The High Resolution Electrocardiogram (HRECG) is used to detect Ventricular Late Potentials (VLPs) in post-myocardial infarction patients. VLPs are low-amplitude, high-frequency signals that are usually found within the terminal part of the QRS complex. The aim of this research was to develop possible alternative methods and improve existing methods of detecting VLP activity. There are two main topics in this work: applications of the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT) to the HRECG. For the CWT application, a Fractionation Factor (FF) method proposed by previous work was further investigated and improved by combining the CWT and DWT for distinction between patients with and those without VLPs. A Differential Fractionation Factor was proposed as an alternative approach to the FF with better results. Observation in the time-scale plot showed a difference in the energy distribution. A 2-dimensional Fractionation Factor was proposed to quantify this difference. A new concept of local intermittency was investigated to exhibit energy nonuniformity and then a Local Intermittency Factor was developed to quantify the degree of nonuniformity. The energy computed with the CWT was also used for patient distinction. Patients with VLPs may be also characterised by a slow rate of energy decay. The CWT can reveal a difference in ECG irregularity between the patients. A new approach of approximate entropy was implemented to quantify this irregularity. For the DWT application, the DWT can reveal irregularity of VLP activity and it was quantified by the approximate entropy to identify patients with VLPs. The wavelet entropy was utilised as an alternative method to the FF. The energy computed with the DWT was used for patient classification. The potentially promising results of both the CWT and DWT applications were obtained from the methods of computing the energy and approximate entropy

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The digital watermarking technique embeds meaningful information into one or more watermark images hidden in one image, in which it is known as a secret carrier. It is difficult for a hacker to extract or remove any hidden watermark from an image, and especially to crack so called digital watermark. The combination of digital watermarking technique and traditional image encryption technique is able to greatly improve anti-hacking capability, which suggests it is a good method for keeping the integrity of the original image. The research works contained in this thesis include: (1)A literature review the hyperchaotic watermarking technique is relatively more advantageous, and becomes the main subject in this programme. (2)The theoretical foundation of watermarking technologies, including the human visual system (HVS), the colour space transform, discrete wavelet transform (DWT), the main watermark embedding algorithms, and the mainstream methods for improving watermark robustness and for evaluating watermark embedding performance. (3) The devised hyperchaotic scrambling technique it has been applied to colour image watermark that helps to improve the image encryption and anti-cracking capabilities. The experiments in this research prove the robustness and some other advantages of the invented technique. This thesis focuses on combining the chaotic scrambling and wavelet watermark embedding to achieve a hyperchaotic digital watermark to encrypt digital products, with the human visual system (HVS) and other factors taken into account. This research is of significant importance and has industrial application value.

acase@tulane.edu / In this thesis, we tackle the statistical problem of demixing a multivariate stochastic process made up of independent, fractional process entries. We consider both Gaussian and non-Gaussian frameworks. The observable, mixed process is then a multivariate fractional stochastic process. In particular, when the components of the unmixed process are self-similar, the mixed process is operator self-similar. Multivariate mixed fractional processes are parameterized by a vector of Hurst parameters and a mixing matrix. We propose a 2-step wavelet-based estimation method to produce estimators of both the demixing matrix and the Hurst parameters. In the first step, an estimator of the demixing matrix is obtained by applying a classical joint diagonalization algorithm to two wavelet variance matrices of the mixed process. In the second step, a univariate-like wavelet regression method is applied to each entry of the demixed process to provide estimators of each individual Hurst parameter. The limiting distribution of the estimators is established for both Gaussian and nonGaussian (Rosenblatt-like) instances. Monte Carlo experiments show that the finite sample estimation performance is very satisfactory. As an application, we model bivariate series of annual tree ring measurements from bristlecone pine trees in White Mountains, California. / 1 / Hui Li

This thesis examines the ability of the wavelet transform to form features which may be used successfully in a discriminant analysis. We apply our methods to two different data sets and consider the problem of selecting the 'best' features for discrimination. In the first data set, our interest is in automatically recognising the variety of a carrot from an image. After necessary image preprocessing we examine the usefulness of shape descriptors and texture features for discrimination. We show that it is better to use the different 'types' of features separately, and that the wavelet coefficients of the outline coordinates are more useful. In the second data set we consider the task of automatically identifying individual haddock from the sounds they produce. We use the smoothing property of wavelets to automatically isolate individual haddock sounds, and use the stationary wavelet transform to overcome the shift dependence of the standard wavelet transform. Again we calculate different 'types' of wavelet features and compare their usefulness in classification and show that including information on the source of the previous sound can substantially increase the correct classification rate. We also apply our techniques to recognise different species of fish which is also highly successful. In each analysis, we explore different allocation rules via regularised discriminant analysis and show that the highest classification rates obtained are only slightly better than linear discriminant analysis. We also consider the problem of selecting the best subset of features for discrimination. We propose two new measures for selecting good subsets and using a genetic algorithm we search for the 'best' subsets. We investigate the relationship between out measures and classification rates showing that our method is better than selection based on F-ratios and we also discover that our two measures are closely related.

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Yes / This paper investigates the performance of wavelet OFDM signals over a wireless communications link. The scheme is shown to be generally similar to Fourier based OFDM, but with some additional features, and improved characteristics. The sensitivity of both schemes to the nonlinear amplification in the transmitter is compared by monitoring the time domain output data and the adjacent channel power ratio (ACPR) performance.

In this thesis, we proposed two frequency-based watermarking algorithms. One is DCT-based method. Embedding watermark in the multi-areas and multi- frequency bands to ensure we can get a less distorted watermark sequence under unintentional circumstance. The other is DWT-based method. The parent-children relationship and the feature of bit-plane coding in the EZW algorithm are exploited to embed watermark. It makes that we can know the watermark exist or not in the progressive transmission system. The experimental results show that the proposed methods both can resist unintentional attacks. The DWT-based method also has a better progressive detection capability.

The presence of subsurface anomalies, such as cavities, faults, unknown tunnels, etc., either natural or man-made, can cause public safety hazards. The detection of these features requires the development of new methods. Seismic Rayleigh surface wave imaging is a relatively new non-destructive testing technique (NDT) which generates subsurface images without drilling boreholes into the ground, and in recent years has been widely used for soil characterization in geotechnical investigations. In the last decade, some researchers have applied the technique to near-surface imaging and showed the possibility and potential for engineering applications. This research presents the development of a technique to process seismic Rayleigh waves to detect and image subsurface anomalies. This study conducted investigations of Rayleigh wave behaviors and developed a new strategy for Rayleigh wave isolation from raw field data. The strategy applies wavelet transforms, instead of the conventional spectral analysis of surface waves (SASW) method, or popular multichannel analysis of surface waves (MASW) techniques, to pair-channel analysis of the isolated Rayleigh wave data for dispersion calculation. Finally, a simple steady inversion technique was applied to yield shear velocity as a function of both depth and distance, and shear velocity field images (SVF), for near surface section display. This research consists of development, computer programming, field tests, data processing and interpretation. Three sites in different scenarios were used for seismic investigations: old mining tunnels in medium dipping coal seams in Stellarton coalfield, mining cavities in steeply dipping gold-bearing veins in West Waverley Gold District and an anomaly in nearly horizontal strata in Liverpool. All these sites are in the province of Nova Scotia, Canada. The results from seismic surface wave technique introduced in this research can be evaluated by field observations, documents and borehole logs. The satisfactory interpretations and success of this investigation shows that this technique is suitable for engineering application for subsurface investigations.