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Analysis of the second heart sound using continuous wavelet transform.

This paper is concerned with a synthesis study of Continuous Wavelet Transform (CWT) in analysing the second heart sound of the phonocardiogram (PCG). The second heart sound S2 consists of two major components (A2 and P2) with a time delay between them which is very important for a diagnosis. It is shown that CWT provides enough features of these components of time, frequency and time delay to aid diagnosis.

Aortic Coarctation↗

PubMed2005

Screening analysis of river seston downstream of an effluent discharge point using near-infrared reflectance spectrometry and wavelet-based spectral region selection.

A methodology for screening analysis of river seston downstream of an industry effluent by using near-infrared reflectance spectrometry was developed. A wavelet transform (WT)-based strategy is used to select a spectral region in which the effect of the effluent on the optical properties of the seston is more evident. The methodology was applied to samples from the River Mumbaba in northeast Brazil. Four sites were monitored: two upstream (1 and 2), one at the discharge point of the effluent (3), and another downstream (4). Soft Independent Modelling of Class Analogies (SIMCA) models were built for site 1 and were then applied to the classification of samples from sites 2 and 4. The results reveal that the WT-based spectral region selection is essential to ensure good sensitivity and specificity with respect to the detection of events associated to the effluent discharges at site 3. In fact, the changes in site 4 caused by the effluent are masked by other environmental factors when the full spectrum is employed.

Brazil↗

PubMed2001

Wavelets for QRS detection.

This paper examines the use of different wavelet functions for QRS complex detection in ECG. Wavelets provide time and frequency analysis simultaneously and offer flexibility with a number of wavelet functions with different properties available. This research has examined wavelet functions with different properties to determine the effects of orthogonality and time/frequency compactness of the wavelet on the ability to correctly detect the QRS. The error in detection (false negatives and positives) is the criterion for determining the efficacy of the wavelet function. The paper reports a significant reduction in error in detection of QRS complexes with mean error reduced to 0.75%. It also reports that wavelet functions that support symmetry and compactness provide better results.

Electrocardiography↗

PubMed2005

Decomposing ERP time-frequency energy using PCA.

OBJECTIVE: Time-frequency transforms (TFTs) offer rich representations of event-related potential (ERP) activity, and thus add complexity. Data reduction techniques for TFTs have been slow to develop beyond time analysis of detail functions from wavelet transforms. Cohen's class of TFTs based on the reduced interference distribution (RID) offer some benefits over wavelet TFTs, but do not offer the simplicity of detail functions from wavelet decomposition. The objective of the current approach is a data reduction method to extract succinct and meaningful events from both RID and wavelet TFTs. METHODS: A general energy-based principal components analysis (PCA) approach to reducing TFTs is detailed. TFT surfaces are first restructured into vectors, recasting the data as a two-dimensional matrix amenable to PCA. PCA decomposition is performed on the two-dimensional matrix, and surfaces are then reconstructed. The PCA decomposition method is conducted with RID and Morlet wavelet TFTs, as well as with PCA for time and frequency domains separately. RESULTS: Three simulated datasets were decomposed. These included Gabor logons and chirped signals. All simulated events were appropriately extracted from the TFTs using both wavelet and RID TFTs. Varying levels of noise were then added to the simulated data, as well as a simulated condition difference. The PCA-TFT method, particularly when used with RID TFTs, appropriately extracted the components and detected condition differences for signals where time or frequency domain analysis alone failed. Response-locked ERP data from a reaction time experiment was also decomposed. Meaningful components representing distinct neurophysiological activity were extracted from the ERP TFT data, including the error-related negativity (ERN). CONCLUSIONS: Effective TFT data reduction was achieved. Activity that overlapped in time, frequency, and topography were effectively separated and extracted. Methodological issues involved in the application of PCA to TFTs are detailed, and directions for further development are discussed. SIGNIFICANCE: The reported decomposition method represents a natural but significant extension of PCA into the TFT domain from the time and frequency domains alone. Evaluation of many aspects of this extension could now be conducted, using the PCA-TFT decomposition as a basis.

Analog-Digital Conversion↗

PubMed2005

Time-frequency analysis of the second cardiac sound in phonocardiogram signals.

The paper is concerned with the analysis of the phonocardiogram signals (PCG) in the time-frequency domain. Three techniques are studied and evaluated in PCG signal analysis. These are the short time Fourier transform (STFT), the Wigner distribution function (WD) and the continuous wavelet transforms (CWTs). The analysis is first carried out on the second cardiac sound (S2) in order to show the aptitude of each method in distinguishing the internal components of this sound. The results we obtain show that the STFT cannot detect the two internal components of S2 (A2 and P2, respectively, the aortic and pulmonary components). The WD can provide time-frequency characteristics of S2, but with insufficient diagnostic information: the two components are not accurately detected and appear to be only one component. It is found that the CWT (it can also provide the time-frequency characteristic of S2) is capable of detecting its two components, A2 and P2, allowing therefore the measurement of the delay between them. This delay, called the split, is very important in the diagnosis of many pathological cases, as it is emphasized in the results we obtain by applying the CWT on different pathological cases (mitral stenosis, pulmonary stenosis and atrial septal defect).

Algorithms↗

PubMed2004

Hydrophobicity analysis of protein primary structures to identify helical regions.

OBJECTIVES: A wavelet based approach for the hydrophobicity analysis of protein primary structures is proposed to predict the presence of alpha helices in the secondary structure. METHODS: The information about hydropathy profile periodicity content together with a score of probability of occurrence of a single amino acid allows the localization of alpha helices. RESULTS: The accuracy is comparable to other consolidated predictors based on different techniques (i.e.: neural networks, hidden markov models). CONCLUSION: This method is particularly suitable to capture the amphiphilic character of the helical structures.

Amino Acid Sequence↗

PubMed2000

Enhancement of bowel sounds by wavelet-based filtering.

This paper evaluates the performance of an automatic method for structural decomposition, noise removal and enhancement of bowel sounds (BS), based on the wavelet transform. The proposed method combines multiresolution analysis with hard thresholding to compose a wavelet transform-based stationary-nonstationary (WTST-NST) filter, for enhanced separation of bowel sounds (BS) from superimposed noise. Quantitative and qualitative analysis of the experimental results, when applying the WTST-NST filter to BS recorded from controls and patients with gastrointestinal dysfunction, prove that the ability of the WTST-NST filter to remove noise and reveal the authentic structure of BS is excellent. By eliminating the need to record a noise reference signal, this method reduces hardware overhead when analysis of BS is the primary aim. The method is independent of subjective human judgement for selection of noise reference templates, is robust to different levels of signal interference, and, due to its simplicity, can easily be used in clinical medicine.

Adult↗

PubMed2004

Using wavelets to analyze AFM images of thin films: surface micelles and supported lipid bilayers.

This paper presents micro- and nanoanalysis of thin films based on images obtained by atomic force microscopy (AFM). The analysis exploits the discrete wavelet transform and the resulting wavelet spectrum to study surface features. It is demonstrated that the wavelet technique can characterize micro- and nanosurface features and distinguish between similar surface structures. The use of a feature extraction method is shown. The method involves the separation of certain frequency content from the original AFM images and analyzing the data independently to gain quantitative information about the images. By using the feature extraction method, soft surfaces in water are analyzed and nanofeatures are measured. The packing of surface micelles of sodium dodecyl sulfate on a self-assembled monolayer is analyzed. The characteristics of pore formation, due to penetration of the antibacterial peptide protegrin, into a solid-supported lipid bilayer are quantified. The sizes of the pores are obtained, and it is observed that the line tension of the pores reduces the fluctuations of the lipid bilayer.

Antimicrobial Cationic Peptides↗

PubMed2000

Wigner functions from the two-dimensional wavelet group.

Following a general procedure developed previously [Ann. Henri Poincaré 1, 685 (2000)], here we construct Wigner functions on a phase space related to the similitude group in two dimensions. Since the group space in this case is topologically homeomorphic to the phase space in question, the Wigner functions so constructed may also be considered as being functions on the group space itself. Previously the similitude group was used to construct wavelets for two-dimensional image analysis; we discuss here the connection between the wavelet transform and the Wigner function.

Journal Article↗

PubMed2003

A comparison of the wavelet and short-time fourier transforms for Doppler spectral analysis.

Doppler spectrum analysis provides a non-invasive means to measure blood flow velocity and to diagnose arterial occlusive disease. The time-frequency representation of the Doppler blood flow signal is normally computed by using the short-time Fourier transform (STFT). This transform requires stationarity of the signal during a finite time interval, and thus imposes some constraints on the representation estimate. In addition, the STFT has a fixed time-frequency window, making it inaccurate to analyze signals having relatively wide bandwidths that change rapidly with time. In the present study, wavelet transform (WT), having a flexible time-frequency window, was used to investigate its advantages and limitations for the analysis of the Doppler blood flow signal. Representations computed using the WT with a modified Morlet wavelet were investigated and compared with the theoretical representation and those computed using the STFT with a Gaussian window. The time and frequency resolutions of these two approaches were compared. Three indices, the normalized root-mean-squared errors of the minimum, the maximum and the mean frequency waveforms, were used to evaluate the performance of the WT. Results showed that the WT can not only be used as an alternative signal processing tool to the STFT for Doppler blood flow signals, but can also generate a time-frequency representation with better resolution than the STFT. In addition, the WT method can provide both satisfactory mean frequencies and maximum frequencies. This technique is expected to be useful for the analysis of Doppler blood flow signals to quantify arterial stenoses.

Algorithms↗

PubMed2003

[Analysis of ventricular fibrillation signals for the evaluation of defibrillation success in the treatment of ventricular fibrillation].

OBJECTIVE: Precise detection of ventricular fibrillation (VF), reliable prediction of defibrillation success and adjustment of the discharge waveform to the patient's transthoracic impedance may contribute to a reduction of electricity-associated myocardial injury caused by unnecessary counter shocks. Specifically, asystole thresholds distinguish between VF and asystole, and thus prevent unnecessary defibrillation attempts. We reviewed various studies and manufacturer characteristics regarding the parameters and algorithms for analyzing arrhythmia ECG signals. METHODS: Asystole threshold values of several defibrillator manufacturers were collected and a literature review was performed including the following parameters: amplitude, frequency, bispectral analysis, amplitude spectrum area, wavelets, nonlinear dynamics, N(alpha)histograms, and combinations of various parameters. RESULTS: The manufacturer dependent asystole thresholds vary substantially. We show ways to optimize an ECG-based analysis for the next technological generation of defibrillators. During advanced cardiac life support (ACLS) the probability of defibrillation success should be estimated. Optimal defibrillation waveform, depending on transthoracic resistance, should be individually determined. In case of prolonged VF with a low ECG amplitude defibrillation should not be attempted unless coronary perfusion has been improved by further measures of ACLS. The combined evaluation of VF amplitude and frequency is effective in predicting defibrillation success. Estimation of further parameters is potentially useful for guiding optimal timing of defibrillation. At present, the implementation of most parameters in out-of-hospital cardiopulmonary resuscitation (CPR) is limited by the lack of technical feasibility of online computing. CONCLUSION: Analysis of VF ECG signals should allow adequate VF detection as well as prediction of defibrillation success. Suitable asystole thresholds for analysis of ECG signals have to be determined, and the adverse effects of CPR associated artefacts on data analysis have to be reduced. Analysis of VF ECG signals is a precondition of individually optimized defibrillation and may contribute substantially to an increased quality of CPR.

Algorithms↗

PubMed2001

Elementary derivative tasks and neural net multiscale analysis of tasks.

Formal neurons implementing wavelets have been shown to build nets that are able to approximate any multidimensional task. In this paper, we use a finite number of formal neurons implementing elementary tasks such as "sombrero" responses or even simpler "window" responses, with adjustable widths. We show this to provide a reasonably efficient, practical and robust, multifrequency analysis of tasks. The translation degree of freedom of wavelets is shown to be unnecessary. A training algorithm, optimizing the output task with respect to the widths of the responses, reveals two distinct training modes. The first mode keeps the formal neurons distinct. The other mode induces some of the formal neurons to become identical, with output weights of equal strengths but opposite signs. Hence this latter mode promotes tasks that are derivatives of the elementary tasks with respect to the width parameter. Such results, obtained from optimizations with respect to a width parameter, can be generalized for any other parameters of the elementary tasks.

Journal Article↗

PubMed2005

Large-scale comparative analysis of pertussis population dynamics: periodicity, synchrony, and impact of vaccination.

Pertussis is a worldwide infectious disease which persists despite massive vaccination campaigns that have gone on for several decades. To obtain an overall view of pertussis dynamics and the impact of vaccination, the authors performed, using the wavelet method, a comparative analysis of pertussis time series in 12 countries to detect and quantify periodicity and synchrony between them. Results showed a clear 3- to 4-year cycle in all countries, but the main finding was that this periodicity was transient. No global pattern in the effect of vaccination on pertussis dynamics was observed, but some spatial synchrony between countries was detected. This large-scale comparative analysis of pertussis dynamics sheds light on the complexity of the multiple interactions involved in global pertussis spatial dynamic patterns. It suggests a need to perform a global survey of human infectious diseases over the long term, which would permit better assessment of the risk of disease outbreaks in the future.

Global Health↗

PubMed1999

Analysis of the velocity curve for height by the wavelet interpolation method in children classified by maturity rate.

The Wavelet Interpolation Method (WIM) developed by Meyer ([1992] Wavelets and Operators. Cambridge: Cambridge University Press) has been proposed as an analytical method for the accurate description of longitudinal growth velocity in height and identification of the age at maximum peak velocity (MPV) in the curve. The distance curve in height was determined by interpolating the longitudinal records of 98 boys and 88 girls, 6-17 years old, with the WIM. The distance curve was then differentiated to obtain a velocity curve. Age at MPV estimated from the velocity curve was utilized as a criterion of maturity rate (timing), and five maturity groups (early, little early, average, little late and late) were defined in both sexes. Four type models were derived from the occurrence of secondary peaks (mid-growth spurt and after-growth spurt): type model A, appearance of a mid-growth spurt and MPV; type model B, appearance of an after-growth spurt and MPV; type model C, appearance of a mid-growth spurt, an after-growth spurt and MPV; and type model D, appearance of MPV only. The individual growth data of boys and girls classified by maturity rate were sorted into the four type models. The frequency of occurrence of the four type models in groups classified by maturity rate was then analyzed, and the characteristics of height growth velocity was examined in boys and girls. Am. J. Hum. Biol. 11:13-30, 1999. Copyright 1999 Wiley-Liss, Inc.

Journal Article↗

PubMed2004

Human auditory event-related processes in the time-frequency plane.

Sensory stimuli produce phase-locked and non-phase-locked changes in brain activity as indexed by EEG and MEG. Time-frequency methods such as wavelets, when carefully applied, allow simultaneous analysis of both types of activity. Here we used wavelets of different time and frequency resolutions in combination with spatial mapping to identify these processes. We found that auditory stimulation leads to a pattern of large-magnitude power increases and small-magnitude power decreases. The power increases, ranging from the theta to the beta frequency band, were accounted for by the transient auditory responses P50m, N100m and P200m. Following these responses, we observed a power reduction of non-phase-locked activity which occurred 250-500 ms after stimulus onset in the 14-24 Hz frequency range and could be localized to the temporal and parietal brain areas. These results indicate that auditory event-related processes consist not only of the well-established transient responses but also of power reductions of ongoing, non-phase-locked brain processes.

Acoustic Stimulation↗

PubMed2004

Automated analysis of the auditory brainstem response using derivative estimation wavelets.

In this paper, we describe an algorithm that automatically detects and labels peaks I-VII of the normal, suprathreshold auditory brainstem response (ABR). The algorithm proceeds in three stages, with the option of a fourth: (1) all candidate peaks and troughs in the ABR waveform are identified using zero crossings of the first derivative, (2) peaks I-VII are identified from these candidate peaks based on their latency and morphology, (3) if required, peaks II and IV are identified as points of inflection using zero crossings of the second derivative and (4) interpeak troughs are identified before peak latencies and amplitudes are measured. The performance of the algorithm was estimated on a set of 240 normal ABR waveforms recorded using a stimulus intensity of 90 dBnHL. When compared to an expert audiologist, the algorithm correctly identified the major ABR peaks (I, III and V) in 96-98% of the waveforms and the minor ABR peaks (II, IV, VI and VII) in 45-83% of waveforms. Whilst peak II was correctly identified in only 83% and peak IV in 77% of waveforms, it was shown that 5% of the peak II identifications and 31% of the peak IV identifications came as a direct result of allowing these peaks to be found as points of inflection.

Adolescent↗

PubMed2002

Analysis of Seidel aberration by use of the discrete wavelet transform.

Seidel aberration coefficients can be expressed by Zernike coefficients. The least-squares matrix-inversion method of determining Zernike coefficients from a sampled wave front with measurement noise has been found to be numerically unstable. We present a method of estimating the Seidel aberration coefficients by using a two-dimensional discrete wavelet transform. This method is applied to analyze the wave front of an optical system, and we obtain not only more-accurate Seidel aberration coefficients, but we also speed the computation. Three simulated wave fronts are fitted, and simulation results are shown for spherical aberration, coma, astigmatism, and defocus.

Journal Article↗

PubMed2004

[Performance analysis of threshold denoising via different kinds of mother wavelets].

An ideal spectrum signal prototype is constructed in this paper based on the infrared ray spectrum of octane levelmeasurement to evaluate the performances of wavelet based threshold denoising approaches via different combinations of mother wavelet functions and thresholds. A performance index eta is defined to assess the signal-to-noise ratios (SNR) of denoising results, inconsideration of the trade-off between the SNR and the distortion of the original signal after wavelet denoising. Three families of mother wavelets (Symlets, Daubechies and Coiflet), four threshold selection rules (Rigrsure, Sqtwolog, Heursure and Manimaxi), and three threshold rescaling methods (One, Sln and Mln) are tested in a series of experiments to estimate the functioning of those wavelets and thresholding parameters. Experimental results show that in the cases investigated in this paper, the best denoising performance is reached via the combinations of Daubechies9 or Symlet7, 11, 14, 15 wavelets, "Rigrsure" threshold selection rule, and "Sln" threshold rescaling method.

English Abstract↗