Continuous wavelet transform and higher-order spectrum: combinatory potentialities in breath sound analysis and electroencephalogram-based pain characterization

The combination of the continuous wavelet transform (CWT) with a higher-order spectrum (HOS) merges two worlds into one that conveys information regarding the non-stationarity, non-Gaussianity and nonlinearity of the systems and/or signals under examination. In the current work, the third-order spectrum (TOS), which is used to detect the nonlinearity and deviation from Gaussianity of two types of biomedical signals, that is, wheezes and electroencephalogram (EEG), is combined with the CWT to offer a time-scale representation of the examined signals. As a result, a CWT/TOS field is formed and a time axis is introduced, creating a time-bifrequency domain, which provides a new means for wheeze nonlinear analysis and dynamic EEG-based pain characterization. A detailed description and examples are provided and discussed to showcase the combinatory potential of CWT/TOS in the field of advanced signal processing.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Continuous wavelet transform in the study of the time-scale properties of intracranial pressure in hydrocephalus

Normal pressure hydrocephalus (NPH) encompasses a heterogeneous group of disorders generally characterized by clinical symptoms, ventriculomegaly and anomalous cerebrospinal fluid (CSF) dynamics. Lumbar infusion tests (ITs) are frequently performed in the preoperatory evaluation of patients who show NPH features. The analysis of intracranial pressure (ICP) signals recorded during ITs could be useful to better understand the pathophysiology underlying NPH and to assist treatment decisions. In this study, 131 ICP signals recorded during ITs were analysed using two continuous wavelet transform (CWT)-derived parameters: Jensen divergence (JD) and spectral flux (SF). These parameters were studied in two frequency bands, associated with different components of the signal: B₁(0.15-0.3 Hz), related to respiratory blood pressure oscillations; and B₂ (0.67-2.5 Hz), related to ICP pulse waves. Statistically significant differences (p < 1.70 × 10^-3, Bonferroni-corrected Wilcoxon signed-rank tests) in pairwise comparisons between phases of ITs were found using the mean and standard deviation of JD and SF. These differences were mainly found in B₂, where a lower irregularity and variability, together with less prominent time-frequency fluctuations, were found in the hypertension phase of ITs. Our results suggest that wavelet analysis could be useful for understanding CSF dynamics in NPH.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Introduction to redundancy rules: the continuous wavelet transform comes of age

Redundancy: it is a word heavy with connotations of lacking usefulness. I often hear that the rationale for not using the continuous wavelet transform (CWT)-even when it appears most appropriate for the problem at hand-is that it is 'redundant'. Sometimes the conversation ends there, as if self-explanatory. However, in the context of the CWT, 'redundant' is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form-the CWT-is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy. Once the signal information is in CWT form, a range of powerful analysis methods can then be employed for its extraction, interpretation and/or manipulation. This theme issue is intended to provide the reader with an overview of the current state of the art of CWT analysis methods from across a wide range of numerate disciplines, including fluid dynamics, structural mechanics, geophysics, medicine, astronomy and finance.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Quantitative feature analysis of continuous analytic wavelet transforms of electrocardiography and electromyography

Theoretical and practical advances in time-frequency analysis, in general, and the continuous wavelet transform (CWT), in particular, have increased over the last two decades. Although the Morlet wavelet has been the default choice for wavelet analysis, a new family of analytic wavelets, known as generalized Morse wavelets, which subsume several other analytic wavelet families, have been increasingly employed due to their time and frequency localization benefits and their utility in isolating and extracting quantifiable features in the time-frequency domain. The current paper describes two practical applications of analysing the features obtained from the generalized Morse CWT: (i) electromyography, for isolating important features in muscle bursts during skating, and (ii) electrocardiography, for assessing heart rate variability, which is represented as the ridge of the main transform frequency band. These features are subsequently quantified to facilitate exploration of the underlying physiological processes from which the signals were generated.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Evaluation of the Continuous Wavelet Transform for Detection of Single-Point Rub in Aeroderivative Gas Turbines with Accelerometers

A common fault in turbomachinery is rotor–casing rub. Shaft vibration, measured with proximity probes, is the most powerful indicator of rotor–stator rub. However, in machines such as aeroderivative turbines, with increasing industrial relevance in power generation, constructive reasons prevent the use of those sensors, being only acceleration signals at selected casing locations available. This implies several shortcomings in the characterization of the machinery condition, associated with a lower information content about the machine dynamics. In this work, we evaluated the performance of Continuous Wavelet Transform to isolate the accelerometer signal features that characterize rotor–casing rub in an aeroderivative turbine. The evaluation is carried out on a novel rotor model of a rotor–flexible casing system. Due to damped transients and other short-lived features that rub induces in the signals, the Continuous Wavelet Transform proves being more effective than both Fourier and Cepstrum Analysis. This creates the chance for enabling early fault diagnosis of rub before it may cause machine shutdown or damage.

Weak Defect Identification for Centrifugal Compressor Blade Crack Based on Pressure Sensors and Genetic Algorithm

The Centrifugal compressor is a piece of key equipment for petrochemical factories. As the core component of a compressor, the blades suffer periodic vibration and flow induced excitation mechanism, which will lead to the occurrence of crack defect. Moreover, the induced blade defect usually has a serious impact on the normal operation of compressors and the safety of operators. Therefore, an effective blade crack identification method is particularly important for the reliable operation of compressors. Conventional non-destructive testing and evaluation (NDT&E) methods can detect the blade defect effectively, however, the compressors should shut down during the testing process which is time-consuming and costly. In addition, it can be known these methods are not suitable for the long-term on-line condition monitoring and cannot identify the blade defect in time. Therefore, the effective on-line condition monitoring and weak defect identification method should be further studied and proposed. Considering the blade vibration information is difficult to measure directly, pressure sensors mounted on the casing are used to sample airflow pressure pulsation signal on-line near the rotating impeller for the purpose of monitoring the blade condition indirectly in this paper. A big problem is that the blade abnormal vibration amplitude induced by the crack is always small and this feature information will be much weaker in the pressure signal. Therefore, it is usually difficult to identify blade defect characteristic frequency embedded in pressure pulsation signal by general signal processing methods due to the weakness of the feature information and the interference of strong noise. In this paper, continuous wavelet transform (CWT) is used to pre-process the sampled signal first. Then, the method of bistable stochastic resonance (SR) based on Woods-Saxon and Gaussian (WSG) potential is applied to enhance the weak characteristic frequency contained in the pressure pulsation signal. Genetic algorithm (GA) is used to obtain optimal parameters for this SR system to improve its feature enhancement performance. The analysis result of experimental signal shows the validity of the proposed method for the enhancement and identification of weak defect characteristic. In the end, strain test is carried out to further verify the accuracy and reliability of the analysis result obtained by pressure pulsation signal.

Comparison of Portable and Bench-Top Spectrometers for Mid-Infrared Diffuse Reflectance Measurements of Soils

Mid-infrared (MIR) spectroscopy has received widespread interest as a method to complement traditional soil analysis. Recently available portable MIR spectrometers additionally offer potential for on-site applications, given sufficient spectral data quality. We therefore tested the performance of the Agilent 4300 Handheld FTIR (DRIFT spectra) in comparison to a Bruker Tensor 27 bench-top instrument in terms of (i) spectral quality and measurement noise quantified by wavelet analysis; (ii) accuracy of partial least squares (PLS) calibrations for soil organic carbon (SOC), total nitrogen (N), pH, clay and sand content with a repeated cross-validation analysis; and (iii) key spectral regions for these soil properties identified with a Monte Carlo spectral variable selection approach. Measurements and multivariate calibrations with the handheld device were as good as or slightly better than Bruker equipped with a DRIFT accessory, but not as accurate as with directional hemispherical reflectance (DHR) data collected with an integrating sphere. Variations in noise did not markedly affect the accuracy of multivariate PLS calibrations. Identified key spectral regions for PLS calibrations provided a good match between Agilent and Bruker DHR data, especially for SOC and N. Our findings suggest that portable FTIR instruments are a viable alternative for MIR measurements in the laboratory and offer great potential for on-site applications.

Temporally stable frequency mapping using continuous wavelet transform analysis in patients with persistent atrial fibrillation

INTRODUCTION

Dominant frequency (DF) derived from fast Fourier transform (FFT) analysis has failed to guide atrial fibrillation (AF) ablation since it cannot guarantee temporal stability. Continuous wavelet transform (CWT) analysis is another frequency analysis that can show the temporal stability of a frequency.

METHODS AND RESULTS

Forty-four consecutive patients with persistent AF (PeAF) underwent pulmonary vein (PV) isolation (PVI) as the first-time catheter ablation. The PVs and left atrium were mapped and electrograms (EGMs) were recorded for 30 seconds at each site. Pseudo-frequency (PF) and coefficient of variation (CV) were calculated by CWT analysis. A PF with CV ≤ 10 was defined as a temporally stable PF (sPF). DF was also calculated by traditional FFT analysis from the first 5 seconds of the recorded EGMs. The highest sPF was shown inside the PVs in 20 patients (PV group), and at the non-PV sites in 24 patients (non-PV group). During the follow-up period of 15.3 ± 4.4 months, the ablation success rate in the PV group was significantly higher than that in the non-PV group (90% vs. 62%, P = 0.023). The location of the highest DF did not have a significant effect on ablation success rate between inside the PVs and at the non-PV sites.

CONCLUSION

PVI results for PeAF were significantly worse for patients with highest sPF at the non-PV sites compared to patients with highest sPF sites inside the PVs. CWT analysis during AF could be used to verify whether PVI alone is sufficient for the first-time catheter ablation in patients with PeAF.

Ultrafast Spectroscopy of Fano-Like Resonance between Optical Phonon and Excitons in CdSe Quantum Dots: Dependence of Coherent Vibrational Wave-Packet Dynamics on Pump Fluence

The main goal of the present work is to study the coherent phonon in strongly confined CdSe quantum dots (QDs) under varied pump fluences. The main characteristics of coherent phonons (amplitude, frequency, phase, spectrogram) of CdSe QDs under the red-edge pump of the excitonic band [1S(e)-1S_3/2(h)] are reported. We demonstrate for the first time that the amplitude of the coherent optical longitudinal-optical (LO) phonon at 6.16 THz excited in CdSe nanoparticles by a femtosecond unchirped pulse shows a non-monotone dependence on the pump fluence. This dependence exhibits the maximum at pump fluence ~0.8 mJ/cm². At the same time, the amplitudes of the longitudinal acoustic (LA) phonon mode at 0.55 THz and of the coherent wave packet of toluene at 15.6, 23.6 THz show a monotonic rise with the increase of pump fluence. The time frequency representation of an oscillating signal corresponding to LO phonons revealed by continuous wavelet transform (CWT) shows a profound destructive quantum interference close to the origin of distinct (optical phonon) and continuum-like (exciton) quasiparticles. The CWT spectrogram demonstrates a nonlinear chirp at short time delays, where the chirp sign depends on the pump pulse fluence. The CWT spectrogram reveals an anharmonic coupling between optical and acoustic phonons.

Time-Frequency Distribution of Seismocardiographic Signals: A Comparative Study

Accurate estimation of seismocardiographic (SCG) signal features can help successful signal characterization and classification in health and disease. This may lead to new methods for diagnosing and monitoring heart function. Time-frequency distributions (TFD) were often used to estimate the spectrotemporal signal features. In this study, the performance of different TFDs (e.g., short-time Fourier transform (STFT), polynomial chirplet transform (PCT), and continuous wavelet transform (CWT) with different mother functions) was assessed using simulated signals, and then utilized to analyze actual SCGs. The instantaneous frequency (IF) was determined from TFD and the error in estimating IF was calculated for simulated signals. Results suggested that the lowest IF error depended on the TFD and the test signal. STFT had lower error than CWT methods for most test signals. For a simulated SCG, Morlet CWT more accurately estimated IF than other CWTs, but Morlet did not provide noticeable advantages over STFT or PCT. PCT had the most consistently accurate IF estimations and appeared more suited for estimating IF of actual SCG signals. PCT analysis showed that actual SCGs from eight healthy subjects had multiple spectral peaks at 9.20 ± 0.48, 25.84 ± 0.77, 50.71 ± 1.83 Hz (mean ± SEM). These may prove useful features for SCG characterization and classification.

Effects of different stresses on cardiac autonomic control and cardiovascular coupling

The objective of this study was to investigate the impacts of different stresses on time-varying autonomic reactivity and cardiovascular coupling. In total, 25 male subjects were recruited. RR intervals (RRI), systolic and diastolic blood pressure (SBP, DBP), stroke volume (SV), cardiac output (CO), and systemic vascular resistance (SVR) values were collected during rest, mental arithmetic task (MAT), and cold pressor test (CPT). Baroreflex sensitivity (BRS) was derived using the transfer function method. Continuous wavelet transformation of RRI was used to describe the time-variant patterns of autonomic neural activities. Wavelet cross correlation and phase synchronization were used to estimate the amplitude and phase coupling between RRI and SBP. MAT was characterized by increased heart rate (HR), SBP, DBP, and CO with decreased BRS attributable to prolonged parasympathetic withdrawal. Moreover, cardiovascular coupling was disrupted in MAT. These results indicated that baroreflex was depressed, and the top-down system started to take action under mental stress. In CPT, SBP, DBP, and SVR increased significantly, whereas HR and BRS remained unchanged. The increase of sympathetic activity was transient, and cardiovascular coupling did not change in CPT. Intriguingly, the frequency of the maximum cross-correlation coefficient in the low-frequency band (0.04-0.15 Hz) was significantly decreased in CPT, which may be due to the change of resonance frequency of the baroreflex loop.NEW & NOTEWORTHY The study is the first to compare the time-variant pattern of autonomic nervous activities and cardiovascular coupling between the mental arithmetic task (MAT) and the cold pressor test (CPT). Our results demonstrated that MAT and CPT elicited different time-varying patterns of autonomic neural activities and cardiovascular synchronization. Both the amplitude and phase consistency of blood pressure and heart rate decreased in MAT. CPT may affect the harmonic frequency of the baroreflex loop.

Towards Real-Time Detection of Gait Events on Different Terrains Using Time-Frequency Analysis and Peak Heuristics Algorithm

Real-time detection of gait events can be applied as a reliable input to control drop foot correction devices and lower-limb prostheses. Among the different sensors used to acquire the signals associated with walking for gait event detection, the accelerometer is considered as a preferable sensor due to its convenience of use, small size, low cost, reliability, and low power consumption. Based on the acceleration signals, different algorithms have been proposed to detect toe off (TO) and heel strike (HS) gait events in previous studies. While these algorithms could achieve a relatively reasonable performance in gait event detection, they suffer from limitations such as poor real-time performance and are less reliable in the cases of up stair and down stair terrains. In this study, a new algorithm is proposed to detect the gait events on three walking terrains in real-time based on the analysis of acceleration jerk signals with a time-frequency method to obtain gait parameters, and then the determination of the peaks of jerk signals using peak heuristics. The performance of the newly proposed algorithm was evaluated with eight healthy subjects when they were walking on level ground, up stairs, and down stairs. Our experimental results showed that the mean F1 scores of the proposed algorithm were above 0.98 for HS event detection and 0.95 for TO event detection on the three terrains. This indicates that the current algorithm would be robust and accurate for gait event detection on different terrains. Findings from the current study suggest that the proposed method may be a preferable option in some applications such as drop foot correction devices and leg prostheses.

Evaluating the Relationship Between Muscle Activation and Spine Kinematics Through Wavelet Coherence

Advances in time-frequency analysis can provide new insights into the important, yet complex relationship between muscle activation (ie, electromyography [EMG]) and motion during dynamic tasks. We use wavelet coherence to compare a fundamental cyclical movement (lumbar spine flexion and extension) to the surface EMG linear envelope of 2 trunk muscles (lumbar erector spinae and internal oblique). Both muscles cohere to the spine kinematics at the main cyclic frequency, but lumbar erector spinae exhibits significantly greater coherence than internal oblique to kinematics at 0.25, 0.5, and 1.0 Hz. Coherence phase plots of the 2 muscles exhibit different characteristics. The lumbar erector spinae precedes trunk extension at 0.25 Hz, whereas internal oblique is in phase with spine kinematics. These differences may be due to their proposed contrasting functions as a primary spine mover (lumbar erector spinae) versus a spine stabilizer (internal oblique). We believe that this method will be useful in evaluating how a variety of factors (eg, pain, dysfunction, pathology, fatigue) affect the relationship between muscles' motor inputs (ie, activation measured using EMG) and outputs (ie, the resulting joint motion patterns).

Towards Real-Time Detection of Freezing of Gait Using Wavelet Transform on Wireless Accelerometer Data

Injuries associated with fall incidences continue to pose a significant burden to persons with Parkinson’s disease (PD) both in terms of human suffering and economic loss. Freezing of gait (FOG), which is one of the symptoms of PD, is a common cause of falls in this population. Although a significant amount of work has been performed to characterize/detect FOG using both qualitative and quantitative methods, there remains paucity of data regarding real-time detection of FOG, such as the requirements for minimum sensor nodes, sensor placement locations, and appropriate sampling period and update time. Here, the continuous wavelet transform (CWT) is employed to define an index for correctly identifying FOG. Since the CWT method uses both time and frequency components of a waveform in comparison to other methods utilizing only the frequency component, we hypothesized that using this method could lead to a significant improvement in the accuracy of FOG detection. We tested the proposed index on the data of 10 PD patients who experience FOG. Two hundred and thirty seven (237) FOG events were identified by the physiotherapists. The results show that the index could discriminate FOG in the anterior–posterior axis better than other two axes, and is robust to the update time variability. These results suggest that real time detection of FOG may be realized by using CWT of a single shank sensor with window size of 2 s and update time of 1 s (82.1% and 77.1% for the sensitivity and specificity, respectively). Although implicated, future studies should examine the utility of this method in real-time detection of FOG.

Multivariate assessment of event-related potentials with the t-CWT method

BACKGROUND

Event-related brain potentials (ERPs) are usually assessed with univariate statistical tests although they are essentially multivariate objects. Brain-computer interface applications are a notable exception to this practice, because they are based on multivariate classification of single-trial ERPs. Multivariate ERP assessment can be facilitated by feature extraction methods. One such method is t-CWT, a mathematical-statistical algorithm based on the continuous wavelet transform (CWT) and Student's t-test.

RESULTS

This article begins with a geometric primer on some basic concepts of multivariate statistics as applied to ERP assessment in general and to the t-CWT method in particular. Further, it presents for the first time a detailed, step-by-step, formal mathematical description of the t-CWT algorithm. A new multivariate outlier rejection procedure based on principal component analysis in the frequency domain is presented as an important pre-processing step. The MATLAB and GNU Octave implementation of t-CWT is also made publicly available for the first time as free and open source code. The method is demonstrated on some example ERP data obtained in a passive oddball paradigm. Finally, some conceptually novel applications of the multivariate approach in general and of the t-CWT method in particular are suggested and discussed.

CONCLUSIONS

Hopefully, the publication of both the t-CWT source code and its underlying mathematical algorithm along with a didactic geometric introduction to some basic concepts of multivariate statistics would make t-CWT more accessible to both users and developers in the field of neuroscience research.

Synchronization of Muscular Oscillations Between Two Subjects During Isometric Interaction

Muscles oscillate with a frequency around 10 Hz. But what happens with myofascial oscillations, if two neuromuscular systems interact? The purpose of this study was to examine this question, initially, on the basis of a case study. Oscillations of the triceps brachii muscles of two subjects were determined through mechanomyography (MMG) during isometric interaction. The MMG-signals were analyzed concerning the interaction of the two subjects with algorithms of nonlinear dynamics. In this case study it could be shown, that the muscles of both neuromuscular systems also oscillate with the known frequency (here 12 Hz) during interaction. Furthermore, both subjects were able to adapt their oscillations against each other. This adjustment induced a significant (α < .05) coherent behavior, which was characterized by a phase shifting of approximately 90°. The authors draw the conclusion, that the complementary neuromuscular partners potentially have the ability of mutual synchronization.

Measuring the effect of aging on vibrations of the carotid artery wall using empirical mode decomposition method

Quantification of arterial elasticity and its dependency to age is considered in this paper. We use radiofrequency (RF) signals from carotid artery ultasonography to evaluate this dependency. Blood pressure, blood flow, and tethering to surrounding tissue are the main causes of the motion of the carotid wall. Tracking carotid artery wall motion from a series of ultrasound B-mode images is challenging due to the presence of noise and variable contrast. Moreover, the process of converting RF signals into the B-mode images causes some information to be lost. Hence, our goal is to extract the carotid wall motions and vibrations from RF signals. After extraction and removing the wall motion by using the phased tracking method combined with continuous wavelet transform, the vibrations of carotid inner wall in different subjects in different ages are compared with each other. Empirical mode decomposition method is used for extracting the first intrinsic mode function for different subjects' vibration and then their zero-crossing rates are compared. The results show the vibrations of the carotid inner wall are clearly decreased by age.

Time-frequency characteristics and dynamics of sleep spindles in WAG/Rij rats with absence epilepsy

In rat models of absence epilepsy, epileptic spike-wave discharges appeared in EEG spontaneously, and the incidence of epileptic activity increases with age. Spike-wave discharges and sleep spindles are known to share common thalamo-cortical mechanism, suggesting that absence seizures might affect some intrinsic properties of sleep spindles. This paper examines time-frequency EEG characteristics of anterior sleep spindles in non-epileptic Wistar and epileptic WAG/Rij rats at the age of 7 and 9 months. Considering non-stationary features of sleep spindles, EEG analysis was performed using Morlet-based continuous wavelet transform. It was found, first, that the average frequency of sleep spindles in non-epileptic Wistar rats was higher than in WAG/Rij (13.2 vs 11.2 Hz). Second, the instantaneous frequency ascended during a spindle event in Wistar rats, but it was constant in WAG/Rij. Third, in WAG/Rij rats, the number and duration of epileptic discharges increased in a period between 7 and 9 months of age, but duration and mean value of intra-spindle frequency did not change. In general, age-dependent aggravation of absence seizures in WAG/Rij rats did not affect EEG properties of sleep spindles; it was suggested that pro-epileptic changes in thalamo-cortical network in WAG/Rij rats might prevent dynamic changes of sleep spindles that were detected in Wistar.

STFT or CWT for the detection of Doppler ultrasound embolic signals

Aiming reliable detection and localization of cerebral blood flow and emboli, embolic signals were added to simulated middle cerebral artery Doppler signals and analysed. Short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used in the evaluation. The following parameters were used in this study: the powers of the embolic signals added were 5, 6, 6.5, 7, 7.5, 8 and 9 dB; the mother wavelets for CWT analysis were Morlet, Mexican hat, Meyer, Gaussian (order 4) and Daubechies (orders 4 and 8); and the thresholds for detection (equated in terms of false positive, false negative and sensitivity) were 2 and 3.5 dB for the CWT and STFT, respectively. The results indicate that although the STFT allows accurately detecting emboli, better time localization can be achieved with the CWT. Among the CWT, the current best overall results were obtained with Mexican Hat mother wavelet, with optimal results for sensitivity (100% detection rate) for nearly all emboli power values studied.

A combined algorithm for T-wave alternans qualitative detection and quantitative measurement

BACKGROUND

T-wave alternans (TWA) provides a noninvasive and clinically useful marker for the risk of sudden cardiac death (SCD). Current most widely used TWA detection algorithms work in two different domains: time and frequency. The disadvantage of the spectral analytical techniques is that they treat the alternans signal as a stationary wave with a constant amplitude and a phase. They cannot detect non-stationary characteristics of the signal. The temporal domain methods are sensitive to the alignment of the T-waves. In this study, we sought to develop a robust combined algorithm (CA) to assess T-wave alternans, which can qualitatively detect and quantitatively measure TWA in time domain.

METHODS

The T wave sequences were extracted and the total energy of each T wave within the specified time-frequency region was calculated. The rank-sum test was applied to the ranked energy sequences of T waves to detect TWA qualitatively. The ECG containing TWA was quantitatively analyzed with correlation method.

RESULTS

Simulation test result proved a mean sensitivity of 91.2% in detecting TWA, and for the SNR not less than 30 dB, the accuracy rate of detection achieved 100%. The clinical data experiment showed that the results from this method vs. spectral method had the correlation coefficients of 0.96.

CONCLUSIONS

A novel TWA analysis algorithm utilizing the wavelet transform and correlation technique is presented in this paper. TWAs are not only correctly detected qualitatively in frequency domain by energy value of T waves, but the alternans frequency and amplitude in temporal domain are measured quantitatively.

Cell classification by moments and continuous wavelet transform methods

Image processing techniques are bringing new insights to biomedical research. The automatic recognition and classification of biomedical objects can enhance work efficiency while identifying new inter-relationships among biological features. In this work, a simple rule-based decision tree classifier is developed to classify typical features of mixed cell types investigated by atomic force microscopy (AFM). A combination of continuous wavelet transform (CWT) and moment-based features are extracted from the AFM data to represent that shape information of different cellular objects at multiple resolution levels. The features are shown to be invariant under operations of translation, rotation, and scaling. The features are then used in a simple rule-based classifier to discriminate between anucleate versus nucleate cell types or to distinguish cells from a fibrous environment such as a tissue scaffold or stint. Since each feature has clear physical meaning, the decision rule of this tree classifier is simple, which makes it very suitable for online processing. Experimental results on AFM data confirm that the performance of this classifier is robust and reliable.