The need for an efficient dimensionality reduction technique has remained a critical challenge for effective analysis of hyperspectral data for vegetation applications. Discrete wavelet transform (DWT), through multiresolution analysis, offers oppurtunities both to reduce dimension and convey information at multiple spectral scales. In this study, we investigated the utility of the Haar DWT for AVIRIS hyperspectral data analysis in three different applications (1) classification of three pine species (Pinus spp.), (2) estimation of leaf area index (LAI) using an empirically-based model, and (3) estimation of LAI using a physically-based model. For pine species classification, different sets of Haar wavelet features were compared to each other and to calibrated radiance. The Haar coefficients selected by stepwise discriminant analysis provided better classification accuracy (74.2%) than the original radiance (66.7%). For empirically-based LAI estimation, the models using the Haar coefficients explained the most variance in observed LAI for both deciduous plots (cross validation R² (CV-R²) = 0.79 for wavelet features vs. CV-R² = 0.69 for spectral bands) and all plots combined (CV R² = 0.71 for wavelet features vs. CV-R² = 0.50 for spectral bands). For physically-based LAI estimation, a look-up-table (LUT) was constructed by a radiative transfer model, DART, using a three-stage approach developed in this study. The approach involved comparison between preliminary LUT reflectances and image spectra to find the optimal set of parameter combinations and input increments. The LUT-based inversion was performed with three different datasets, the original reflectance bands, the full set of the wavelet extracted features, and the two wavelet subsets containing 99.99% and 99.0% of the cumulative energy of the original signal. The energy subset containing 99.99% of the cumulative signal energy provided better estimates of LAI (RMSE = 0.46, R² = 0.77) than the original spectral bands (RMSE = 0.69, R² = 0.42). This study has demonstrated that the application of the discrete wavelet transform can provide more accurate species discrimination within the same genus than the original hyperspectral bands and can improve the accuracy of LAI estimates from both empirically- and physically-based models. / Ph. D.

Alzheimer’s disease slowly destroys an individual’s memory, and it is estimated to impact more than 5.5 million Americans. Over time, Alzheimer’s disease can cause behavior and personality changes. Current diagnosis techniques are challenging because individuals may show no clinical signs of the disease in the initial stages. As of today, there is no cure for Alzheimer’s. Therefore, symptom management is key, and it is critical that Alzheimer’s is detected early before major cognitive damage. The approach implemented in this thesis explores the idea of using the Discrete Wavelet Transform (DWT) and Convolutional Neural Networks (CNN) for Alzheimer’s detection. The neural network is trained and tested using Magnetic Resonance Image (MRI) brain scans from the ADNI1 (Alzheimer’s Disease Neuroimaging Initiative) dataset; and various mother wavelets and network hyperparameters are implemented to identify the optimal model. The resulting model can successfully identify patients with mild Alzheimer’s disease (AD) and the ones that are cognitively normal (NL) with an average accuracy of accuracy of 77.53±2.37%, an f1-score of 77.03±3.24%, precision of 80.63±11.03%, recall or sensitivity or 77.90±11.52%, and a specificity of 77.53±2.37%.

This work deals with theory of wavelet transform and Mallat’s algorithm. It also includes the programming method of creating VST plug-in modules and describes the developement of the plug-in module, witch uses the modificated coeficients of wavelet transform to applicate the music effect.

Este trabalho apresenta o estudo e o desenvolvimento de um algoritmo híbrido para detecção, classificação e localização de faltas em sistemas com três terminais utilizando como principal ferramenta a transformada wavelet (TW) em suas versões discreta (TWD) e estacionária (TWE). O algoritmo é dito híbrido, pois alia duas metodologias para localizar a falta. A primeira baseada na análise de componentes de alta freqüência (ondas viajantes) e a segunda, baseada na extração dos componentes fundamentais para o cálculo da impedância aparente. A metodologia proposta foi concebida de maneira a trabalhar com dados sincronizados dos três terminais ou apenas dados locais para estimar a localização da falta. O localizador híbrido escolhe automaticamente qual a melhor técnica de localização ser utilizada para alcançar uma localização confiável e precisa. Deste modo, um método pode suprir as dificuldades do outro, ou, no mínimo, fornecer mais informações para que, junto ao conhecimento do operador, uma localização próxima da ótima possa ser alcançada. Com o objetivo de testar e validar a aplicabilidade do algoritmo de localização de faltas híbrido para linhas com três terminais, utilizou-se de dados de sinais faltosos obtidos através de simulações do software ATP (Altenative Transients Program), levando-se em conta a variação de diversos parâmetros que poderiam influenciar o desempenho do algoritmo proposto. Os resultados alcançados pelo algoritmo frente às situações avaliadas são bastante animadores, apontando a uma promissora aplicabilidade do mesmo. / This work presents a study and development of a hybrid algorithm for fault detection, classification and location in tree terminal lines based on wavelet transform (WT). It will be presented in two versions: discrete wavelet transform (DWT) and stationary wavelet transform (SWT). The algorithm is called hybrid because it uses two fault location methodologies: one based on fundamental components and other based on traveling waves. The proposed methodology works either with synchronized tree terminal data or only local data. The hybrid fault locator chooses automatically which location technique to be used in order to reach a reliable and accurate fault location. In this manner, this technique can avoid some difficulties present in other techniques, aiming to reach an optimized fault location. The proposed hybrid fault location was evaluated by simulated fault signals obtained by alternative transient program (ATP). In the tests, several parameters, which would influence the performance of the hybrid algorithm, were varied, such as: fault inception angle, fault resistance, fault type, etc. The results obtained by the proposed methodology are very encouraging and it points out to a very promising application.

Este trabalho apresenta o estudo e o desenvolvimento de um algoritmo híbrido para detecção, classificação e localização de faltas em sistemas com três terminais utilizando como principal ferramenta a transformada wavelet (TW) em suas versões discreta (TWD) e estacionária (TWE). O algoritmo é dito híbrido, pois alia duas metodologias para localizar a falta. A primeira baseada na análise de componentes de alta freqüência (ondas viajantes) e a segunda, baseada na extração dos componentes fundamentais para o cálculo da impedância aparente. A metodologia proposta foi concebida de maneira a trabalhar com dados sincronizados dos três terminais ou apenas dados locais para estimar a localização da falta. O localizador híbrido escolhe automaticamente qual a melhor técnica de localização ser utilizada para alcançar uma localização confiável e precisa. Deste modo, um método pode suprir as dificuldades do outro, ou, no mínimo, fornecer mais informações para que, junto ao conhecimento do operador, uma localização próxima da ótima possa ser alcançada. Com o objetivo de testar e validar a aplicabilidade do algoritmo de localização de faltas híbrido para linhas com três terminais, utilizou-se de dados de sinais faltosos obtidos através de simulações do software ATP (Altenative Transients Program), levando-se em conta a variação de diversos parâmetros que poderiam influenciar o desempenho do algoritmo proposto. Os resultados alcançados pelo algoritmo frente às situações avaliadas são bastante animadores, apontando a uma promissora aplicabilidade do mesmo. / This work presents a study and development of a hybrid algorithm for fault detection, classification and location in tree terminal lines based on wavelet transform (WT). It will be presented in two versions: discrete wavelet transform (DWT) and stationary wavelet transform (SWT). The algorithm is called hybrid because it uses two fault location methodologies: one based on fundamental components and other based on traveling waves. The proposed methodology works either with synchronized tree terminal data or only local data. The hybrid fault locator chooses automatically which location technique to be used in order to reach a reliable and accurate fault location. In this manner, this technique can avoid some difficulties present in other techniques, aiming to reach an optimized fault location. The proposed hybrid fault location was evaluated by simulated fault signals obtained by alternative transient program (ATP). In the tests, several parameters, which would influence the performance of the hybrid algorithm, were varied, such as: fault inception angle, fault resistance, fault type, etc. The results obtained by the proposed methodology are very encouraging and it points out to a very promising application.

Work is aimed at the time-frequency decomposition of a signal application for monitoring the EKG trend progression. Goal is to create algorithm which would watch changes in the ST segment in EKG recording and its realization in the Matlab program. Analyzed is substance of the origin of EKG and its measuring. For trend calculations after reading the signal is necessary to preprocess the signal, it consists of filtration and detection of necessary points of EKG signal. For taking apart, also filtration and measuring the signal is used wavelet transformation. Source of the data is biomedicine database Physionet. As an outcome of the algorithm are drawn ST segment trends for three recordings from three different patients and its comparison with reference method of ST qualification. For qualification of the heart stability, as a system, where designed methods watching differences in position of the maximal value in two-zone spectrum and the Poincare mapping method. Realized method is attached to this thesis.

In the past two decades, there has been huge amount of interest in Multiresolution Analysis Algorithms (MAAs) and their applications. Processing some of their applications such as medical imaging are computationally intensive, power hungry and requires large amount of memory which cause a high demand for efficient algorithm implementation, low power architecture and acceleration. Recently, some MAAs such as Finite Ridgelet Transform (FRIT) Haar Wavelet Transform (HWT) are became very popular and they are suitable for a number of image processing applications such as detection of line singularities and contiguous edges, edge detection (useful for compression and feature detection), medical image denoising and segmentation. Efficient hardware implementation and acceleration of these algorithms particularly when addressing large problems are becoming very chal-lenging and consume lot of power which leads to a number of issues including mobility, reliability concerns. To overcome the computation problems, Field Programmable Gate Arrays (FPGAs) are the technology of choice for accelerating computationally intensive applications due to their high performance. Addressing the power issue requires optimi- sation and awareness at all level of abstractions in the design flow. The most important achievements of the work presented in this thesis are summarised here. Two factorisation methodologies for HWT which are called HWT Factorisation Method1 and (HWTFM1) and HWT Factorasation Method2 (HWTFM2) have been explored to increase number of zeros and reduce hardware resources. In addition, two novel efficient and optimised architectures for proposed methodologies based on Distributed Arithmetic (DA) principles have been proposed. The evaluation of the architectural results have shown that the proposed architectures results have reduced the arithmetics calculation (additions/subtractions) by 33% and 25% respectively compared to direct implementa-tion of HWT and outperformed existing results in place. The proposed HWTFM2 is implemented on advanced and low power FPGA devices using Handel-C language. The FPGAs implementation results have outperformed other existing results in terms of area and maximum frequency. In addition, a novel efficient architecture for Finite Radon Trans-form (FRAT) has also been proposed. The proposed architecture is integrated with the developed HWT architecture to build an optimised architecture for FRIT. Strategies such as parallelism and pipelining have been deployed at the architectural level for efficient im-plementation on different FPGA devices. The proposed FRIT architecture performance has been evaluated and the results outperformed some other existing architecture in place. Both FRAT and FRIT architectures have been implemented on FPGAs using Handel-C language. The evaluation of both architectures have shown that the obtained results out-performed existing results in place by almost 10% in terms of frequency and area. The proposed architectures are also applied on image data (256 £ 256) and their Peak Signal to Noise Ratio (PSNR) is evaluated for quality purposes. Two architectures for cyclic convolution based on systolic array using parallelism and pipelining which can be used as the main building block for the proposed FRIT architec-ture have been proposed. The first proposed architecture is a linear systolic array with pipelining process and the second architecture is a systolic array with parallel process. The second architecture reduces the number of registers by 42% compare to first architec-ture and both architectures outperformed other existing results in place. The proposed pipelined architecture has been implemented on different FPGA devices with vector size (N) 4,8,16,32 and word-length (W=8). The implementation results have shown a signifi-cant improvement and outperformed other existing results in place. Ultimately, an in-depth evaluation of a high level power macromodelling technique for design space exploration and characterisation of custom IP cores for FPGAs, called func-tional level power modelling approach have been presented. The mathematical techniques that form the basis of the proposed power modeling has been validated by a range of custom IP cores. The proposed power modelling is scalable, platform independent and compares favorably with existing approaches. A hybrid, top-down design flow paradigm integrating functional level power modelling with commercially available design tools for systematic optimisation of IP cores has also been developed. The in-depth evaluation of this tool enables us to observe the behavior of different custom IP cores in terms of power consumption and accuracy using different design methodologies and arithmetic techniques on virous FPGA platforms. Based on the results achieved, the proposed model accuracy is almost 99% true for all IP core's Dynamic Power (DP) components.

Systeme der Computer Vision spielen in der Automatisierung vieler Prozesse eine wichtige Rolle. Die wichtigste Aufgabe solcher Systeme ist die Automatisierung des visuellen Erkennungsprozesses und die Extraktion der relevanten Information aus Bildern oder Bildsequenzen. Eine wichtige Komponente dieser Systeme ist die Bildsegmentierung, denn sie bestimmt zu einem großen Teil die Qualitaet des Gesamtsystems. Fuer die Segmentierung von Bildern und Bildsequenzen werden neue Algorithmen vorgeschlagen. Das Konzept der Multiresolution wird als eigenstaendig dargestellt, es existiert unabhaengig von der Wavelet-Transformation. Die Wavelet-Transformation wird zur Verarbeitung von Bildern und Bildsequenzen zu einer 2D- bzw. 3D-Wavelet- Transformation erweitert. Fuer die Segmentierung von Bildern wird der Algorithmus Resolution Mosaic Expectation Maximization (RM-EM) vorgeschlagen. Das Ergebnis der Vorverarbeitung sind unterschiedlich aufgeloesten Teilbilder, das Aufloesungsmosaik. Durch dieses Mosaik lassen sich raeumliche Korrelationen zwischen den Pixeln ausnutzen. Die Verwendung unterschiedlicher Aufloesungen beschleunigt die Verarbeitung und verbessert die Ergebnisse. Fuer die Extraktion von bewegten Objekten aus Bildsequenzen werden neue Algorithmen vorgeschlagen, die auf der 3D-Wavelet-Transformation und auf der Analyse mit 3D-Wavelet-Packets beruhen. Die neuen Algorithmen haben den Vorteil, dass sie sowohl die raeumlichen als auch die zeitlichen Bewegungsinformationen beruecksichtigen. Wegen der geringen Berechnungskomplexitaet der Wavelet-Transformation ist fuer den ersten Segmentierungsschritt Hardware auf der Basis von FPGA entworfen worden. Aktuelle Anwendungen werden genutzt, um die Algorithmen zu evaluieren: die Segmentierung von Magnetresonanzbildern des menschlichen Gehirns und die Detektion von bewegten Objekten in Bildsequenzen von Verkehrsszenen. Die neuen Algorithmen sind robust und fuehren zu besseren Segmentierungsergebnissen. / More and more computer vision systems take part in the automation of various applications. The main task of such systems is to automate the process of visual recognition and to extract relevant information from the images or image sequences acquired or produced by such applications. One essential and critical component in almost every computer vision system is image segmentation. The quality of the segmentation determines to a great extent the quality of the final results of the vision system. New algorithms for image and video segmentation based on the multiresolution analysis and the wavelet transform are proposed. The concept of multiresolution is explained as existing independently of the wavelet transform. The wavelet transform is extended to two and three dimensions to allow image and video processing. For still image segmentation the Resolution Mosaic Expectation Maximization (RM-EM) algorithm is proposed. The resolution mosaic enables the algorithm to employ the spatial correlation between the pixels. The level of the local resolution depends on the information content of the individual parts of the image. The use of various resolutions speeds up the processing and improves the results. New algorithms based on the 3D wavelet transform and the 3D wavelet packet analysis are proposed for extracting moving objects from image sequences. The new algorithms have the advantage of considering the relevant spatial as well as temporal information of the movement. Because of the low computational complexity of the wavelet transform an FPGA hardware for the primary segmentation step was designed. Actual applications are used to investigate and evaluate all algorithms: the segmentation of magnetic resonance images of the human brain and the detection of moving objects in image sequences of traffic scenes. The new algorithms show robustness against noise and changing ambient conditions and gave better segmentation results.

Nano scale processing of IC chips has become the prime production technique as the microelectronic industry aims towards scaling down product dimensions while increasing accuracy and performance. Accurate control of temperature and a good monitoring mechanism for thickness of the deposition layers during epitaxial growth are critical parameters influencing a good yield. The two-fold objective of this thesis is to establish the feasibility of an alternative to the current pyrometric and ellipsometric techniques to simultaneously measure temperature and thickness during wafer processing. TAP-NDE is a non-contact, non-invasive, laser-based ultrasound technique that is employed in this study to contemporarily profile the thermal and spatial characteristics of the wafer. The Gabor wavelet transform allows the wave dispersion to be unraveled and the group velocity of individual frequency components to be extracted from the experimentally acquired time waveform. The thesis illustrates the formulation of a theoretical model that is used to identify the frequencies sensitive to temperature and thickness changes. The group velocity of the corresponding frequency components is determined and their corresponding changes with respect to temperature for different thickness are analytically modeled. TAP-NDE is then used to perform an experimental analysis on Silicon wafers of different thickness to determine the maximum possible resolution of TAP-NDE towards temperature sensitivity, and to demonstrate the ability to differentiate between wafers of different deposition layer thickness at temperatures up to 600?C. Temperature resolution is demonstrated for ?10?C resolution and for ?5?C resolution; while thickness differentiation is carried out with wafers carrying 4000? and 8000? of aluminum deposition layer. The experimental group velocities of a set of selected frequency components extracted using the Gabor Wavelet time-frequency analysis as compared to their corresponding theoretical group velocities show satisfactory agreement. As a result of this work, it is seen that TAP-NDE is a suitable tool to identify and characterize thickness and temperature changes simultaneously during thermal annealing that can replace the current need for separate characterization of these two important parameters in semiconductor manufacturing.

Nano scale processing of IC chips has become the prime production technique as the microelectronic industry aims towards scaling down product dimensions while increasing accuracy and performance. Accurate control of temperature and a good monitoring mechanism for thickness of the deposition layers during epitaxial growth are critical parameters influencing a good yield. The two-fold objective of this thesis is to establish the feasibility of an alternative to the current pyrometric and ellipsometric techniques to simultaneously measure temperature and thickness during wafer processing. TAP-NDE is a non-contact, non-invasive, laser-based ultrasound technique that is employed in this study to contemporarily profile the thermal and spatial characteristics of the wafer. The Gabor wavelet transform allows the wave dispersion to be unraveled and the group velocity of individual frequency components to be extracted from the experimentally acquired time waveform. The thesis illustrates the formulation of a theoretical model that is used to identify the frequencies sensitive to temperature and thickness changes. The group velocity of the corresponding frequency components is determined and their corresponding changes with respect to temperature for different thickness are analytically modeled. TAP-NDE is then used to perform an experimental analysis on Silicon wafers of different thickness to determine the maximum possible resolution of TAP-NDE towards temperature sensitivity, and to demonstrate the ability to differentiate between wafers of different deposition layer thickness at temperatures up to 600?C. Temperature resolution is demonstrated for ?10?C resolution and for ?5?C resolution; while thickness differentiation is carried out with wafers carrying 4000? and 8000? of aluminum deposition layer. The experimental group velocities of a set of selected frequency components extracted using the Gabor Wavelet time-frequency analysis as compared to their corresponding theoretical group velocities show satisfactory agreement. As a result of this work, it is seen that TAP-NDE is a suitable tool to identify and characterize thickness and temperature changes simultaneously during thermal annealing that can replace the current need for separate characterization of these two important parameters in semiconductor manufacturing.