Statistical Properties and Applications of Empirical Mode Decomposition

Signal analysis is key to extracting information buried in noise. The decomposition of signal is a data analysis tool for determining the underlying physical components of a processed data set. However, conventional signal decomposition approaches such as wavelet analysis, Wagner-Ville, and various short-time Fourier spectrograms are inadequate to process real world signals. Moreover, most of the given techniques require \emph{a prior} knowledge of the processed signal, to select the proper decomposition basis, which makes them improper for a wide range of practical applications. Empirical Mode Decomposition (EMD) is a non-parametric and adaptive basis driver that is capable of breaking-down non-linear, non-stationary signals into an intrinsic and finite components called Intrinsic Mode Functions (IMF). In addition, EMD approximates a dyadic filter that isolates high frequency components, e.g. noise, in higher index IMFs. Despite of being widely used in different applications, EMD is an ad hoc solution. The adaptive performance of EMD comes at the expense of formulating a theoretical base. Therefore, numerical analysis is usually adopted in literature to interpret the behavior. This dissertation involves investigating statistical properties of EMD and utilizing the outcome to enhance the performance of signal de-noising and spectrum sensing systems. The novel contributions can be broadly summarized in three categories: a statistical analysis of the probability distributions of the IMFs and a suggestion of Generalized Gaussian distribution (GGD) as a best fit distribution; a de-noising scheme based on a null-hypothesis of IMFs utilizing the unique filter behavior of EMD; and a novel noise estimation approach that is used to shift semi-blind spectrum sensing techniques into fully-blind ones based on the first IMF. These contributions are justified statistically and analytically and include comparison with other state of art techniques

Typical and atypical development of the brain’s functional network architecture

The human brain is a complex organ that gives rise to many behaviors. Specialized neural regions cooperate as functional networks that form an intricate functional architecture. Development provides a unique window into how brain functioning and human thinking are affected if the necessary neural features and connections are not fully formed. Similarly, developmental disorders can shed light on atypical trajectories of neural systems that may lead to or be a consequence of symptomatic behavior. A description of the typical and atypical development of functional networks is essential to identify the features of brain organization critical for mature human thinking and to provide better diagnosis, treatment, and prognosis in neurodevelopmental disorders. Recently, resting state functional MRI has been found to illuminate functionally related regions, giving access to functional networks and the organization of brain’s functional architecture. This thesis aims to harness resting-state functional connectivity to explore how functional networks coordinate over the course of development. First, I present our work investigating the organizing principles of typical developmental patterns in functional networks (Chapter 2). Then, I apply these approaches to the atypical development of functional networks in Tourette syndrome (TS), a developmental disorder characterized by motor and vocal tics. In this work, we tested whether the patterns in functional networks that distinguish individuals with TS from controls differ between children and adults and alter the typical developmental pattern of functional networks (Chapter 3). Lastly, I present our work to identify and describe the coordination of specific functional networks that develop atypically in TS (Chapter 4)

A data analytics approach to gas turbine prognostics and health management

As a consequence of the recent deregulation in the electrical power production industry, there has been a shift in the traditional ownership of power plants and the way they are operated. To hedge their business risks, the many new private entrepreneurs enter into long-term service agreement (LTSA) with third parties for their operation and maintenance activities. As the major LTSA providers, original equipment manufacturers have invested huge amounts of money to develop preventive maintenance strategies to minimize the occurrence of costly unplanned outages resulting from failures of the equipments covered under LTSA contracts. As a matter of fact, a recent study by the Electric Power Research Institute estimates the cost benefit of preventing a failure of a General Electric 7FA or 9FA technology compressor at $10 to$20 million. Therefore, in this dissertation, a two-phase data analytics approach is proposed to use the existing monitoring gas path and vibration sensors data to first develop a proactive strategy that systematically detects and validates catastrophic failure precursors so as to avoid the failure; and secondly to estimate the residual time to failure of the unhealthy items. For the first part of this work, the time-frequency technique of the wavelet packet transforms is used to de-noise the noisy sensor data. Next, the time-series signal of each sensor is decomposed to perform a multi-resolution analysis to extract its features. After that, the probabilistic principal component analysis is applied as a data fusion technique to reduce the number of the potentially correlated multi-sensors measurement into a few uncorrelated principal components. The last step of the failure precursor detection methodology, the anomaly detection decision, is in itself a multi-stage process. The obtained principal components from the data fusion step are first combined into a one-dimensional reconstructed signal representing the overall health assessment of the monitored systems. Then, two damage indicators of the reconstructed signal are defined and monitored for defect using a statistical process control approach. Finally, the Bayesian evaluation method for hypothesis testing is applied to a computed threshold to test for deviations from the healthy band. To model the residual time to failure, the anomaly severity index and the anomaly duration index are defined as defects characteristics. Two modeling techniques are investigated for the prognostication of the survival time after an anomaly is detected: the deterministic regression approach, and parametric approximation of the non-parametric Kaplan-Meier plot estimator. It is established that the deterministic regression provides poor prediction estimation. The non parametric survival data analysis technique of the Kaplan-Meier estimator provides the empirical survivor function of the data set comprised of both non-censored and right censored data. Though powerful because no a-priori predefined lifetime distribution is made, the Kaplan-Meier result lacks the flexibility to be transplanted to other units of a given fleet. The parametric analysis of survival data is performed with two popular failure analysis distributions: the exponential distribution and the Weibull distribution. The conclusion from the parametric analysis of the Kaplan-Meier plot is that the larger the data set, the more accurate is the prognostication ability of the residual time to failure model.PhDCommittee Chair: Mavris, Dimitri; Committee Member: Jiang, Xiaomo; Committee Member: Kumar, Virendra; Committee Member: Saleh, Joseph; Committee Member: Vittal, Sameer; Committee Member: Volovoi, Vital

Novel Deep Learning Techniques For Computer Vision and Structure Health Monitoring

This thesis proposes novel techniques in building a generic framework for both the regression and classification tasks in vastly different applications domains such as computer vision and civil engineering. Many frameworks have been proposed and combined into a complex deep network design to provide a complete solution to a wide variety of problems. The experiment results demonstrate significant improvements of all the proposed techniques towards accuracy and efficiency

Automatic Segmentation and Classification of Red and White Blood cells in Thin Blood Smear Slides

In this work we develop a system for automatic detection and classification of cytological images which plays an increasing important role in medical diagnosis. A primary aim of this work is the accurate segmentation of cytological images of blood smears and subsequent feature extraction, along with studying related classification problems such as the identification and counting of peripheral blood smear particles, and classification of white blood cell into types five. Our proposed approach benefits from powerful image processing techniques to perform complete blood count (CBC) without human intervention. The general framework in this blood smear analysis research is as follows. Firstly, a digital blood smear image is de-noised using optimized Bayesian non-local means filter to design a dependable cell counting system that may be used under different image capture conditions. Then an edge preservation technique with Kuwahara filter is used to recover degraded and blurred white blood cell boundaries in blood smear images while reducing the residual negative effect of noise in images. After denoising and edge enhancement, the next step is binarization using combination of Otsu and Niblack to separate the cells and stained background. Cells separation and counting is achieved by granulometry, advanced active contours without edges, and morphological operators with watershed algorithm. Following this is the recognition of different types of white blood cells (WBCs), and also red blood cells (RBCs) segmentation. Using three main types of features: shape, intensity, and texture invariant features in combination with a variety of classifiers is next step. The following features are used in this work: intensity histogram features, invariant moments, the relative area, co-occurrence and run-length matrices, dual tree complex wavelet transform features, Haralick and Tamura features. Next, different statistical approaches involving correlation, distribution and redundancy are used to measure of the dependency between a set of features and to select feature variables on the white blood cell classification. A global sensitivity analysis with random sampling-high dimensional model representation (RS-HDMR) which can deal with independent and dependent input feature variables is used to assess dominate discriminatory power and the reliability of feature which leads to an efficient feature selection. These feature selection results are compared in experiments with branch and bound method and with sequential forward selection (SFS), respectively. This work examines support vector machine (SVM) and Convolutional Neural Networks (LeNet5) in connection with white blood cell classification. Finally, white blood cell classification system is validated in experiments conducted on cytological images of normal poor quality blood smears. These experimental results are also assessed with ground truth manually obtained from medical experts

Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced

A Better Looking Brain: Image Pre-Processing Approaches for fMRI Data

Researchers in the field of functional neuroimaging have faced a long standing problem in pre-processing low spatial resolution data without losing meaningful details within. Commonly, the brain function is recorded by a technique known as echo-planar imaging that represents the measure of blood flow (BOLD signal) through a particular location in the brain as an array of intensity values changing over time. This approach to record a movie of blood flow in the brain is known as fMRI. The neural activity is then studied from the temporal correlation patterns existing within the fMRI time series. However, the resulting images are noisy and contain low spatial detail, thus making it imperative to pre-process them appropriately to derive meaningful activation patterns. Two of the several standard preprocessing steps employed just before the analysis stage are denoising and normalization. Fundamentally, it is difficult to perfectly remove noise from an image without making assumptions about signal and noise distributions. A convenient and commonly used alternative is to smooth the image with a Gaussian filter, but this method suffers from various obvious drawbacks, primarily loss of spatial detail. A greater challenge arises when we attempt to derive average activation patterns from fMRI images acquired from a group of individuals. The brain of one individual differs from others in a structural sense as well as in a functional sense. Commonly, the inter-individual differences in anatomical structures are compensated for by co-registering each subject\u27s data to a common normalization space, known as spatial normalization. However, there are no existing methods to compensate for the differences in functional organization of the brain. This work presents first steps towards data-driven robust algorithms for fMRI image denoising and multi-subject image normalization by utilizing inherent information within fMRI data. In addition, a new validation approach based on spatial shape of the activation regions is presented to quantify the effects of preprocessing and also as a tool to record the differences in activation patterns between individual subjects or within two groups such as healthy controls and patients with mental illness. Qualititative and quantitative results of the proposed framework compare favorably against existing and widely used model-driven approaches such as Gaussian smoothing and structure-based spatial normalization. This work is intended to provide neuroscience researchers tools to derive more meaningful activation patterns to accurately identify imaging biomarkers for various neurodevelopmental diseases and also maximize the specificity of a diagnosis