Browsing by Author "Wu, Hau-Tieng"

Biomedical time series are non-invasive windows through which we may observe human systems. Although a vast amount of information is hidden in the medical field's growing collection of long-term, high-resolution, and multi-modal biomedical time series, effective algorithms for extracting that information have not yet been developed. We are particularly interested in the physiological dynamics of a human system, namely the changes in state that the system experiences over time (which may be intrinsic or extrinsic in origin). We introduce a mathematical model for a particular class of biomedical time series, called the wave-shape oscillatory model, which quantifies the sense in which dynamics are hidden in those time series. There are two key ideas behind the new model. First, instead of viewing a biomedical time series as a sequence of measurements made at the sampling rate of the signal, we can often view it as a sequence of cycles occurring at irregularly-sampled time points. Second, the "shape" of an individual cycle is assumed to have a one-to-one correspondence with the state of the system being monitored; as such, changes in system state (dynamics) can be inferred by tracking changes in cycle shape. Since physiological dynamics are not random but are well-regulated (except in the most pathological of cases), we can assume that all of the system's states lie on a low-dimensional, abstract Riemannian manifold called the phase manifold. When we model the correspondence between the hidden system states and the observed cycle shapes using a diffeomorphism, we allow the topology of the phase manifold to be recovered by methods belonging to the field of unsupervised manifold learning. In particular, we prove that the physiological dynamics hidden in a time series adhering to the wave-shape oscillatory model can be well-recovered by applying the diffusion maps algorithm to the time series' set of oscillatory cycles. We provide several applications of the wave-shape oscillatory model and the associated algorithm for dynamics recovery, including unsupervised and supervised heartbeat classification, derived respiratory monitoring, intra-operative cardiovascular monitoring, supervised and unsupervised sleep stage classification, and f-wave extraction (a single-channel blind source separation problem).

We present a novel algorithm, called eOptShrink, for denoising matrices in the presence of high-dimensional, colored, and dependent noise with a separable covariance structure. Our approach is data-driven and does not require estimation of the covariance structure of the noise.The eOptShrink algorithm utilizes a new imputation and rank estimation technique to achieve optimal shrinkage. We study the asymptotic behavior of the singular values and singular vectors of the random matrix associated with the noisy data, including the sticking property of non-outlier singular values and the delocalization of non-outlier singular vectors with a convergence rate. These theoretical results provide guarantees for the imputation, rank estimation, and eOptShrink algorithm with a convergence rate.

We apply eOptShrink to recover fetal electrocardiogram (ECG) for both the fetal heart rate analysis and morphological analysis of its waveform from two or three trans-abdominal maternal ECG channels.

For the fetal heart rate analysis, the algorithm is evaluated on publicly available database, 2013 PhyioNet/Computing in Cardiology Challenge, set A CinC2013.

For the morphological analysis, we analyze CinC2013 and another publicly available database, Non-Invasive Fetal ECG Arrhythmia Database nifeadb, and propose to simulate semi-real databases by mixing the MIT-BIH Normal Sinus Rhythm Database and MITDB Arrhythmia Database.

For the fetal R peak detection, the proposed algorithm outperforms all algorithms under comparison. For the morphological analysis, the algorithm provides an encouraging result in recovery of the fetal ECG waveform, including PR, QT and ST intervals, even when the fetus has arrhythmia, both in real and simulated databases.

Biomedical time series contain rich information about human systems, however, effective algorithms for analyzing long-term physiological time series have not yet been developed because of the huge volume size, high dimensionality and large noise nature of the data. Motivated by such challenging task, we proposed a novel spectral embedding algorithm, which we coined Robust and Scalable Embedding via Landmark Diffusion (ROSELAND). The solution is a generic and not limited to analyze physiological waveforms. In short, we measure the affinity between two points via a set of landmarks, which is composed of a small number of points, and ``diffuse'' on the dataset via the landmark set to achieve a spectral embedding. The algorithm is applied to study the arterial blood pressure waveform dynamics during a liver transplant operation lasting for 12 hours long. In addition, we show that Roseland is not only numerically scalable, but also preserves the geometric properties via its diffusion nature under the manifold setup; that is, we theoretically explore the asymptotical behavior of Roseland under the manifold setup, and provide a L-infinity spectral convergence with a rate. Moreover, we offer a high dimensional noise analysis with the help of Gaussian approximation, and show that Roseland is robust to noise.

This dissertation introduces algorithms that analyze oscillatory signals adaptively. It consists of three chapters. The first chapter reviews the adaptive time-frequency analysis of 1-dimensional signals. It introduces models that capture the time-varying behavior of oscillatory signals. Then it explains two state-of-the-art algorithms, named the SynchroSqueezed Transform (SST) and the Concentration of Frequency and Time (ConceFT), that extract the instantaneous information of signals; this chapter ends with a discussion of some of the shortcomings of SST and ConceFT, which will be remedied by the new methods introduced in the remainder of this thesis. The second chapter introduces the Ramanujan DeShape Algorithm (RDS); it incorporates the periodicity transform to extract adaptively the fundamental frequency of a non-harmonic signal. The third part proposes an algorithm that rotates the time-frequency content of an oscillatory signal to obtain a time-frequency representation that has fewer artifacts. Numerical results illustrate the theoretical analysis.