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

Unsupervised Morphological Multiscale Segmentation of Scanning Electron Microscopy Images

This paper deals with a problem of unsupervised multiscale segmentation in the domain of scanning electron microscopy, which is tackled by mathematical morphology techniques. The proposed approach includes various steps. First, the image is decomposed into various compact scales of representation, where objects at each scale are homogeneous in size. Multiscale decomposition is based on a morphological scale-space followed by scale merging using hierarchical clustering and earth mover distance. Then the compact scales are segmented independently using watershed transform. Finally the segmented scales are combined using a tree of objects in order to obtain a multiscale segmentation

Classification of Human Ventricular Arrhythmia in High Dimensional Representation Spaces

We studied classification of human ECGs labelled as normal sinus rhythm, ventricular fibrillation and ventricular tachycardia by means of support vector machines in different representation spaces, using different observation lengths. ECG waveform segments of duration 0.5-4 s, their Fourier magnitude spectra, and lower dimensional projections of Fourier magnitude spectra were used for classification. All considered representations were of much higher dimension than in published studies. Classification accuracy improved with segment duration up to 2 s, with 4 s providing little improvement. We found that it is possible to discriminate between ventricular tachycardia and ventricular fibrillation by the present approach with much shorter runs of ECG (2 s, minimum 86% sensitivity per class) than previously imagined. Ensembles of classifiers acting on 1 s segments taken over 5 s observation windows gave best results, with sensitivities of detection for all classes exceeding 93%.Comment: 9 pages, 2 tables, 5 figure

Signal Processing Methods for Heart Rate Detection Using the Seismocardiogram

Cardiac diseases are one of the major causes of death. Heart monitoring/diagnostic techniques have been developed over decades to address this concern. Monitoring a vital sign such as heart rate is a powerful technique for heart abnormalities detection (e.g., arrhythmia). The novelty of this work is that offers new heart rate detection methods which are both robust and adaptive compared to existing heart rate detec- tion methods. Utilized data sets in this research have been provided from two sources of PhysioNet and a research group. In this work, utilized methods for heart rate detection include Signal Energy Thresholding (SET), Empirical Mode Decomposition (EMD) and Empirical Wavelet Transform (EWT). To the best of the author’s knowledge, this work is the first to use EMD and EWT for heart rate detection from Seismocardiogram (SCG) signal. Obtained result from applying SET to ECG signal is selected as our ground truth. Then, all three methods are used for heart rate detection from the SCG signal. The average error of SET method, EWT and EMD respectively 13.9 ms, 13.8 ms and 16 ms. Based on the obtained results, EMD and EWT are promising techniques for heart rate detection and interpretation from the SCG signal. Another contribution of this work is arrhythmia detection using EWT. EWT provides us with the instantaneous frequency changes of the corresponding modes to ECG signal. Based on the estimated power spectral density of each mode, power spectral density of arrhythmia affected ECG is higher (≥ 50dB) compared to the power spectral density of a normal ECG (≤ 20dB). This provides the potential for arrhythmia detection using EWT