition, the AR method outperformed the FFT method at smaller Doppler angles. The experimental data for Doppler angles, ranging from 33 degrees to 72 degrees, showed that the AR method using only eight flow samples had an average estimation error of 3.6 degrees, which compares favorably to the average error of 4.7 degrees for the FFT method using 64 flow samples. Because accurate estimates can be obtained using a small number of flow samples, it is concluded that real-time, two-dimensional estimation of the Doppler angle over a wide range of angles is possible using the AR method.

Algorithms↗

PubMed2006

Tutorial on univariate autoregressive spectral analysis.

In the present paper, the theoretical basis of autoregressive (AR) modelling in spectral analysis is explained in simple terms. Spectral analysis gives information about the frequency content and sources of variation in a time series. The AR method is an alternative to discrete Fourier transform, and the method of choice for high-resolution spectral estimation of a short time series. In biomedical engineering, AR modelling is used especially in the spectral analysis of heart rate variability and electroencephalogram tracings. In AR modelling, each value of a time series is regressed on its past values. The number of past values used is called the model order. An AR model or process may be used in either process synthesis or process analysis, each of which can be regarded as a filter. The AR analysis filter divides the time series into two additive components, the predictable time series and the prediction error sequence. When the prediction error sequence has been separated from the modelled time series, the AR model can be inverted, and the prediction error sequence can be regarded as an input and the measured time series as an output to the AR synthesis filter. When a time series passes through a filter, its amplitudes of frequencies are rescaled. The properties of the AR synthesis filter are used to determine the amplitude and frequency of the different components of a time series. Heart rate variability data are here used to illustrate the method of AR spectral analysis. Some basic definitions of discrete-time signals, necessary for understanding of the content of the paper, are also presented.

Heart Rate↗

PubMed1989

A real-time system for the spectral analysis of the EEG.

We have developed an inexpensive and portable system for processing multiple channels of electroencephalograms (EEG) in real-time to assist the electroencephalographer in identifying subtle changes in these data, particularly in the interpretation of long records. Up to 16 channels of data are spectrally decomposed with a selection of bandwidth, windows, scaling methods, epoch averaging, and smoothing options available. The resulting power spectral estimate may be displayed or printed in a variety of formats, including color encoding of selectable spectral bands. Both the sampled EEG and its spectra may be stored for off-line reprocessing, for archiving, or for statistical analysis in the time or frequency domains.

Analog-Digital Conversion↗

PubMed1998

Spectral analysis methods for neurological signals.

This paper reviews some novel spectral analysis techniques that are useful for neurological signals in general and EEG signals in particular. First, some drawbacks and limitations of the commonly used Fast Fourier transforms (FFTs) are presented, and then alternative algorithms are outlined. An auto-regressive (AR) modeling based spectral estimation procedure is presented to overcome the problems of lower resolution and 'leakage' effects inherent in the FFT algorithm. For signals which are transient in nature or rapidly time-varying, two alternative algorithms are presented. The first is an adaptive AR parameter estimation algorithm and the second is a wavelet based time-frequency representation algorithm. Finally, a Spectral Distance measure and the Itakura distance measure are presented to quantify the differences between the spectra of two signals in a succinct manner. The application and performance of all the algorithms is illustrated using electroencephalograms (EEGs) recorded in animals during hypoxic asphyxic injury to brain.

Algorithms↗

PubMed2005

High-resolution frequency estimation technique for recovering phase distribution in interferometers.

An integral approach to phase measurement is presented. First, the use of a high-resolution technique for the pixelwise detection of phase steps is proposed. Next, the robustness of the algorithm that is developed is improved by incorporation of a denoising procedure during spectral estimation. The pixelwise knowledge of phase steps is then applied to the Vandermonde system of equations for retrieval of phase values at each pixel point. Conceptually, our proposal involves the design of an annihilating filter that has zeros at the frequencies associated with the polynomial that describes the fringe intensity. The parametric estimation of this annihilating filter yields the desired spectral information embedded in the signal, which in our case represents the phase steps. The proposed method offers the advantage of extracting the interference phase of nonsinusoidal waveforms in the presence of miscalibration error of the piezoelectric transducer. In addition, in contrast to previously reported methods, this method does not require the application of selective phase steps between data frames for nonsinusoidal waveforms.

Journal Article↗

PubMed1991

Estimation of time delay between EEG signals for epileptic focus localization: statistical error considerations.

A theoretical analysis of the variance for the time delay estimate between two EEG signals, obtained via the phase spectrum method, is presented. Explicit theoretical formulae for the variance are obtained and compared via simulations to experimentally derived results for estimate variability. The variance of the time delay estimate is inversely proportional to the frequency range of interest, to the number of data segments utilized for spectral estimation, and to the coherence between the two EEG signals. The simulations indicate that the formulae can be used even with non-gaussian and relatively narrow-band EEG-like data. A minimum-variance estimate for the time delay is also presented.

Computer Simulation↗

PubMed1996

Neuromagnetic study of movement-related changes in rhythmic brain activity.

Neuromagnetic fields from the left cerebral hemisphere of five healthy, right-handed subjects were investigated in a typical Bereitschaftspotential paradigm consisting of self-paced voluntary movement of the right index finger. To assess movement-related spectral changes of the spontaneous magnetoencephalogram. latency-dependent short-time spectra were obtained by Fourier analysis for each single trial. The number of trials in which the spectral estimate for a certain frequency and latency deviated from reference values was then transformed into a probabilistic relative power measure. A spectral power depression around 20 Hz was observed starting about 2.5 s before movement onset, followed by elevated power in the 20-35 Hz range starting about 500 ms after movement onset. Generally, the power increase differed from the prior depression in both spectrum and topography, suggesting different generating processes rather than just a 'rebound' effect of the idling rhythm generator. The time course and topography of spectral power changes are discussed in relation to the corresponding properties of the movement-related neuromagnetic fields (readiness field, motor field, and movement-evoked field I).

Adult↗

PubMed2000

A chemometric approach to the estimation of the absorption spectra of dye probe merocyanine 540 in aqueous and phospholipid environments.

Merocyanine 540 (MC540) is a widely used dye probe for membranous environments. However, fundamental knowledge of the spectral features of this dye in aqueous and hydrophobic environments is still lacking. Such knowledge is important because biomembranes involve a hydrophobic environment surrounded by a hydrophilic environment. Because many investigations so far have been performed based on indistinct spectral estimations, the interpretation of the data obtained using this dye as a fluorescent transmembrane probe remains controversial. In order to determine the exact spectra in both aqueous and hydrophobic environments, we adopted principal factor analysis (PFA), a method of multivariate analysis. The PFA method can also determine the number of molecular species present in the reaction mixture, which is three in pure water and two in phospholipid suspension. Two of the species in both water and phospholipid suspension were the monomer and dimer. The third species in water was the trimer, but its amount was so small at 10 microM MC540 solution that the spectral data in water can be approximated neglecting this molecular species. The monomer spectrum changed its form markedly with a bathochromic shift when transferred from the water to phospholipid environment, whereas the dimer remained similar in its shape except for a remarkable red shift. In water, the dissociation constants, K(1) and K(2), for the assumed stacking-model reactions, M+M <--> M(2) and M+M(2) <--> M(3), were 3.1 x 10(-4) M and 5.7 x 10(-4) M, respectively. In the phospholipid environment, the dissociation constant K* for the assumed stacking-model reaction, M(*)+M(*) <--> *M(2), was 1.9x10(-5)M. The fluorescent intensities of MC540 were also measured in both water and phospholipid environments. A comparison based on the absorption and fluorescence spectra suggested that the temporal increase in the amount of the monomer on the excitable membrane contributes to the fluorescent intensity change observed in the transmembrane potential change.

Fluorescent Dyes↗