This thesis consists of two topics: statistical selection and profile monitoring. Statistical selection is related to ranking and selection in simulation and profile monitoring is related to statistical process control. Ranking and selection (R&S) is to select a system with the largest or smallest performance measure among a finite number of simulated alternatives with some guarantee about correctness. Fully sequential procedures have been shown to be efficient, but their actual probabilities of correct selection tend to be higher than the nominal level, implying that they consume unnecessary observations. In the first part, we study three conservativeness sources in fully sequential indifference-zone (IZ) procedures and use experiments to quantify the impact of each source in terms of the number of observations, followed by an asymptotic analysis on the impact of the critical one. Then we propose new asymptotically valid procedures that lessen the critical conservativeness source, by mean update with or without variance update. Experimental results showed that new procedures achieved meaningful improvement on the efficiency. The second part is developing a wavelet-based distribution-free tabular CUSUM chart based on adaptive thresholding. WDFTCa is designed for rapidly detecting shifts in the mean of a high-dimensional profile whose noise components have a continuous nonsingular multivariate distribution. First computing a discrete wavelet transform of the noise vectors for randomly sampled Phase I (in-control) profiles, WDFTCa uses a matrix-regularization method to estimate the covariance matrix of the wavelet-transformed noise vectors; then those vectors are aggregated (batched) so that the nonoverlapping batch means of the wavelet-transformed noise vectors have manageable covariances. Lower and upper in-control thresholds are computed for the resulting batch means of the wavelet-transformed noise vectors using the associated marginal Cornish-Fisher expansions that have been suitably adjusted for between-component correlations. From the thresholded batch means of the wavelet-transformed noise vectors, Hotelling’s T^2-type statistics are computed to set the parameters of a CUSUM procedure. To monitor shifts in the mean profile during Phase II (regular) operation, WDFTCa computes a similar Hotelling’s T^2-type statistic from successive thresholded batch means of the wavelet-transformed noise vectors using the in-control thresholds; then WDFTCa applies the CUSUM procedure to the resulting T^2-type statistics. Experimentation with several normal and nonnormal test processes revealed that WDFTCa outperformed existing nonadaptive profile-monitoring schemes.

A novel wavelet-based scheme to increase coefficient independence in hyperspectral images is introduced for lossless coding. The proposed regression wavelet analysis (RWA) uses multivariate regression to exploit the relationships among wavelettransformed components. It builds on our previous nonlinear schemes that estimate each coefficient from neighbor coefficients. Specifically, RWA performs a pyramidal estimation in the wavelet domain, thus reducing the statistical relations in the residuals and the energy of the representation compared to existing wavelet-based schemes. We propose three regression models to address the issues concerning estimation accuracy, component scalability, and computational complexity. Other suitable regression models could be devised for other goals. RWA is invertible, it allows a reversible integer implementation, and it does not expand the dynamic range. Experimental results over a wide range of sensors, such as AVIRIS, Hyperion, and Infrared Atmospheric Sounding Interferometer, suggest that RWA outperforms not only principal component analysis and wavelets but also the best and most recent coding standard in remote sensing, CCSDS-123.

Complex industrial processes are represented by data that are well known to be multiscaled due to the variety of events that occur in a process at different time and frequency localizations. Wavelet based multiscale analysis approaches provide an excellent means to examine these events. However, the scope of the existing wavelet based methods in the fields of statistical applications, such as process monitoring and defect identification are still limited. Recent literature contains several wavelet decomposition based multiscale process monitoring approaches including many real life process monitoring applications, such as tool-life monitoring, bearing defect monitoring, and monitoring of ultra-precision processes such as chemical mechanical planarization (CMP) in wafer fabrication. However, all of the above mentioned wavelet based methodologies are offline and depend on the visual observations of the wavelet coefficients and details. The offline analysis paradigm was imposed by the high computation needs of the multiscale analysis, whereas the visual observation based approach was necessitated by the lack of statistical means to identify undesirable events. One of the most recent multiscale application, that deals with detecting delamination in CMP, addressed the need for online analysis by developing a moving window based approach to reduce computation time. This research presents 1) development of a fully online multiscale analysis approach where the speed of wavelet based analysis of the data matches the rate of data generation, 2) development of a statistical tool based on Sequential Probability Ratio Test (SPRT) to detect events of interest, and 3) development of an approach to display the analysis results through real time graphs for ease of process supervisory decision making. The developed methodologies are programmed using MATLAB 6.5 and implemented on several data sets obtained from metal and oxide CMP of wafer fabrication. The results and analysis are presented.

In this thesis, the problem of multiple access interference (MAI) suppression for the multi-carrier (MC) code division multiple access (CDMA) system, based on the wavelet-based (WB) multi-carrier modulation, associated with the combining process is investigated for Rayleigh fading channel. The main concern of this thesis is to derive a new scheme, based on the linearly constrained constant modulus (LCCM) criterion with the robust inverse QR decomposition (IQRD) recursive least squares (RLS) algorithm to improve the performance of the conventional MC-CDMA system with combining process. To verify the merits of the new algorithm, the effect due to imperfect channel parameters estimation and frequency offset are investigated. We show that the proposed robust LCCM IQRD-RLS algorithm outperforms the conventional LCCM-gradient algorithm [6], in terms of output SINR, improvement percentage index (IPI), and bit error rate (BER) for MAI suppression under channel mismatch environment. Also, the performance of the WB MC-CDMA system is superior to the one with conventional MC-CDMA system. It is more robust to the channel mismatch and frequency offset. Moreover, the WB MC-CDMA system with robust LCCM IQRD-RLS algorithm does have better performance over other conventional approaches, such as the LCCM-gradient algorithm, maximum ratio combining (MRC), blind adaptation algorithm and partitioned linear interference canceller (PLIC) approach with LMS algorithm, in terms of the capability of MAI suppression and bit error rate (BER).

Geoscience applications generate large datasets; thus, compression is necessary to facilitate the storage and transmission of geoscience data. One focus is on the coding of hyperspectral imagery and the prominent JPEG2000 standard. Certain aspects of the encoder, such as rate-allocation between bands and spectral decorrelation, are not covered by the JPEG2000 standard. This thesis investigates the performance of several JPEG2000 encoding strategies. Additionally, a relatively low-complexity 3D embedded wavelet-based coder, 3D-tarp, is proposed for the compression of geoscience data. 3D-tarp employs an explicit estimate of the probability of coefficient significance to drive a nonadaptive arithmetic coder, resulting in a simple implementation suited to vectorized hardware acceleration. Finally, an embedded wavelet-based coder is proposed for the shapeaptive coding of ocean-temperature data. 3D binary set-splitting with $k$-d trees, 3D-BISK, replaces the octree splitting structure of other shapeaptive coders with $k$-d trees, a simpler set partitioning structure that is well-suited to shapeaptive coding.

O julgamento da qualidade de um método de estimativa/simulação é mais adequado se os resultados puderem ser comparados a dados reais. Uma vez que na mineração isto é inviável, este trabalho é baseado em um modelo de depósito mineral de cobre - representando a geologia e a distribuição de dados de modo heterogêneos. O modelo reproduz um depósito com preenchimento hidrotermal em uma falha inversa e as rochas encaixantes são meta-arenito e folhelho dobrados. O objetivo é comparar os resultados obtidos pelo método de Simulação Baseada em Wavelets - método o qual utiliza a estatística espacial de alta-ordem para reproduzir as estruturas da geologia - com o método clássico de Simulação Sequencial Gaussiana, a fim de avaliar um método de geoestatística de multiponto aplicado a variável contínua. Para comparar os resultados, foi calculado o valor potencial e para qual pilha (minério ou estéril) deveria ir cada bloco. Os resultados mostram que, matematicamente, a Simulação Sequencial Gaussiana obteve resultados melhores, uma vez que destinou melhor seus blocos e perdeu menos dinheiro com estéril na pilha de minério e minério de pilha de estéril. Porém, é notória a influência da imagem de treinamento nos resultados da Simulação Baseada em Wavelets, o que mostra que a Simulação Baseada em Wavelets de variáveis contínuas é promissora se a imagem de treinamento for adequada. O grande problema é que sua escolha ou criação é demasiadamente complexa, pois necessita de precisão local e global. / The judgment of the quality of an estimation/simulation method is more suitable if the results can be compared to real data. Once in mining that is not feasible, this work is based on a synthetic mineral deposit - represented by a very heterogeneous geology and spatial data distribution. The model reproduces a deposit with hydrothermal filling in a n inverse fault and the bedrocks are folded meta-sandstone and phyllite. The objective is to compare the results obtained by Wavelet-based Simulation method - which uses the spatial high-order statistic to reproduce the geologic structures - with the classic method of Sequential Gaussian Simulation in order to evaluate a multipoint geostatistical method applied to a continuous variable. To compare the results, the potential value was calculated and to which pile (ore or waste) each block should go. The results show that, mathematically, Sequential Gaussian Simulation\'s results are better, since its blocks allocated better and lost less money on waste in ore pile and ore in waste pile. However, it is clear the influence of the training image on the results of Wavelet-based Simulation. This shows that the Wavelet-based Simulation of continuous variables is promising if the training image is appropriate. The big problem is that choosing or creating it is too complex, because it requires local and global precision.

O julgamento da qualidade de um método de estimativa/simulação é mais adequado se os resultados puderem ser comparados a dados reais. Uma vez que na mineração isto é inviável, este trabalho é baseado em um modelo de depósito mineral de cobre - representando a geologia e a distribuição de dados de modo heterogêneos. O modelo reproduz um depósito com preenchimento hidrotermal em uma falha inversa e as rochas encaixantes são meta-arenito e folhelho dobrados. O objetivo é comparar os resultados obtidos pelo método de Simulação Baseada em Wavelets - método o qual utiliza a estatística espacial de alta-ordem para reproduzir as estruturas da geologia - com o método clássico de Simulação Sequencial Gaussiana, a fim de avaliar um método de geoestatística de multiponto aplicado a variável contínua. Para comparar os resultados, foi calculado o valor potencial e para qual pilha (minério ou estéril) deveria ir cada bloco. Os resultados mostram que, matematicamente, a Simulação Sequencial Gaussiana obteve resultados melhores, uma vez que destinou melhor seus blocos e perdeu menos dinheiro com estéril na pilha de minério e minério de pilha de estéril. Porém, é notória a influência da imagem de treinamento nos resultados da Simulação Baseada em Wavelets, o que mostra que a Simulação Baseada em Wavelets de variáveis contínuas é promissora se a imagem de treinamento for adequada. O grande problema é que sua escolha ou criação é demasiadamente complexa, pois necessita de precisão local e global. / The judgment of the quality of an estimation/simulation method is more suitable if the results can be compared to real data. Once in mining that is not feasible, this work is based on a synthetic mineral deposit - represented by a very heterogeneous geology and spatial data distribution. The model reproduces a deposit with hydrothermal filling in a n inverse fault and the bedrocks are folded meta-sandstone and phyllite. The objective is to compare the results obtained by Wavelet-based Simulation method - which uses the spatial high-order statistic to reproduce the geologic structures - with the classic method of Sequential Gaussian Simulation in order to evaluate a multipoint geostatistical method applied to a continuous variable. To compare the results, the potential value was calculated and to which pile (ore or waste) each block should go. The results show that, mathematically, Sequential Gaussian Simulation\'s results are better, since its blocks allocated better and lost less money on waste in ore pile and ore in waste pile. However, it is clear the influence of the training image on the results of Wavelet-based Simulation. This shows that the Wavelet-based Simulation of continuous variables is promising if the training image is appropriate. The big problem is that choosing or creating it is too complex, because it requires local and global precision.

A classificação automática de gênero musical tem como finalidade o conforto de ouvintes de músicas auxiliando no gerenciamento das coleções de músicas digitais. Existem sistemas que se baseiam em cabeçalhos de metadados (tais como nome de artista, gênero cadastrado, etc.) e também os que extraem parâmetros dos arquivos de música para a realização da tarefa. Enquanto a maioria dos trabalhos do segundo tipo utilizam-se do conteúdo rítmico e tímbrico, este utiliza-se apenas de conceitos da teoria da informação e da geometria de fractais. Entropia, lacunaridade e dimensão do fractal são os parâmetros que treinam os classificadores. Os testes foram realizados com duas coleções criadas para este trabalho e os resultados foram proeminentes / The goal of automatic music genre classification is givingmusic listeners ease and confort when managing digital music databases. Some systems are based on tags of metadata (such as artist name, genre labeled, etc.), while others explore characteristics from the music files to complete the task. While the majority of works of the second type analyse rhytmic, timbric and pitch content, this one explores only information theoretic and fractal geometry concepts. Entropy, fractal dimension and lacunarity are the parameters adopted to train the classifiers. Tests were carried out on two databases assembled by the author. Results were prominent

In this thesis, the problem of multiple access interference (MAI) suppression for the multi-carrier (MC) code division multiple access (CDMA) system, based on the multi-carrier modulation with modified Gaussian wavelet, associated with the combining process is investigated for Rayleigh fading channel. The main concern of this thesis is to derive a new scheme, based on the linearly constrained constant modulus (LCCM) criterion with the robust inverse QR decomposition (IQRD) recursive least squares (RLS) algorithm to improve the performance of the wavelet-based MC-CDMA system with combining process. To verify the merits of the new algorithm, the effect due to imperfect channel parameters estimation and near-far effect are investigated. We show that the proposed robust LCCM IQRD-RLS algorithm outperforms the conventional LCCM-gradient algorithm, in terms of output SINR, for MAI suppression under channel mismatch environment. Also, the performance of the modified Gaussian wavelet-based MC-CDMA system is superior to the one with wavelet-based MC-CDMA system. It is more robust to the channel mismatch and near-far effect. Moreover, the modified Gaussian wavelet-based MC-CDMA system with robust LCCM IQRD-RLS algorithm does have better performance over other conventional approaches, such as the LCCM-gradient algorithm, maximum ratio combining (MRC), and blind adaptation algorithm, in terms of the capability of MAI suppression and bit error rate (BER).

A classificação automática de gênero musical tem como finalidade o conforto de ouvintes de músicas auxiliando no gerenciamento das coleções de músicas digitais. Existem sistemas que se baseiam em cabeçalhos de metadados (tais como nome de artista, gênero cadastrado, etc.) e também os que extraem parâmetros dos arquivos de música para a realização da tarefa. Enquanto a maioria dos trabalhos do segundo tipo utilizam-se do conteúdo rítmico e tímbrico, este utiliza-se apenas de conceitos da teoria da informação e da geometria de fractais. Entropia, lacunaridade e dimensão do fractal são os parâmetros que treinam os classificadores. Os testes foram realizados com duas coleções criadas para este trabalho e os resultados foram proeminentes / The goal of automatic music genre classification is givingmusic listeners ease and confort when managing digital music databases. Some systems are based on tags of metadata (such as artist name, genre labeled, etc.), while others explore characteristics from the music files to complete the task. While the majority of works of the second type analyse rhytmic, timbric and pitch content, this one explores only information theoretic and fractal geometry concepts. Entropy, fractal dimension and lacunarity are the parameters adopted to train the classifiers. Tests were carried out on two databases assembled by the author. Results were prominent