In particle image velocimetry (PIV) the measurement signal is contained in the recorded intensity of the particle image pattern superimposed on a variety of noise sources. The inherent amount of signal mutual information between consecutive images governs the strength of the resulting PIV cross correlation and ultimately the accuracy and uncertainty of the produced PIV measurements. Hence we posit that the correlation signal-to-noise-ratio (SNR) metrics calculated from the correlation plane can be used to quantify the quality of the correlation and the resulting uncertainty of an individual measurement. A new SNR metric termed "mutual information" (MI) which quantifies the amount of common information (particle pattern) between two consecutive images is also introduced and investigated. This measure provides a direct estimation of the apparent NIFIFO parameter of an image pair providing an alternative approach towards uncertainty estimation but also connecting the current development to one of the most fundamental principles of PIV and the previous established theory. We extend the original work by Charonko and Vlachos and present a framework for evaluating the correlation strength using a set of different metrics, which in turn are used to develop models for uncertainty estimation. Several corrections have been applied in this work. The metrics and corresponding models presented herein are expanded to be applicable to both standard and filtered correlations by applying a subtraction of the minimum correlation value to remove the effect of the background image noise. In addition, the notion of a "valid" measurement is redefined with respect to the correlation peak width in order to be consistent with uncertainty quantification principles and distinct from an "outlier" measurement. Finally the type and significance of the error distribution function is investigated. These advancements lead to robust uncertainty estimation models, which are tested against both synthetic benchmark data as well as actual experimental measurements. In this work, U68.5 uncertainties are estimated at the 68.5% confidence level while U95 uncertainties are estimated at 95% confidence level. For all cases the resulting calculated coverage factors approximate the expected theoretical confidence intervals thus demonstrating the applicability of these new models for estimation of uncertainty for individual PIV measurements. / Master of Science

We present a scalable information-optimal compressive imager optimized for the target classification task, discriminating between two target classes. Compressive projections are optimized using the Cauchy-Schwarz Mutual Information (CSMI) metric, which provides an upper-bound to the probability of error of target classification. The optimized measurements provide significant performance improvement relative to random and PCA secant projections. We validate the simulation performance of information-optimal compressive measurements with experimental data.

Foi desenvolvido um programa para fusão de imagens médicas para utilização nos sistemas de planejamento de tratamento de radioterapia CAT3D e de radiocirurgia MNPS. Foi utilizada uma metodologia de maximização da informação mútua para fazer a fusão das imagens de modalidades diferentes pela medida da dependência estatística entre os pares de voxels. O alinhamento por pontos referenciais faz uma aproximação inicial para o processo de otimização não linear pelo método de downhill simplex para gerar o histograma conjugado. A função de transformação de coordenadas utiliza uma interpolação trilinear e procura pelo valor de máximo global em um espaço de 6 dimensões, com 3 graus de liberdade para translação e 3 graus de liberdade para rotação, utilizando o modelo de corpo rígido. Este método foi avaliado com imagens de TC, RM e PET do banco de dados da Universidade Vanderbilt, para verificar sua exatidão pela comparação das coordenadas de transformação de cada fusão de imagens com os valores de referência. O valor da mediana dos erros de alinhamento das imagens foi de 1,6 mm para a fusão de TC-RM e de 3,5 mm para PET-RM, com a exatidão dos padrões de referência estimada em 0,4 mm para TC-RM e 1,7 mm para PET-RM. Os valores máximos de erros foram de 5,3 mm para TC-RM e de 7,4 mm para PET-RM e 99,1% dos erros foram menores que o tamanho dos voxels das imagens. O tempo médio de processamento para a fusão de imagens foi de 24 s. O programa foi concluído com sucesso e inserido na rotina de 59 serviços de radioterapia, dos quais 42 estão no Brasil e 17 na América Latina. Este método não apresenta limitações quanto às resoluções diferentes das imagens, tamanhos de pixels e espessuras de corte. Além disso, o alinhamento pode ser realizado com imagens transversais, coronais ou sagitais. / Software for medical images fusion was developed for utilization in CAT3D radiotherapy and MNPS radiosurgery treatment planning systems. A mutual information maximization methodology was used to make the image registration of different modalities by measure of the statistical dependence between the voxels pairs. The alignment by references points makes an initial approximation to the non linear optimization process by downhill simplex method for estimation of the joint histogram. The coordinates transformation function use a trilinear interpolation and search for the global maximum value in a 6 dimensional space, with 3 degree of freedom for translation and 3 degree of freedom for rotation, by making use of the rigid body model. This method was evaluated with CT, MR and PET images from Vanderbilt University database to verify its accuracy by comparison of transformation coordinates of each images fusion with gold-standard values. The median of images alignment error values was 1.6 mm for CT-MR fusion and 3.5 mm for PET-MR fusion, with gold-standard accuracy estimated as 0.4 mm for CT-MR fusion and 1.7 mm for PET-MR fusion. The maximum error values were 5.3 mm for CT-MR fusion and 7.4 mm for PET-MR fusion, and 99.1% of alignment errors were images subvoxels values. The mean computing time was 24 s. The software was successfully finished and implemented in 59 radiotherapy routine services, of which 42 are in Brazil and 17 are in Latin America. This method doesn’t have limitation about different resolutions from images, pixels sizes and slice thickness. Besides, the alignment may be accomplished by axial, coronal or sagital images.

Foi desenvolvido um programa para fusão de imagens médicas para utilização nos sistemas de planejamento de tratamento de radioterapia CAT3D e de radiocirurgia MNPS. Foi utilizada uma metodologia de maximização da informação mútua para fazer a fusão das imagens de modalidades diferentes pela medida da dependência estatística entre os pares de voxels. O alinhamento por pontos referenciais faz uma aproximação inicial para o processo de otimização não linear pelo método de downhill simplex para gerar o histograma conjugado. A função de transformação de coordenadas utiliza uma interpolação trilinear e procura pelo valor de máximo global em um espaço de 6 dimensões, com 3 graus de liberdade para translação e 3 graus de liberdade para rotação, utilizando o modelo de corpo rígido. Este método foi avaliado com imagens de TC, RM e PET do banco de dados da Universidade Vanderbilt, para verificar sua exatidão pela comparação das coordenadas de transformação de cada fusão de imagens com os valores de referência. O valor da mediana dos erros de alinhamento das imagens foi de 1,6 mm para a fusão de TC-RM e de 3,5 mm para PET-RM, com a exatidão dos padrões de referência estimada em 0,4 mm para TC-RM e 1,7 mm para PET-RM. Os valores máximos de erros foram de 5,3 mm para TC-RM e de 7,4 mm para PET-RM e 99,1% dos erros foram menores que o tamanho dos voxels das imagens. O tempo médio de processamento para a fusão de imagens foi de 24 s. O programa foi concluído com sucesso e inserido na rotina de 59 serviços de radioterapia, dos quais 42 estão no Brasil e 17 na América Latina. Este método não apresenta limitações quanto às resoluções diferentes das imagens, tamanhos de pixels e espessuras de corte. Além disso, o alinhamento pode ser realizado com imagens transversais, coronais ou sagitais. / Software for medical images fusion was developed for utilization in CAT3D radiotherapy and MNPS radiosurgery treatment planning systems. A mutual information maximization methodology was used to make the image registration of different modalities by measure of the statistical dependence between the voxels pairs. The alignment by references points makes an initial approximation to the non linear optimization process by downhill simplex method for estimation of the joint histogram. The coordinates transformation function use a trilinear interpolation and search for the global maximum value in a 6 dimensional space, with 3 degree of freedom for translation and 3 degree of freedom for rotation, by making use of the rigid body model. This method was evaluated with CT, MR and PET images from Vanderbilt University database to verify its accuracy by comparison of transformation coordinates of each images fusion with gold-standard values. The median of images alignment error values was 1.6 mm for CT-MR fusion and 3.5 mm for PET-MR fusion, with gold-standard accuracy estimated as 0.4 mm for CT-MR fusion and 1.7 mm for PET-MR fusion. The maximum error values were 5.3 mm for CT-MR fusion and 7.4 mm for PET-MR fusion, and 99.1% of alignment errors were images subvoxels values. The mean computing time was 24 s. The software was successfully finished and implemented in 59 radiotherapy routine services, of which 42 are in Brazil and 17 are in Latin America. This method doesn’t have limitation about different resolutions from images, pixels sizes and slice thickness. Besides, the alignment may be accomplished by axial, coronal or sagital images.

Estudos de correlação entre variações de preços de ações e variação de índices de mercado são importantes na compreensão da relação entre o retorno e o risco envolvido na alocação de recursos (investimentos). De acordo com o risco envolvido, deve haver um adequado retorno. Esta questão é abordada pelo modelo CAPM Capital Asset Pricing Model , que parte da premissa de que o risco sistemático de um ativo pode ser mensurado pela sua sensibilidade aos movimentos do mercado, e para isso se supõe que os retornos dos títulos são linearmente relacionados às flutuações de um índice de mercado amplo com um grau conhecido de sensibilidade. No entanto, pode haver relações não lineares entre os retornos dos títulos e as flutuações do índice de mercado. Sendo assim, o presente trabalho analisa uma medida de correlação global vinda da teoria da informação, que mensura qualquer tipo de relação entre duas variáveis, isto é, lineares e não lineares. O objetivo é mostrar a presença de correlações não lineares no mercado de capitais brasileiro. Demonstra-se que a correlação global é expressiva e maior ou igual à correlação linear em toda a amostra constituída de todas as ações que se mantiveram no Índice da Bolsa de Valores de São Paulo (IBOVESPA) de maio de 2001 a abril de 2008, totalizando 84 meses (7 anos). / Correlations among stock price variations and stock market indices variations are important in understanding the relationship between return and risk involved in the allocation of resources (investments). According to the risk involved there exists an appropriate return. This issue is addressed by the CAPM Capital Asset Pricing Model , based on the premise that the systematic risk of an asset can be measured by its sensitivity to market movements and it is assumed that the returns are linearly related to the fluctuations of a market index with a known degree of sensitivity. However, nonlinear relationships may occur. Thus, the present study analyzes a global measure of correlation of information coming from theory, which measures any type of relationship between two variables, i.e. linear and nonlinear. The goal here is to show the presence of nonlinear correlations in the Brazilian capital market. The overall correlation obtained is expressive and greater than the linear correlation across the sample of 33 stock assets from the theoretical portfolio of São Paulo Exchange Index (IBOVESPA), from May 2001 to April 2008, totaling 84 months (7 years).

<p>The arrival of microarray technology has produced a lot of expression profiles of genes. The amount of data now available is so huge that new alternate and efficient methods are needed to analyse it. One of the approaches that have been taken is the use of reverse engineering to build up a picture of how the genes are interacting, where one of the obstacles is the amount of calculations needed. Liang et al. (1998) introduced an algorithm called REVEAL, where reverse engineering with entropy and mutual information are used in an attempt to generate the rules of regulation in genetic networks.</p><p>In this dissertation it was investigated if it was possible to compliment the REVEAL algorithm with heuristics. The heuristic approach probed consists of setting a threshold on mutual information values, thereby dismissing combinations of input genes producing values below the threshold value as being non-relevant.</p><p>Four experiments were performed, where each consisted of a different combination of rule complexity, size of network and number of inputs per gene tested.</p><p>The findings of this study are that applying a threshold on mutual information is a realistic option that can reduce the number of calculations and also act as a filter that divides the important information from the irrelevant information. However this method has its limitations; since it is not known in advance where to place the threshold it will always be a chance that true connections fall below the threshold and therefore will be disregarded and not further analysed.</p>

Empowered by linear precoding and decoding, a spatially multiplexed multiple-input multiple-output (MIMO) system becomes a convenient framework to offer high data rate, diversity and interference management. While most of the current precoding/decoding designs have assumed perfect channel state information (CSI) at the receiver, and sometimes even at the transmitter, in this thesis we design the precoder and decoder with imperfect CSI at both the transmit and the receive sides, and investigate the joint impact of channel estimation errors and channel correlation on system structure and performance. The mean-square error (MSE) related performance metrics are used as the design criteria. We begin with the minimum total MSE precoding/decoding design for a single-user MIMO system assuming imperfect CSI at both ends. Here the CSI includes the channel estimate and channel correlation information. The structures of the optimum precoder and decoder are determined. Compared to the perfect CSI case, linear filters are added to the transceiver structure to improve system robustness against imperfect CSI. The effects of channel estimation error and channel correlation are quantified by simulations. With imperfect CSI at both ends, the exact capacity expression for a single-user MIMO channel is difficult to obtain. Instead, a tight capacity lower-bound is used for system design. The optimum structure of the transmit covariance matrix for the lower-bound has not been found in the existing literature. By transforming the transmitter design into a joint precoding/decoding design problem, we derive the expression of the optimum transmit covariance matrix. The close relationship between the maximum mutual information design and the minimum total MSE design is also discovered assuming imperfect CSI. For robust multiuser MIMO communications, minimum average sum MSE transceiver (precoder-decoder pairs) design problems are formulated for both the uplink and the downlink, assuming imperfect channel estimation and channel correlation at the base station (BS). We propose improved iterative algorithms based on the associated Karush-Kuhn-Tucker (KKT) conditions. Under the assumption of imperfect CSI, an uplink--downlink duality in average sum MSE is proved. As an alternative for the uplink optimization, a sequential semidefinite programming (SDP) method is proposed. Simulation results are provided to corroborate the analysis. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2008-07-25 10:53:45.175

Estudos de correlação entre variações de preços de ações e variação de índices de mercado são importantes na compreensão da relação entre o retorno e o risco envolvido na alocação de recursos (investimentos). De acordo com o risco envolvido, deve haver um adequado retorno. Esta questão é abordada pelo modelo CAPM Capital Asset Pricing Model , que parte da premissa de que o risco sistemático de um ativo pode ser mensurado pela sua sensibilidade aos movimentos do mercado, e para isso se supõe que os retornos dos títulos são linearmente relacionados às flutuações de um índice de mercado amplo com um grau conhecido de sensibilidade. No entanto, pode haver relações não lineares entre os retornos dos títulos e as flutuações do índice de mercado. Sendo assim, o presente trabalho analisa uma medida de correlação global vinda da teoria da informação, que mensura qualquer tipo de relação entre duas variáveis, isto é, lineares e não lineares. O objetivo é mostrar a presença de correlações não lineares no mercado de capitais brasileiro. Demonstra-se que a correlação global é expressiva e maior ou igual à correlação linear em toda a amostra constituída de todas as ações que se mantiveram no Índice da Bolsa de Valores de São Paulo (IBOVESPA) de maio de 2001 a abril de 2008, totalizando 84 meses (7 anos). / Correlations among stock price variations and stock market indices variations are important in understanding the relationship between return and risk involved in the allocation of resources (investments). According to the risk involved there exists an appropriate return. This issue is addressed by the CAPM Capital Asset Pricing Model , based on the premise that the systematic risk of an asset can be measured by its sensitivity to market movements and it is assumed that the returns are linearly related to the fluctuations of a market index with a known degree of sensitivity. However, nonlinear relationships may occur. Thus, the present study analyzes a global measure of correlation of information coming from theory, which measures any type of relationship between two variables, i.e. linear and nonlinear. The goal here is to show the presence of nonlinear correlations in the Brazilian capital market. The overall correlation obtained is expressive and greater than the linear correlation across the sample of 33 stock assets from the theoretical portfolio of São Paulo Exchange Index (IBOVESPA), from May 2001 to April 2008, totaling 84 months (7 years).

The arrival of microarray technology has produced a lot of expression profiles of genes. The amount of data now available is so huge that new alternate and efficient methods are needed to analyse it. One of the approaches that have been taken is the use of reverse engineering to build up a picture of how the genes are interacting, where one of the obstacles is the amount of calculations needed. Liang et al. (1998) introduced an algorithm called REVEAL, where reverse engineering with entropy and mutual information are used in an attempt to generate the rules of regulation in genetic networks. In this dissertation it was investigated if it was possible to compliment the REVEAL algorithm with heuristics. The heuristic approach probed consists of setting a threshold on mutual information values, thereby dismissing combinations of input genes producing values below the threshold value as being non-relevant. Four experiments were performed, where each consisted of a different combination of rule complexity, size of network and number of inputs per gene tested. The findings of this study are that applying a threshold on mutual information is a realistic option that can reduce the number of calculations and also act as a filter that divides the important information from the irrelevant information. However this method has its limitations; since it is not known in advance where to place the threshold it will always be a chance that true connections fall below the threshold and therefore will be disregarded and not further analysed.

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