Searcharxiv⌕ Search

arXiv subjects

Hau-tieng Wu

Publications and source records attributed to Hau-tieng Wu.

At least 37 records · Page 2Linked to original sources
arXiv2016

Heart beat classification from single-lead ECG using the Synchrosqueezing Transform

The processing of ECG signal provides a wealth of information on cardiac function and overall cardiovascular health. While multi-lead ECG recordings are often necessary for a proper assessment of cardiac rhythms, they are not always available or practical, for example in fetal ECG applications. Moreover, a wide range of small non-obtrusive single-lead ECG ambulatory monitoring devices are now available, from which heart rate variability (HRV) and other health-related metrics are derived. Proper beat detection and classification of abnormal rhythms is important for reliable HRV assessment and can be challenging in single-lead ECG monitoring devices. In this manuscript, we modeled the heart rate signal as an adaptive non-harmonic model and used the newly developed synchrosqueezing transform (SST) to characterize ECG patterns. We show how the proposed model can be used to enhance heart beat detection and classification between normal and abnormal rhythms. In particular, using the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database and the Association for the Advancement of Medical Instrumentation (AAMI) beat classes, we trained and validated a support vector machine (SVM) classifier on a portion of the annotated beat database using the SST-derived instantaneous phase, the R-peak amplitudes and R-peak to R-peak interval durations, based on a single ECG lead. We obtained sensitivities and positive predictive values comparable to other published algorithms using multiple leads and many more features.

stat.AP↗
arXiv2016

Wave-shape function analysis -- when cepstrum meets time-frequency analysis

We propose to combine cepstrum and nonlinear time-frequency (TF) analysis to study mutiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm.

physics.data-an↗
arXiv2016

Sleep Apnea Detection Based on Thoracic and Abdominal Movement Signals of Wearable Piezo-Electric Bands

Physiologically, the thoracic (THO) and abdominal (ABD) movement signals, captured using wearable piezo-electric bands, provide information about various types of apnea, including central sleep apnea (CSA) and obstructive sleep apnea (OSA). However, the use of piezo-electric wearables in detecting sleep apnea events has been seldom explored in the literature. This study explored the possibility of identifying sleep apnea events, including OSA and CSA, by solely analyzing {one or both the THO and ABD signals. An adaptive non-harmonic model was introduced to model the THO and ABD signals, which allows us to design features for sleep apnea events. To confirm the suitability of the extracted features, a support vector machine was applied to classify three categories -- normal and hypopnea, OSA, and CSA. According to a database of} 34 subjects, the overall classification accuracies were on average $75.9\%\pm 11.7\%$ and $73.8\%\pm 4.4\%$, respectively, based on the cross validation. When the features determined from the THO and ABD signals were combined, the overall classification accuracy became $81.8\%\pm 9.4\%$. These features were applied for designing a state machine for online apnea event detection. Two event-by-event accuracy indices, S and I, were proposed for evaluating the performance {of the state machine. For the same database, the} S index was $84.01\%\pm 9.06\%$, and the I index was $77.21\%\pm 19.01\%$. The results indicate the considerable potential of applying the proposed algorithm to clinical examinations for both screening and homecare purposes.

physics.med-ph↗
arXiv2016

Extract fetal ECG from single-lead abdominal ECG by de-shape short time Fourier transform and nonlocal median

The multiple fundamental frequency detection problem and the source separation problem from a single-channel signal containing multiple oscillatory components and a nonstationary noise are both challenging tasks. To extract the fetal electrocardiogram (ECG) from a single-lead maternal abdominal ECG, we face both challenges. In this paper, we propose a novel method to extract the fetal ECG signal from the single channel maternal abdominal ECG signal, without any additional measurement. The algorithm is composed of three main ingredients. First, the maternal and fetal heart rates are estimated by the de-shape short time Fourier transform, which is a recently proposed nonlinear time-frequency analysis technique; second, the beat tracking technique is applied to accurately obtain the maternal and fetal R peaks; third, the maternal and fetal ECG waveforms are established by the nonlocal median. The algorithm is evaluated on a simulated fetal ECG signal database ({\em fecgsyn} database), and tested on two real databases with the annotation provided by experts ({\em adfecgdb} database and {\em CinC2013} database). In general, the algorithm could be applied to solve other detection and source separation problems, and reconstruct the time-varying wave-shape function of each oscillatory component.

q-bio.QM↗
arXiv2016

Minimum-latency Time-frequency Analysis Using Asymmetric Window Functions

We study the real-time dynamics retrieval from a time series via the time-frequency (TF) analysis with the minimal latency guarantee. While different from the well-known intrinsic latency definition in the filter design, a rigorous definition of intrinsic latency for different time-frequency representations (TFR) is provided, including the short time Fourier transform (STFT), synchrosqeezing transform (SST) and reassignment method (RM). To achieve the minimal latency, a systematic method is proposed to construct an asymmetric window from a well-designed symmetric one based on the concept of minimum-phase, if the window satisfies some weak conditions. We theoretically show that the TFR determined by SST with the constructed asymmetric window does have a smaller intrinsic latency. Finally, the music onset detection problem is studied to show the strength of the proposed algorithm.

cs.MM↗
arXiv2016

Carrier frequencies, holomorphy and unwinding

We prove that functions of intrinsic-mode type (a classical models for signals) behave essentially like holomorphic functions: adding a pure carrier frequency $e^{int}$ ensures that the anti-holomorphic part is much smaller than the holomorphic part $ \| P_{-}(f)\|_{L^2} \ll \|P_{+}(f)\|_{L^2}.$ This enables us to use techniques from complex analysis, in particular the \textit{unwinding series}. We study its stability and convergence properties and show that the unwinding series can stabilize and show that the unwinding series can provide a high resolution time-frequency representation, which is robust to noise.

math.NA↗
arXiv2016

Modeling the pulse signal by wave-shape function and analyzing by synchrosqueezing transform

We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST) to model and analyze oscillatory physiological signals. To demonstrate how the model and algorithm work, we apply them to study the pulse wave signal. By extracting features called the spectral pulse signature, {and} based on functional regression, we characterize the hemodynamics from the radial pulse wave signals recorded by the sphygmomanometer. Analysis results suggest the potential of the proposed signal processing approach to extract health-related hemodynamics features.

stat.AP↗
arXiv2016

Convex Optimization approach to signals with fast varying instantaneous frequency

Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic model, the time-frequency representation of a signal is obtained by directly minimizing a functional, which involves few properties an "ideal time-frequency representation" should satisfy, for example, the signal reconstruction and concentrative time frequency representation. FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) is applied to achieve an efficient numerical approximation of the functional. We coin the algorithm as {\it Time-frequency bY COnvex OptimizatioN} (Tycoon). The numerical results confirm the potential of the Tycoon algorithm.

math.NA↗
arXiv2015

When interpolation-induced reflection artifact meets time-frequency analysis

While extracting the temporal dynamical features based on the time-frequency analyses, like the reassignment and synchrosqueezing transform, attracts more and more interest in bio-medical data analysis, we should be careful about artifacts generated by interpolation schemes, in particular when the sampling rate is not significantly higher than the frequency of the oscillatory component we are interested in. In this study, we formulate the problem called the reflection effect and provide a theoretical justification of the statement. We also show examples in the anesthetic depth analysis with clear but undesirable artifacts. The results show that the artifact associated with the reflection effect exists not only theoretically but practically. Its influence is pronounced when we apply the time-frequency analyses to extract the time-varying dynamics hidden inside the signal. In conclusion, we have to carefully deal with the artifact associated with the reflection effect by choosing a proper interpolation scheme.

stat.AP↗
arXiv2015

Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: A comprehensive study

Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several of quantum systems, a systematic comparison among these methods is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, indicating the versatility of TF analysis as a new viable venue for exploring quantum dynamics.

physics.data-an↗
arXiv2015

Alternating Projection, Ptychographic Imaging and Phase Synchronization

We demonstrate necessary and sufficient conditions of the local convergence of the alternating projection algorithm to a unique solution up to a global phase factor. Additionally, for the ptychography imaging problem, we discuss phase synchronization and graph connection Laplacian, and show how to construct an accurate initial guess to accelerate convergence speed to handle the big imaging data in the coming new light source era.

math.OC↗
arXiv2015

Spectral Convergence of the connection Laplacian from random samples

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously shown by Belkin and Niyogi \cite{belkin_niyogi:2007} that the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the manifold in the limit of infinitely many data points sampled independently from the uniform distribution over the manifold. Recently, we introduced Vector Diffusion Maps and showed that the connection Laplacian of the tangent bundle of the manifold can be approximated from random samples. In this paper, we present a unified framework for approximating other connection Laplacians over the manifold by considering its principle bundle structure. We prove that the eigenvectors and eigenvalues of these Laplacians converge in the limit of infinitely many independent random samples. We generalize the spectral convergence results to the case where the data points are sampled from a non-uniform distribution, and for manifolds with and without boundary.

math.NA↗
arXiv2014

Graph connection Laplacian and random matrices with random blocks

Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the dataset under investigation. Developing this understanding is important in making sense of the output of the algorithms based on GCL. We hence develop a theory explaining the behavior of the spectral distribution of a large class of random matrices, in particular random matrices with random block entries of fixed size. Part of the theory covers the case where there is significant dependence between the blocks. Numerical work shows that the agreement between our theoretical predictions and numerical simulations is generally very good.

math.PR↗
arXiv2014

Assess Sleep Stage by Modern Signal Processing Techniques

In this paper, two modern adaptive signal processing techniques, Empirical Intrinsic Geometry and Synchrosqueezing transform, are applied to quantify different dynamical features of the respiratory and electroencephalographic signals. We show that the proposed features are theoretically rigorously supported, as well as capture the sleep information hidden inside the signals. The features are used as input to multiclass support vector machines with the radial basis function to automatically classify sleep stages. The effectiveness of the classification based on the proposed features is shown to be comparable to human expert classification -- the proposed classification of awake, REM, N1, N2 and N3 sleeping stages based on the respiratory signal (resp. respiratory and EEG signals) has the overall accuracy $81.7\%$ (resp. $89.3\%$) in the relatively normal subject group. In addition, by examining the combination of the respiratory signal with the electroencephalographic signal, we conclude that the respiratory signal consists of ample sleep information, which supplements to the information stored in the electroencephalographic signal.

physics.med-ph↗
arXiv2014

A new time-frequency method to reveal quantum dynamics of atomic hydrogen in intense laser pulses: Synchrosqueezing Transform

This study introduces a new adaptive time-frequency (TF) analysis technique, synchrosqueezing transform (SST), to explore the dynamics of a laser-driven hydrogen atom at an {\it ab initio} level, upon which we have demonstrated its versatility as a new viable venue for further exploring quantum dynamics. For a signal composed of oscillatory components which can be characterized by instantaneous frequency, the SST enables rendering the decomposed signal based on the phase information inherited in the linear TF representation with mathematical support. Compared with the classical type TF methods, the SST clearly depicts several intrinsic quantum dynamical processes such as selection rules, AC Stark effects, and high harmonic generation.

physics.data-an↗
arXiv2014

Real-time dynamics acquisition from irregular samples -- with application to anesthesia evaluation

The first objective of this paper is to introduce a unified approach to the D/A conversion, a real-time algorithm referred to as {\it blending operator}, based on spline functions of arbitrarily desired order, to interpolate the irregular data samples, while preserving all polynomials of the same spline order, with assured maximum order of approximation. This helps remove the two main obstacles for adapting the recently proposed time-frequency analysis technique {\it Synchrosqueezing transform} (SST) to irregular data samples in order to allow online computation. Secondly, for real-time dynamic information extraction from an oscillatory signal via SST, a family of vanishing-moment and minimum-supported spline-wavelets (to be called VM wavelets) are introduced for on-line computation of the CWT and its derivative. The second objective of this paper is to apply the proposed real-time algorithm and VM wavelets to clinical applications, particularly to the study of the "anesthetic depth" of a patient during surgery, with emphasis on analyzing two dynamic quantities: the "instantaneous frequencies" and the "non-rhythmic to rhythmic ratios" of the patient's respiration, based on a one-lead electrocardiogram (ECG) signal.It is envisioned that the proposed algorithm and VM wavelets should enable real-time monitoring of "anesthetic depth", during surgery, from the respiration signal via ECG measurement.

math.NA↗
arXiv2014

Connection graph Laplacian methods can be made robust to noise

Recently, several data analytic techniques based on connection graph laplacian (CGL) ideas have appeared in the literature. At this point, the properties of these methods are starting to be understood in the setting where the data is observed without noise. We study the impact of additive noise on these methods, and show that they are remarkably robust. As a by-product of our analysis, we propose modifications of the standard algorithms that increase their robustness to noise. We illustrate our results in numerical simulations.

math.ST↗