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PubMed1999

Wavelet transform to quantify heart rate variability and to assess its instantaneous changes.

Heart rate variability is a recognized parameter for assessing autonomous nervous system activity. Fourier transform, the most commonly used method to analyze variability, does not offer an easy assessment of its dynamics because of limitations inherent in its stationary hypothesis. Conversely, wavelet transform allows analysis of nonstationary signals. We compared the respective yields of Fourier and wavelet transforms in analyzing heart rate variability during dynamic changes in autonomous nervous system balance induced by atropine and propranolol. Fourier and wavelet transforms were applied to sequences of heart rate intervals in six subjects receiving increasing doses of atropine and propranolol. At the lowest doses of atropine administered, heart rate variability increased, followed by a progressive decrease with higher doses. With the first dose of propranolol, there was a significant increase in heart rate variability, which progressively disappeared after the last dose. Wavelet transform gave significantly better quantitative analysis of heart rate variability than did Fourier transform during autonomous nervous system adaptations induced by both agents and provided novel temporally localized information.

Adrenergic beta-Antagonists↗
PubMed1993

Using the discrete wavelet transform for time-frequency analysis of the surface EMG signal.

The frequency content of the surface electromyographic (SEMG) signal is used to study neural activity, and force development and fatigue in muscle. The fast Fourier transform (FFT), or short time Fourier transform (STFT), are commonly used to determine the frequency content of the SEMG, but have the drawback of assumed signal stationarity. A relatively new technique, the wavelet transform (WT), is well suited to nonstationary signals, and has gained widespread use in speech and image processing. We applied the discrete wavelet transform (DWT) based on the Daubechies wavelet to SEMG data. The DWT decomposed the SEMG into 11 time-frequency bands; the data was also processed with an FFT algorithm. Comparison of these results show that the DWT provided information in the correct frequency bands. These results are encouraging, as time-frequency signal decomposition will allow movement and force generation patterns to be directly related to SEMG frequency components. The main disadvantage of the DWT seems to be that because the signal is down sampled at each successive DWT scale, the transform is sparse at lower frequency scales. However, we believe that the continuous discrete wavelet transform will overcome this deficiency and provide an additional method of SEMG frequency analysis.

Algorithms↗
PubMed1998

Protein structure analysis using the resonant recognition model and wavelet transforms.

An approach based on the resonant recognition model and the discrete wavelet transform is introduced here for characterising proteins' biological function. The protein sequence is converted into a numerical series by assigning the electron-ion interaction potential to each amino acid from N-terminal to C-terminal. A set of peaks is found after performing a wavelet transform onto a numerical series representing a group of homologous proteins. These peaks are related to protein structural and functional properties and named characteristic vector of that protein group. Further more, the amino acids contributing mostly to a protein's biological functions, the so-called 'hot spots' amino acids, are predicted by the continuous wavelet transform. It is found that the hot spots are clustered around the protein's cleft structure. The wavelets approach provides a novel methods for amino acid sequence analysis as well as an expansion for the newly established macromolecular interaction model: the resonant recognition model.

Amino Acid Sequence↗
PubMed2006

Time-frequency analysis of spike-wave discharges using a modified wavelet transform.

The continuous Morlet wavelet transform was used for the analysis of the time-frequency pattern of spike-wave discharges (SWD) as can be recorded in a genetic animal model of absence epilepsy (rats of the WAG/Rij strain). We developed a new wavelet transform that allows to obtain the time-frequency dynamics of the dominating rhythm during the discharges. SWD were analyzed pre- and post-administration of certain drugs. SWD recorded predrug demonstrate quite uniform time-frequency dynamics of the dominant rhythm. The beginning of the discharge has a short period with the highest frequency value (up to 15 Hz). Then the frequency decreases to 7-9 Hz and frequency modulation occurs during the discharge in this range with a period of 0.5-0.7 s. Specific changes of SWD time-frequency dynamics were found after the administration of psychoactive drugs, addressing different brain mediator and modulator systems. Short multiple SWDs appeared under low (0.5 mg/kg) doses of haloperidol, they are characterized by a fast frequency decrease to 5-6 Hz at the end of every discharge. The frequency of the dominant frequency of SWD was not stable in long lasting SWD after 1.0 mg/kg or more haloperidol: then two periodicities were found. Long lasting SWD seen after the administration of vigabatrin showed a stable frequency of the discharge. The EEG after Ketamin showed a distinct 5 s quasiperiodicity. No clear changes of time-frequency dynamics of SWD were found after perilamine. It can be concluded that the use of the modified Morlet wavelet transform allows to describe significant parameters of the dynamics in the time-frequency domain of the dominant rhythm of SWD that were not previously detected.

Algorithms↗
PubMed2005

Time-frequency component analyser and its application to brain oscillatory activity.

Currently, event-related potential (ERP) signals are analysed in the time domain (ERP technique) or in the frequency domain (Fourier analysis and variants). In techniques of time-domain and frequency-domain analysis (short-time Fourier transform, wavelet transform) assumptions concerning linearity, stationarity, and templates are made about the brain signals. In the time-frequency component analyser (TFCA), the assumption is that the signal has one or more components with non-overlapping supports in the time-frequency plane. In this study, the TFCA technique was applied to ERPs. TFCA determined and extracted the oscillatory components from the signal and, simultaneously, localized them in the time-frequency plane with high resolution and negligible cross-term contamination. The results obtained by means of TFCA were compared with those obtained by means of other commonly used techniques of ERP analysis, such as bilinear time-frequency distributions and wavelet analysis. It is suggested that TFCA may serve as an appropriate tool for capturing the localized ERP components in the time-frequency domain and for studying the intricate, frequency-based dynamics of the human brain.

Adolescent↗
PubMed2001

Analysis and localization of epileptic events using wavelet packets.

This article compares results obtained in previous studies using time-frequency representations (Wigner-Ville, Choi-Williams and Parametric) and the wavelet transform with those obtained with wavelet packet functions to show new findings about their quality in the analysis of ECoG recordings in human intractable epilepsy: data from 21 patients have been analyzed and processed with four types of wavelet functions, including Orthogonal, Biorthogonal and Non-Orthogonal basis. These functions were compared in order to test their quality to represent spikes in the ECoG. The energy based on the wavelet coefficients to different scales was also calculated. The best results were found with the biorthogonal-6.8 wavelet on 5-7 scales, which gave 0.92 sensitivity, but with a high percentage of false positives; this representation was highly correlated with spike events on time and duration. To improve these results we have studied the wavelet packet coefficients energy. We found that reconstruction wavelet packet coefficients at 4 and 9 nodes contain significant information to characterize the spike event. These nodes' reconstruction coefficients were multiplied and this product was highly correlated with spikes events on time and duration. With this procedure we improved the sensitivity up to 0.96 with the same biorthogonal-6.8 wavelet at four levels. With this technique we do not sacrifice computation time: 896 samples are processed at only 0.16 s, so that it is possible to show the spike scattering path on line, because 896 samples (7 s)/16 channels are processed at 3.13 s.

Adult↗
PubMed2000

Single trial analysis of event related potentials: non-linear de-noising with wavelets.

We present and apply a method for single trial analysis of event related potentials (ERPs) that combines techniques from non-linear time series analysis with the wavelet transform. For this method, convincing results have already been achieved for simulated data as well as for intracranially recorded ERPs (Physica D 140 (2000) 257). However, ERPs are affected by a variety of external and internal experimental parameters, which makes the appropriate configuration of single trial analysis difficult. Thus, several pitfalls may occur in realistic applications. In this paper, we applied the method of non-linear de-noising with wavelets to both intra- and extracranially recorded ERPs, and show examples of how and where this single trial analysis can be used to obtain additional information on dynamic neural processes.

Brain↗
PubMed2004

Solar turbulence in earth's global and regional temperature anomalies.

This paper presents a study of the influence of solar activity on the earth's temperature. In particular, we focus on the repercussion of the fluctuations of the solar irradiance on the temperature of the Northern and Southern hemispheres as well as on land and ocean regions. While solar irradiance data are not directly analyzed, we make use of a published solar irradiance reconstruction for long-time-scale fluctuations, and for short-time-scale fluctuations we hypothesize that solar irradiance and solar flare intermittency are coupled in such a way that the solar flare frequency fluctuations are stochastically equivalent to those of the solar irradiance. The analysis is based upon wavelet multiresolution techniques and scaling analysis methods for processing time series. The limitations of the correlation analysis applied to the short-time-scale fluctuations are discussed. The scaling analysis uses both the standard deviation and the entropy of the diffusion generated by the temperature signals. The joint use of these two scaling methods yields evidence of a Lévy component in the temporal persistence of the temperature fluctuations within the temporal range from a few weeks to a few years. This apparent Lévy persistence of the temperature fluctuations is found, by using an appropriate model, to be equivalent to the Lévy scaling of the solar flare intermittency. The mean monthly temperature data sets cover the period from 1856 to 2002.

Journal Article↗
PubMed2001

Colored noise and computational inference in neurophysiological (fMRI) time series analysis: resampling methods in time and wavelet domains.

Even in the absence of an experimental effect, functional magnetic resonance imaging (fMRI) time series generally demonstrate serial dependence. This colored noise or endogenous autocorrelation typically has disproportionate spectral power at low frequencies, i.e., its spectrum is (1/f)-like. Various pre-whitening and pre-coloring strategies have been proposed to make valid inference on standardised test statistics estimated by time series regression in this context of residually autocorrelated errors. Here we introduce a new method based on random permutation after orthogonal transformation of the observed time series to the wavelet domain. This scheme exploits the general whitening or decorrelating property of the discrete wavelet transform and is implemented using a Daubechies wavelet with four vanishing moments to ensure exchangeability of wavelet coefficients within each scale of decomposition. For (1/f)-like or fractal noises, e.g., realisations of fractional Brownian motion (fBm) parameterised by Hurst exponent 0 < H < 1, this resampling algorithm exactly preserves wavelet-based estimates of the second order stochastic properties of the (possibly nonstationary) time series. Performance of the method is assessed empirically using (1/f)-like noise simulated by multiple physical relaxation processes, and experimental fMRI data. Nominal type 1 error control in brain activation mapping is demonstrated by analysis of 13 images acquired under null or resting conditions. Compared to autoregressive pre-whitening methods for computational inference, a key advantage of wavelet resampling seems to be its robustness in activation mapping of experimental fMRI data acquired at 3 Tesla field strength. We conclude that wavelet resampling may be a generally useful method for inference on naturally complex time series.

Artifacts↗
PubMed2001

Analysis of asymmetry in mammograms via directional filtering with Gabor wavelets.

This paper presents a procedure for the analysis of left-right (bilateral) asymmetry in mammograms. The procedure is based upon the detection of linear directional components by using a multiresolution representation based upon Gabor wavelets. A particular wavelet scheme with two-dimensional Gabor filters as elementary functions with varying tuning frequency and orientation, specifically designed in order to reduce the redundancy in the wavelet-based representation, is applied to the given image. The filter responses for different scales and orientation are analyzed by using the Karhunen-Loève (KL) transform and Otsu's method of thresholding. The KL transform is applied to select the principal components of the filter responses, preserving only the most relevant directional elements appearing at all scales. The selected principal components, thresholded by using Otsu's method, are used to obtain the magnitude and phase of the directional components of the image. Rose diagrams computed from the phase images and statistical measures computed thereof are used for quantitative and qualitative analysis of the oriented patterns. A total of 80 images from 20 normal cases, 14 asymmetric cases, and six architectural distortion cases from the Mini-MIAS (Mammographic Image Analysis Society, London, U.K.) database were used to evaluate the scheme using the leave-one-out methodology. Average classification accuracy rates of up to 74.4% were achieved.

Breast Neoplasms↗
PubMed2001

Wavelet entropy: a new tool for analysis of short duration brain electrical signals.

Since traditional electrical brain signal analysis is mostly qualitative, the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals. These methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of brain dynamics. Here, new method based on orthogonal discrete wavelet transform (ODWT) is applied. It takes as a basic element the ODWT of the EEG signal, and defines the relative wavelet energy, the wavelet entropy (WE) and the relative wavelet entropy (RWE). The relative wavelet energy provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The WE carries information about the degree of order/disorder associated with a multi-frequency signal response, and the RWE measures the degree of similarity between different segments of the signal. In addition, the time evolution of the WE is calculated to give information about the dynamics in the EEG records. Within this framework, the major objective of the present work was to characterize in a quantitative way functional dynamics of order/disorder microstates in short duration EEG signals. For that aim, spontaneous EEG signals under different physiological conditions were analyzed. Further, specific quantifiers were derived to characterize how stimulus affects electrical events in terms of frequency synchronization (tuning) in the event related potentials.

Adult↗
PubMedDate not supplied

Hardware design for the computation of heart rate variability.

The decrease in heart rate variability is an indication of abnormal heart function. Proposed here is a hardware design of a standalone system that calculates and evaluates heart rate variability, distinguishing healthy from unhealthy subjects. Previous approaches are mostly based on the fast Fourier transform and the power spectral analysis. Described is an alternative approach thatfollows a recently proposed idea: the analysis of heart rate signals with the use of wavelets. The proposed system follows simple gated architecture and is composed offour main units: a processing unit that prepares the input signal for analysis, a unit that manages control signals, the wavelet computation unit and the wavelet coefficient evaluation unit. The hardware design is cost-effective, simple and easy to implement. Experimental results proved that this system is efficient and produces a clean and accurate separation between the healthy and unhealthy groups of patients for the first nine scales of wavelet analysis.

Analysis of Variance↗
PubMed2003

Myoelectric signal compression using zero-trees of wavelet coefficients.

Recent progress in the diagnostic use of the myoelectric signal for neuromuscular diseases, coupled with increasing interests in telemedicine applications, mandate the need for an effective compression technique. The efficacy of the embedded zero-tree wavelet compression algorithm is examined with respect to some important analysis parameters (the length of the analysis segment and wavelet type) and measurement conditions (muscle type and contraction type). It is shown that compression performance improves with segment length, and that good choices of wavelet type include the Meyer wavelet and the fifth order biorthogonal wavelet. The effects of different muscle sites and contraction types on compression performance are less conclusive.A comparison of a number of lossy compression techniques has revealed that the EZW algorithm exhibits superior performance to a hard thresholding wavelet approach, but falls short of adaptive differential pulse code modulation. The bit prioritization capability of the EZW algorithm allows one to specify the compression factor online, making it an appealing technique for streaming data applications, as often encountered in telemedicine.

Adult↗
PubMed2001

Wavelet transform of heart rate variability to assess autonomic nervous system activity does not predict arousal from general anesthesia.

PURPOSE: The relationship between autonomic nervous system (ANS) activity and general anesthesia has been explored. Studies have demonstrated partial recovery of heart rate variability (HRV), representative of ANS activity, in the postoperative period, but the arousal period has not been precisely studied. The goals of this study were to analyze modifications of ANS activity during general anesthesia and, more particularly, around the arousal period, to look for predictors of arousal. METHODS: We analyzed HRV changes using wavelet transform, a time-frequency analysis that, in contrast to Fourier transform, is able to assess abrupt changes of ANS activity. Seventeen patients (mean +/- SD age: 40.9 +/- 16.4 yr) under general anesthesia for hip or knee surgery, were included in the study. The analysis began one hour before anesthesia, focussed on eye opening, and ended three hours after arousal. RESULTS: There was a dramatic decrease in HRV after induction, that extended throughout anesthesia and represented a decrease in global autonomic regulation with, however, a relative predominance of vagal tone. At the moment of eye opening, there was an abrupt change in HRV, representing a sudden shift of ANS balance towards the predominance of sympathetic activity, while none of these indices changed seconds before arousal. CONCLUSIONS: Wavelet analysis of HRV appears to be powerful tool to precisely assess instantaneous changes of HRV during anesthesia. Using this method, there were no identifiable precursory HRV indices of arousal.

Adult↗
PubMed2003

Wavelets in bioinformatics and computational biology: state of art and perspectives.

MOTIVATION: At a recent meeting, the wavelet transform was depicted as a small child kicking back at its father, the Fourier transform. Wavelets are more efficient and faster than Fourier methods in capturing the essence of data. Nowadays there is a growing interest in using wavelets in the analysis of biological sequences and molecular biology-related signals. RESULTS: This review is intended to summarize the potential of state of the art wavelets, and in particular wavelet statistical methodology, in different areas of molecular biology: genome sequence, protein structure and microarray data analysis. I conclude by discussing the use of wavelets in modeling biological structures.

Algorithms↗
PubMed2003

[Advance in signal analysis of auditory evoked potential].

Signal analysis of the auditory evoked potential (AEP) has been the interesting field in biomedicine and signal processing for a long time. Recent advances in the analytic method of AEP are summed up in this paper. Seven methods, including spectral analysis, adaptive filtering, wavelet transform, chaos theory, artificial neutral network, regularization, and independent component analysis are mainly introduced. All of them are promising for extracting the signal with less stimulation and adequate quality, and for displaying their efficient application in the analysis of AEP.

Electroencephalography↗
PubMed2005

Analysis of esophageal atrial recordings through wavelet packets decomposition.

In this paper the processing of esophageal atrial electrograms by means of wavelet packets (WP) decomposition is presented. WP is described as a flexible, signal-adaptive, tool, which can be easily tuned to enhance characteristics of esophageal signals. Two aspects are mainly investigated: (i) the possibility to obtain automatic, reliable detection of atrial activation in 24h Holter recordings and (ii) the development of an algorithm for discrimination between atrial flutter (AFLU) and atrial fibrillation (AF) episodes. WP decomposition was used as a framework for pre-processing the esophageal signal and to build a set of orthonormal sub-signals which can be selected and combined according to the signal processing task to be performed: (i) in the detection of atrial activation, sub-band signal characteristics were explored at different scales by using the modulus maxima criteria and (ii) in the discrimination between AFLU and AF the coarser approximation of the esophageal signal was studied by spectral analysis. A reliable detection of atrial activation was obtained (Sensitivity (SE): 99.08%; positive predictability (+P): 98.98%). In addition a quantitative index able to discriminate between AFLU (SE: 97.5%; +P: 98.7%) and AF (SE: 98.7%; +P: 97.5%) episodes was introduced.

Atrial Fibrillation↗
PubMed1998

Spectral analysis of the laser Doppler perfusion signal in human skin before and after exercise.

Spectral analysis based on wavelet transformation of the periodic oscillations of the cutaneous laser Doppler flowmetry (LDF) signal was used to analyze exercise-induced changes in flow motion in humans. The measurements were performed on the forearm skin in nine healthy, less-trained subjects before and after exercise. Periodic oscillations with frequencies of around 1, 0.3, 0.1, and 0.04 Hz were demonstrated, which are proposed to represent the influence of heart beat, respiration, intrinsic myogenic activity, and the neurogenic factors, respectively, on cutaneous blood flow. We also demonstrated oscillations with a frequency of around 0.01 Hz both before and after exercise. The mean spectral amplitude in the frequency range from 0.0095 to 2.3 Hz increased twofold (P = 0.004) in response to exercise. This increase results from a significant increase in the amplitude of oscillations of around 1, 0.3, and 0.1 Hz. The amplitude of oscillations of around 1 and 0.3 Hz increased onefold in response to exercise (P = 0.02 for both frequencies), whereas the amplitude of oscillations of around 0.1 Hz increased threefold (P = 0.008). Furthermore, to evaluate relative changes of each particular oscillation in response to exercise, the absolute amplitude of each frequency interval was divided by the mean spectral amplitude. In this way, the relative contribution of oscillations of around 0.01 and 0.04 Hz were shown to decrease significantly following exercise (P = 0.008 and P = 0.004, respectively). The relative contribution of the oscillations of around 0.1 Hz increased, although not statistically significant (P = 0.08), while the relative contribution of the oscillations of around 0.3 and 1 Hz to the total flow motion remained unchanged in response to exercise (P = 0.84 and P = 0.95, respectively). These findings indicate an increased contribution of the oscillations of around 0.1 Hz to the regulation of the cutaneous blood flow following exercise, whereas oscillations of around 0.04 and 0.01 Hz contribute less. We conclude that spectral analysis using a wavelet transformation of the LDF signal is a valuable tool for use in the evaluation of exercise-induced changes in the dynamics of cutaneous microvascular blood flow, but further studies are necessary to clarify the physiological origin of these oscillations.

Exercise↗