A Multiscale Approach for Statistical Characterization of Functional Images

Increasingly, scientific studies yield functional image data, in which the observed data consist of sets of curves recorded on the pixels of the image. Examples include temporal brain response intensities measured by fMRI and NMR frequency spectra measured at each pixel. This article presents a new methodology for improving the characterization of pixels in functional imaging, formulated as a spatial curve clustering problem. Our method operates on curves as a unit. It is nonparametric and involves multiple stages: (i) wavelet thresholding, aggregation, and Neyman truncation to effectively reduce dimensionality; (ii) clustering based on an extended EM algorithm; and (iii) multiscale penalized dyadic partitioning to create a spatial segmentation. We motivate the different stages with theoretical considerations and arguments, and illustrate the overall procedure on simulated and real datasets. Our method appears to offer substantial improvements over monoscale pixel-wise methods. An Appendix which gives some theoretical justifications of the methodology, computer code, documentation and dataset are available in the online supplements

Speech enhancement by perceptual adaptive wavelet de-noising

This thesis work summarizes and compares the existing wavelet de-noising methods. Most popular methods of wavelet transform, adaptive thresholding, and musical noise suppression have been analyzed theoretically and evaluated through Matlab simulation. Based on the above work, a new speech enhancement system using adaptive wavelet de-noising is proposed. Each step of the standard wavelet thresholding is improved by optimized adaptive algorithms. The Quantile based adaptive noise estimate and the posteriori SNR based threshold adjuster are compensatory to each other. The combination of them integrates the advantages of these two approaches and balances the effects of noise removal and speech preservation. In order to improve the final perceptual quality, an innovative musical noise analysis and smoothing algorithm and a Teager Energy Operator based silent segment smoothing module are also introduced into the system. The experimental results have demonstrated the capability of the proposed system in both stationary and non-stationary noise environments

Signal processing techniques for machine condition monitoring

The purpose of this dissertation is to analyse and compare a wide range of wavelet de-noising parameters and determine which parameters are best suited to the de-noising of rolling element bearing vibration signals. The condition of rolling element bearings is often monitored by recording the vibration of the bearing using accelerometers and analysing the signal for particular frequency content. When a bearing experiences a mechanical fault the vibration signal will contain frequencies relating to the failing component. Monitoring the bearing vibration can provide advanced warning that a bearing failure is imminent. However, when a mechanical fault is in the early stages of development the fault frequency can be very low in magnitude and difficult to detect. Improving the signal to noise ratio of these fault frequencies can provide earlier detection of the fault. One method to improve the signal to noise ratio of a bearing fault frequency is to reduce the noise component in the vibration signal using wavelet theory. Wavelet de-noising has many parameters that can be varied which changes how the de-noising process modifies the vibration signal in the time domain. This dissertation makes comparison between the many de-noising parameters available and assesses which parameters provide the best increase in signal to noise ratio. The wavelet de-noising process alone does not identify the frequencies relating to a bearing fault. The frequency content within the vibration time domain signal is required to be extracted and assessed to determine the effect of the wavelet de-noising process. Three frequency extraction methods were used to analyse the de-noised signals and indicate the magnitude of signal to noise ratio improvement achieved through de-noising. This dissertation shows that cepstrum analysis of the time domain signal responded best to the wavelet de-noising process and large improvements in signal to noise ratio were realised

Uncovering hidden information and relations in time series data with wavelet analysis: three case studies in finance

This thesis aims to provide new insights into the importance of decomposing aggregate time series data using the Maximum Overlap Discrete Wavelet Transform. In particular, the analysis throughout this thesis involves decomposing aggregate financial time series data at hand into approximation (low-frequency) and detail (high-frequency) components. Following this, information and hidden relations can be extracted for different investment horizons, as matched with the detail components. The first study examines the ability of different GARCH models to forecast stock return volatility in eight international stock markets. The results demonstrate that de-noising the returns improves the accuracy of volatility forecasts regardless of the statistical test employed. After de-noising, the asymmetric GARCH approach tends to be preferred, although that result is not universal. Furthermore, wavelet de-noising is found to be more important at the key 99% Value-at-Risk level compared to the 95% level. The second study examines the impact of fourteen macroeconomic news announcements on the stock and bond return dynamic correlation in the U.S. from the day of the announcement up to sixteen days afterwards. Results conducted over the full sample offer very little evidence that macroeconomic news announcements affect the stock-bond return dynamic correlation. However, after controlling for the financial crisis of 2007-2008 several announcements become significant both on the announcement day and afterwards. Furthermore, the study observes that news released early in the day, i.e. before 12 pm, and in the first half of the month, exhibit a slower effect on the dynamic correlation than those released later in the month or later in the day. While several announcements exhibit significance in the 2008 crisis period, only CPI and Housing Starts show significant and consistent effects on the correlation outside the 2001, 2008 and 2011 crises periods. The final study investigates whether recent returns and the time-scaled return can predict the subsequent trading in ten stock markets. The study finds little evidence that recent returns do predict the subsequent trading, though this predictability is observed more over the long-run horizon. The study also finds a statistical relation between trading and return over the long-time investment horizons of [8-16] and [16-32] day periods. Yet, this relation is mostly a negative one, only being positive for developing countries. It also tends to be economically stronger during bull-periods

Machine Learning Methods for Better Water Quality Prediction

In any aquatic system analysis, the modelling water quality parameters are of considerable significance. The traditional modelling methodologies are dependent on datasets that involve large amount of unknown or unspecified input data and generally consist of time-consuming processes. The implementation of artificial intelligence (AI) leads to a flexible mathematical structure that has the capability to identify non-linear and complex relationships between input and output data. There has been a major degradation of the Johor River Basin because of several developmental and human activities. Therefore, setting up of a water quality prediction model for better water resource management is of critical importance and will serve as a powerful tool. The different modelling approaches that have been implemented include: Adaptive Neuro-Fuzzy Inference System (ANFIS), Radial Basis Function Neural Networks (RBF-ANN), and Multi-Layer Perceptron Neural Networks (MLP-ANN). However, data obtained from monitoring stations and experiments are possibly polluted by noise signals as a result of random and systematic errors. Due to the presence of noise in the data, it is relatively difficult to make an accurate prediction. Hence, a Neuro-Fuzzy Inference System (WDT-ANFIS) based augmented wavelet de-noising technique has been recommended that depends on historical data of the water quality parameter. In the domain of interests, the water quality parameters primarily include ammoniacal nitrogen (AN), suspended solid (SS) and pH. In order to evaluate the impacts on the model, three evaluation techniques or assessment processes have been used. The first assessment process is dependent on the partitioning of the neural network connection weights that ascertains the significance of every input parameter in the network. On the other hand, the second and third assessment processes ascertain the most effectual input that has the potential to construct the models using a single and a combination of parameters, respectively. During these processes, two scenarios were introduced: Scenario 1 and Scenario 2. Scenario 1 constructs a prediction model for water quality parameters at every station, while Scenario 2 develops a prediction model on the basis of the value of the same parameter at the previous station (upstream). Both the scenarios are based on the value of the twelve input parameters. The field data from 2009 to 2010 was used to validate WDT-ANFIS. The WDT-ANFIS model exhibited a significant improvement in predicting accuracy for all the water quality parameters and outperformed all the recommended models. Also, the performance of Scenario 2 was observed to be more adequate than Scenario 1, with substantial improvement in the range of 0.5% to 5% for all the water quality parameters at all stations. On validating the recommended model, it was found that the model satisfactorily predicted all the water quality parameters (R2 values equal or bigger than 0.9). © 201