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PubMed2001

Use of wavelet transforms in analysis of time-activity data from cardiac PET.

UNLABELLED: Because of its intrinsic quantitative properties, PET permits measurement of myocardial perfusion and metabolism in absolute terms (i.e., mL/g/min). However, quantification has been limited by errors produced in image acquisition, selection of regions of interest, and data analysis. The goal of this study was to evaluate a newly developed, novel, wavelet-based noise-reduction approach that can objectively extract biologic signals hidden within dynamic PET data. METHODS: Quantification of myocardial perfusion using dynamic PET imaging with 82Rb, H2(15)O, and 13NH3 was selected to evaluate the effects of the wavelet-based noise-reduction protocol. Dynamic PET data were fitted to appropriate mathematic models before and after wavelet-based noise reduction to get flow estimates. Time-activity curves, precision, accuracy, and differentiating capacity derived from the wavelet protocol were compared with those obtained from unmodified data processing. A total of 84 human studies was analyzed, including 43 at rest (18 82Rb scans, 18 H2(15)O scans, and 7 13NH3 scans) and 41 after coronary hyperemia with dipyridamole (17 82Rb scans, 17 H2(15)O scans, and 7 13NH3 scans). RESULTS: For every tracer tested under all conditions, the wavelet method improved the shape of blood and tissue time-activity curves, increased estimate-to-error ratios, and maintained fidelity of flow in regions as small as 0.85 cm3. It also improved the accuracy of flow estimates derived from 82Rb to the level of that achieved with H2(15)O, which was not affected markedly by the wavelet process. In studies of patients with coronary disease, regional heterogeneity of myocardial perfusion was preserved and flow estimates in infarcted regions were differentiated more easily from normal regions. CONCLUSION: The wavelet-based noise-reduction method effectively and objectively extracted tracer time-activity curves from data with low signal-to-noise ratios and improved the accuracy and precision of measurements with all tracer techniques studied. The approach should be generalizable to other image modalities such as functional MRI and CT and, therefore, improve the ability to quantify dynamic physiologic processes.

Coronary Circulation↗
PubMed2004

Wavelet-based multifractal analysis of fMRI time series.

Functional magnetic resonance imaging (fMRI) time series are investigated with a multifractal method based on the Wavelet Modulus Maxima (WTMM) method to extract local singularity ("fractal") exponents. The spectrum of singularity exponents of each fMRI time series is quantified by spectral characteristics including its maximum and the corresponding dimension. We found that the range of Hölder exponents in voxels with activation is close to 1, whereas exponents are close to 0.5 in white matter voxels without activation. The maximum dimension decreases going from white matter to gray matter, and is lower still for activated time series. The full-width-at-half-maximum of the spectra is higher in activated areas. The proposed method becomes particularly effective when combining these spectral characteristics into a single parameter. Using these multifractal parameters, it is possible to identify activated areas in the human brain in both hybrid and in vivo fMRI data sets without knowledge of the stimulation paradigm applied.

Brain↗
PubMed2006

Wavelet versus detrended fluctuation analysis of multifractal structures.

We perform a comparative study of applicability of the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maxima (WTMM) method in proper detecting of monofractal and multifractal character of data. We quantify the performance of both methods by using different sorts of artificial signals generated according to a few well-known exactly soluble mathematical models: monofractal fractional Brownian motion, bifractal Lévy flights, and different sorts of multifractal binomial cascades. Our results show that in the majority of situations in which one does not know a priori the fractal properties of a process, choosing MFDFA should be recommended. In particular, WTMM gives biased outcomes for the fractional Brownian motion with different values of Hurst exponent, indicating spurious multifractality. In some cases WTMM can also give different results if one applies different wavelets. We do not exclude using WTMM in real data analysis, but it occurs that while one may apply MFDFA in a more automatic fashion, WTMM must be applied with care. In the second part of our work, we perform an analogous analysis on empirical data coming from the American and from the German stock market. For this data both methods detect rich multifractality in terms of broad f(alpha), but MFDFA suggests that this multifractality is poorer than in the case of WTMM.

Journal Article↗
PubMed2006

[Dynamic analysis of heart rate variability based on wavelet transform].

The analysis of heart rate variability (HRV) has become a tool for noninvasively detecting the cardiovascular modulation of autonomic nervous system. Traditional analysis in frequency domain mainly includes calculating the power and detecting the peak frequency of each physiological frequency band. Whether employing the classical method or AR model to estimate the spectrum, the approximate stationarity of HRV is presupposed. Only in short term analysis can data meet this condition, while in long term the nonstationarity of HRV notably appears. A dynamic analysis method based on wavelet transform was proposed in this paper, which not only can obtain the traditional indices in frequency domain, but can compute their dynamic values varying with time, called short-time power and short-time LF/HF ratio. The latter can dynamically evaluate the activity of autonomic nervous. Finally the method was applied to trace the balance of autonomic nervous in Atropin drag experiment.

Adult↗
PubMed2004

Wavelet and Fourier analysis of ventricular and main arteries pulsations in anesthetized dogs.

The purpose of this study was to characterize time-frequency behavior using the Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) to analyze ventricular and arterial pressure signals from anesthetized mongrel dogs. Both ventricular and arterial pressure pulsations were recorded using catheter-tip manometers and the CWT was applied to these signals to obtain module coefficients, associated contours, and the 3-D representation of these modules. FFT was applied to obtain the Fourier spectrum. The mathematical analysis of the cardiovascular pressure pulsations permitted the identification of the evolution of the frequency components for the aortic and pulmonary valve functions as well as the intra-ventricular and respiratory influences on the cardiovascular dynamics. The CWT is a very sensitive and reliable procedure for determining the three-dimensional (time-frequency-amplitude) of the oscillatory phenomena during each cardiac cycle, providing more, although complementary, information than the spectral analysis obtained with the FFT. Thanks to the FFT, exact values in Hz could be found for the different events produced in each cycle, and thus the information provided by CWT could be related to the information provided by FFT. The combination of both mathematical methodologies permitted identification of each component of the analyzed signals. The 3D representation allowed an easy comparison of the relative importance of the complex magnitudes in frequency for the different components of the pulsatile waves.

Anesthesia↗
PubMed2005

A wavelet approach for the analysis of folding trajectory of protein Trp-cage.

Understanding how protein folds into a functional native structure is arguably one of the most challenging problems remaining in computational biology. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape in terms of various reaction coordinates such as the fraction of native contacts, the radius of gyration, the RMS deviation from the native and so on. In this paper, we present a wavelet approach towards understanding the global state changes during protein folding. The approach is based on the wavelet analysis on the trajectories of various reaction coordinates to identify the significant intermediate states or structural motifs in the folding process. We demonstrate through an example protein Trp-cage that this approach extracts crucial information about protein folding intermediate states as well as the time correlation among these states. Furthermore, the current approach reveals a meaningful structural pattern that had been overlooked in previous works, which provides a better understanding of the folding mechanism as well as the limitation of the current force fields.

Algorithms↗
PubMed2002

Wavelet-based multifractal analysis of human balance.

Center of pressure (COP) traces have been used to investigate the dynamics of human balance. In this paper we employ a wavelet-based multifractal methodology to identify structural differences in mediolateral and anterioposterior sway between COP traces of healthy and Parkinson's patients. Two statistical techniques are used to summarize the differences in multifractal spectrum (MFS) for both groups. The first technique is a multivariate repeated measures analysis on estimated MF spectra for subjects. The second technique obtains two characteristic measures from each subject's estimated MFS: (i) location and (ii) half-width of the spectrum. These measures present an intuitive summary of the MFS for each subject, allowing for statistical comparisons between the two groups. Both analyzes lead to significant discrimination between Parkinson versus healthy subject's MFS. We find that COP time series of Parkinson patients exhibit a greater degree of roughness as compared to healthy subjects' COP traces. Furthermore, MFS for Parkinson patients are narrower, suggesting a reduction in complexity as compared to the healthy group. The methodology presented here may be helpful in development of clinically relevant measures, including the assessment of severity of conditions as the measures developed here correlate with standard severity measures.

Analysis of Variance↗
PubMed2002

Application of wavelet transform to uterine electromyographic signals recorded using abdominal surface electrodes.

OBJECTIVE: The aim of this study was to explore the use of the wavelet transform technique to extract and display simultaneously the time, frequency and amplitude information corresponding to electromyographic (EMG) activity of the uterus during labor recorded using abdominal electrodes. METHODS: Uterine EMG signals were recorded from patients in labor using three pairs of electrodes placed across the maternal abdomen. In all the patients uterine activity was also recorded either from an intrauterine pressure catheter (IUPC) or a tocodynamometer. The EMG signals were analyzed using spectral analysis and wavelet analysis. RESULTS: Uterine EMG bursts corresponded with uterine activity measured with either the IUPC or the tocodynamometer. Using wavelet analysis a time-frequency-amplitude plot was obtained to separate out the frequency components relating to uterine EMG activity. CONCLUSION: This study showed that the wavelet transform could be a useful tool to study the uterine EMG activity. Continued studies on frequency content, amplitude and origin of uterine EMG activity could be helpful in understanding uterine contraction.

Algorithms↗
PubMed2004

Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry.

We present an analysis of a spatial carrier-fringe pattern in three-dimensional (3-D) shape measurement by using the wavelet transform, a tool excelling for its multiresolution in the time- and space-frequency domains. To overcome the limitation of the Fourier transform, we introduce the Gabor wavelet to analyze the phase distributions of the spatial carrier-fringe pattern. The theory of wavelet transform profilometry, an accuracy check by means of a simulation, and an example of 3-D shape measurement are shown.

Algorithms↗
PubMed2005

Wavelet transforms for optical pulse analysis.

An exploration of wavelet transforms for ultrashort optical pulse characterization is given. Some of the most common wavelets are examined to determine the advantages of using the causal quasi-wavelet suggested in Proceedings of the LEOS 15th Annual Meeting (IEEE, 2002), Vol. 2, p. 592, in terms of pulse analysis and, in particular, chirp extraction. Owing to its ability to distinguish between past and future pulse information, the causal quasi-wavelet is found to be highly suitable for optical pulse characterization.

Journal Article↗
PubMed2006

[HRV signal analysis based on wavelet transform].

In accordance with the character of heart rate variability(HRV) signal, we have divided HRV signal into 1/f fractal component and 1/f non-fractal component by use of wavelet transform. This division will be beneficial to the acqusition of the character of HRV signal as well as to the quantitative analysis of 1/f fractal component.

Algorithms↗
PubMed2004

Comparative analysis on wavelet-based detection of finite duration low-amplitude signals related to ventricular late potentials.

Ventricular late potentials (VLPs) are considered as a noninvasive marker of patients with myocardial infarction, who are prone to the development of ventricular tachycardia. This paper investigates the effects of variations in physical properties of myocardial infarcts in terms of their effects on the parametric variations in VLP analysis. A sufficiently large set of signals underlining the behavior of physical parameters was employed to represent the effect of physical size, position, orientation and type of infarct. The approximated signals are variations from real electrocardiography signals by adding potentials representing late potentials based on duration, frequency, amplitude and position. The aim is not to exactly model VLP but rather to generate an approximate set of signals to examine the performance of the standard methods for different possibilities in infarct dynamics. We investigate some of the detection approaches together with their related assumptions, and try to pinpoint the drawbacks and inaccuracies of these methods and also their assumptions. The three widely accepted criteria--QRS duration, root-mean-square and duration of the signal at the end of QRS for VLP detection--were used in the investigation. Results from the application of these parameters to the set of signals are presented. In addition we investigate the physical nature of an infarct and list a number of possible reasons that might be the cause of a low success rate for the detection of additive potentials. To improve the performance of the common methods, two more wavelet transform parameters are added to those of the standard methods. The method derived from this analysis is presented as an alternative means for the detection of late signals named as delayed potentials, a more general class that includes VLP as a subset.

Algorithms↗
PubMed2006

[Wavelet-based pulse-abnormality analysis for heroin addicts].

Using wavelet transforms method, time-frequency characteristics of pulse signals from 15 heroin addicts and 15 healthy persons were analyzed. According to 3-D and contour plots used to display discrete dyadic wavelet transforms, the significant difference of time-frequency characteristics between the signals of heroin addicts and healthy persons were revealed. A primary criterion was also obtained,with the criterion, 15 heroin addicts were entirely identified, while two healthy subjects were misidentified. The research result shows that the wavelet-based multiresolution analysis is a very effective method to extract characteristics of pulse signals. It is valuable to the diagnosis and therapy for heroin addicts.

Adult↗
PubMed2006

Application of wavelet-based similarity analysis to epileptic seizures prediction.

Epileptic seizures prediction is an interesting issue in epileptology, since it can promise a novel approach to control seizures and understand the mechanism of epileptic seizures. In this paper, we describe a new method, called wavelet-based nonlinear similarity index (WNSI), to predict epileptic seizures using EEG recordings in real time. This method combines wavelet techniques and nonlinear dynamics. The test results of EEG recordings of rats and humans show that WNSI can track the hidden dynamical changes of brain electrical activity. Particularly, we found that it can obtain the best performance of seizure prediction at the beta (10-30 Hz) frequency band of EEG signals. A possible reason is suggested from the functional connectivity of the brain. In terms of this study, it is recommended that wavelet technique is very useful to improve the performance of epileptic seizures prediction.

Algorithms↗
PubMed2005

Analysis on the erythrocyte shape changes using wavelet transforms.

The mechanics of red blood cell shape changes under normal and deformed conditions are analyzed using wavelet based approach. Images of intact and deformed human red blood cells obtained from normal adults are subject to morphological image processing and the corresponding shape descriptions at two different levels of approximations using different wavelet functions are analyzed. The results demonstrate that using wavelets it is possible to classify normal and deformed red blood cell shapes. Uniform and consistent results are obtained for cells with similar shapes, for all chosen wavelet functions. The variation indices are significant (p < 0.005) for all the chosen wavelet functions at both the approximation levels. Further it seems that this approach could be useful for identifying closely identical cell shapes. As cell shape deformations are significant in describing the flow behavior in micro or macro vessels the study seems to be clinically relevant. The methodologies, algorithms and observations based on wavelet based analysis are discussed in detail.

Algorithms↗
PubMed2005

The shift-invariant discrete wavelet transform and application to speech waveform analysis.

The discrete wavelet transform may be used as a signal-processing tool for visualization and analysis of nonstationary, time-sampled waveforms. The highly desirable property of shift invariance can be obtained at the cost of a moderate increase in computational complexity, and accepting a least-squares inverse (pseudoinverse) in place of a true inverse. A new algorithm for the pseudoinverse of the shift-invariant transform that is easier to implement in array-oriented scripting languages than existing algorithms is presented together with self-contained proofs. Representing only one of the many and varied potential applications, a recorded speech waveform illustrates the benefits of shift invariance with pseudoinvertibility. Visualization shows the glottal modulation of vowel formants and frication noise, revealing secondary glottal pulses and other waveform irregularities. Additionally, performing sound waveform editing operations (i.e., cutting and pasting sections) on the shift-invariant wavelet representation automatically produces quiet, click-free section boundaries in the resulting sound. The capabilities of this wavelet-domain editing technique are demonstrated by changing the rate of a recorded spoken word. Individual pitch periods are repeated to obtain a half-speed result, and alternate individual pitch periods are removed to obtain a double-speed result. The original pitch and formant frequencies are preserved. In informal listening tests, the results are clear and understandable.

Algorithms↗
PubMed1999

Wavelet-based fractal analysis of airborne pollen.

The most abundant biological particles in the atmosphere are pollen grains and spores. Self-protection of a pollen allergy is possible through information about future pollen contents in the air. In spite of the importance of airborne pollen concentration forecasting, it has not been possible to predict the pollen concentrations with great accuracy, and about 25% of daily pollen forecasts result in failures. Previous analyses of the dynamic characteristics of atmospheric pollen time series indicate that the system can be described by a low dimensional chaotic map. We apply a wavelet transform to study the multifractal characteristics of an airborne pollen time series. The information and the correlation dimensions correspond to a chaotic system showing a loss of information with time evolution.

Journal Article↗
PubMed2005

Rotation-invariant multiresolution texture analysis using radon and wavelet transforms.

A new rotation-invariant texture-analysis technique using Radon and wavelet transforms is proposed. This technique utilizes the Radon transform to convert the rotation to translation and then applies a translation-invariant wavelet transform to the result to extract texture features. A kappa-nearest neighbors classifier is employed to classify texture patterns. A method to find the optimal number of projections for the Radon transform is proposed. It is shown that the extracted features generate an efficient orthogonal feature space. It is also shown that the proposed features extract both of the local and directional information of the texture patterns. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. To test and evaluate the method, we employed several sets of textures along with different wavelet bases. Experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent texture-analysis methods.

Algorithms↗