Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets

A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method

The spectral analysis of nonstationary categorical time series using local spectral envelope

Most classical methods for the spectral analysis are based on the assumption that the time series is stationary. However, many time series in practical problems shows nonstationary behaviors. The data from some fields are huge and have variance and spectrum which changes over time. Sometimes,we are interested in the cyclic behavior of the categorical-valued time series such as EEG sleep state data or DNA sequence, the general method is to scale the data, that is, assign numerical values to the categories and then use the periodogram to find the cyclic behavior. But there exists numerous possible scaling. If we arbitrarily assign the numerical values to the categories and proceed with a spectral analysis, then the results will depend on the particular assignment. We would like to find the all possible scaling that bring out all of the interesting features in the data. To overcome these problems, there have been many approaches in the spectral analysis. Our goal is to develop a statistical methodology for analyzing nonstationary categorical time series in the frequency domain. In this dissertation, the spectral envelope methodology is introduced for spectral analysis of categorical time series. This provides the general framework for the spectral analysis of the categorical time series and summarizes information from the spectrum matrix. To apply this method to nonstationary process, I used the TBAS(Tree-Based Adaptive Segmentation) and local spectral envelope based on the piecewise stationary process. In this dissertation,the TBAS(Tree-Based Adpative Segmentation) using distance function based on the Kullback-Leibler divergence was proposed to find the best segmentation

A Neural Model of How the Brain Computes Heading from Optic Flow in Realistic Scenes

Animals avoid obstacles and approach goals in novel cluttered environments using visual information, notably optic flow, to compute heading, or direction of travel, with respect to objects in the environment. We present a neural model of how heading is computed that describes interactions among neurons in several visual areas of the primate magnocellular pathway, from retina through V1, MT+, and MSTd. The model produces outputs which are qualitatively and quantitatively similar to human heading estimation data in response to complex natural scenes. The model estimates heading to within 1.5° in random dot or photo-realistically rendered scenes and within 3° in video streams from driving in real-world environments. Simulated rotations of less than 1 degree per second do not affect model performance, but faster simulated rotation rates deteriorate performance, as in humans. The model is part of a larger navigational system that identifies and tracks objects while navigating in cluttered environments.National Science Foundation (SBE-0354378, BCS-0235398); Office of Naval Research (N00014-01-1-0624); National-Geospatial Intelligence Agency (NMA201-01-1-2016

Time-varying model identification for time-frequency feature extraction from EEG data

A novel modelling scheme that can be used to estimate and track time-varying properties of nonstationary signals is investigated. This scheme is based on a class of time-varying AutoRegressive with an eXogenous input (ARX) models where the associated time-varying parameters are represented by multi-wavelet basis functions. The orthogonal least square (OLS) algorithm is then applied to refine the model parameter estimates of the time-varying ARX model. The main features of the multi-wavelet approach is that it enables smooth trends to be tracked but also to capture sharp changes in the time-varying process parameters. Simulation studies and applications to real EEG data show that the proposed algorithm can provide important transient information on the inherent dynamics of nonstationary processes

Image segmentation in the wavelet domain using N-cut framework

We introduce a wavelet domain image segmentation algorithm based on Normalized Cut (NCut) framework in this thesis. By employing the NCut algorithm we solve the perceptual grouping problem of image segmentation which aims at the extraction of the global impression of an image. We capitalize on the reduced set of data to be processed and statistical features derived from the wavelet-transformed images to solve graph partitioning more efficiently than before. Five orientation histograms are computed to evaluate similarity/dissimilarity measure of local structure. We use properties of the wavelet transform filtering to capture edge information in vertical, horizontal and diagonal orientations. This approach allows for direct processing of compressed data and results in faster implementation of NCut framework than that in the spatial domain and also decent quality of segmentation of natural scene images

BEMDEC: An Adaptive and Robust Methodology for Digital Image Feature Extraction

The intriguing study of feature extraction, and edge detection in particular, has, as a result of the increased use of imagery, drawn even more attention not just from the field of computer science but also from a variety of scientific fields. However, various challenges surrounding the formulation of feature extraction operator, particularly of edges, which is capable of satisfying the necessary properties of low probability of error (i.e., failure of marking true edges), accuracy, and consistent response to a single edge, continue to persist. Moreover, it should be pointed out that most of the work in the area of feature extraction has been focused on improving many of the existing approaches rather than devising or adopting new ones. In the image processing subfield, where the needs constantly change, we must equally change the way we think. In this digital world where the use of images, for variety of purposes, continues to increase, researchers, if they are serious about addressing the aforementioned limitations, must be able to think outside the box and step away from the usual in order to overcome these challenges. In this dissertation, we propose an adaptive and robust, yet simple, digital image features detection methodology using bidimensional empirical mode decomposition (BEMD), a sifting process that decomposes a signal into its two-dimensional (2D) bidimensional intrinsic mode functions (BIMFs). The method is further extended to detect corners and curves, and as such, dubbed as BEMDEC, indicating its ability to detect edges, corners and curves. In addition to the application of BEMD, a unique combination of a flexible envelope estimation algorithm, stopping criteria and boundary adjustment made the realization of this multi-feature detector possible. Further application of two morphological operators of binarization and thinning adds to the quality of the operator

Wavelet methods in speech recognition

In this thesis, novel wavelet techniques are developed to improve parametrization of speech signals prior to classification. It is shown that non-linear operations carried out in the wavelet domain improve the performance of a speech classifier and consistently outperform classical Fourier methods. This is because of the localised nature of the wavelet, which captures correspondingly well-localised time-frequency features within the speech signal. Furthermore, by taking advantage of the approximation ability of wavelets, efficient representation of the non-stationarity inherent in speech can be achieved in a relatively small number of expansion coefficients. This is an attractive option when faced with the so-called 'Curse of Dimensionality' problem of multivariate classifiers such as Linear Discriminant Analysis (LDA) or Artificial Neural Networks (ANNs). Conventional time-frequency analysis methods such as the Discrete Fourier Transform either miss irregular signal structures and transients due to spectral smearing or require a large number of coefficients to represent such characteristics efficiently. Wavelet theory offers an alternative insight in the representation of these types of signals. As an extension to the standard wavelet transform, adaptive libraries of wavelet and cosine packets are introduced which increase the flexibility of the transform. This approach is observed to be yet more suitable for the highly variable nature of speech signals in that it results in a time-frequency sampled grid that is well adapted to irregularities and transients. They result in a corresponding reduction in the misclassification rate of the recognition system. However, this is necessarily at the expense of added computing time. Finally, a framework based on adaptive time-frequency libraries is developed which invokes the final classifier to choose the nature of the resolution for a given classification problem. The classifier then performs dimensionaIity reduction on the transformed signal by choosing the top few features based on their discriminant power. This approach is compared and contrasted to an existing discriminant wavelet feature extractor. The overall conclusions of the thesis are that wavelets and their relatives are capable of extracting useful features for speech classification problems. The use of adaptive wavelet transforms provides the flexibility within which powerful feature extractors can be designed for these types of application