Monitoring the functional connectivity between brain networks is becoming increasingly important in elucidating brain functionality in normal and disease states. Current methods of detecting networks in the recorded EEG such as correlation and coherence are limited by the fact that they assume stationarity of the relationship between channels, and rely on linear dependencies. Here we utilize mutual information (MI) as the metric for determining nonlinear statistical dependencies between electroencephalographic (EEG) channels. Previous work investigating MI between EEG channels in subjects with widespread diseases of the cerebral cortex had subjects simply rest quietly with their eyes closed. In motor disorders such as Parkinson’s disease (PD), abnormalities are only expected during performance of motor tasks, but this makes the assumption of stationarity of relationships between EEG channels untenable. We therefore propose a novel EEG segmentation method based on the temporal dynamics of the cross-spectrogram of the computed Independent Components (ICs). After suitable thresholding of the MI values between channels in the temporally segmented EEG, graphical theoretical analysis approaches are applied to the derived networks. The method was applied to EEG data recorded from six normal subjects and seven PD subjects on and off medication performing a motor task involving either their right hand only or both hands simultaneously. One-way analysis of variance (ANOVA) tests demonstrated statistically significant difference between subject groups. This proposed segmentation/MI network method appears to be a promising approach for EEG analysis.

Monitoring the functional connectivity between brain networks is becoming increasingly important in elucidating brain functionality in normal and disease states. Current methods of detecting networks in the recorded EEG such as correlation and coherence are limited by the fact that they assume stationarity of the relationship between channels, and rely on linear dependencies. Here we utilize mutual information (MI) as the metric for determining nonlinear statistical dependencies between electroencephalographic (EEG) channels. Previous work investigating MI between EEG channels in subjects with widespread diseases of the cerebral cortex had subjects simply rest quietly with their eyes closed. In motor disorders such as Parkinson’s disease (PD), abnormalities are only expected during performance of motor tasks, but this makes the assumption of stationarity of relationships between EEG channels untenable. We therefore propose a novel EEG segmentation method based on the temporal dynamics of the cross-spectrogram of the computed Independent Components (ICs). After suitable thresholding of the MI values between channels in the temporally segmented EEG, graphical theoretical analysis approaches are applied to the derived networks. The method was applied to EEG data recorded from six normal subjects and seven PD subjects on and off medication performing a motor task involving either their right hand only or both hands simultaneously. One-way analysis of variance (ANOVA) tests demonstrated statistically significant difference between subject groups. This proposed segmentation/MI network method appears to be a promising approach for EEG analysis.

Considerable research has been done on measuring dependence between random variables. The correlation coefficient is the most widely studied linear measure of dependence. However, the limitation of linearity limits its application. The informational coefficient of correlation is defined in terms of mutual information. It also has some deficiencies, such as it is only normalized to continuous random variables. Based on the concept of the informational coefficient of correlation, a new dependence measure, which we call the L-measure, is proposed in this work which generalizes Linfoot's measure for both continuous and discrete random variables. To further elucidate its properties, simulated models are used, and estimation algorithms are also discussed. Furthermore, another measure based on the L-measure, which we call the intrinsic L-measure, is studied for the purpose of studying nonlinear dependence. Based on criteria for a dependence measure presented by Renyi and simulation results in this thesis, we believe that the L-measure is satisfactory as a dependence measure. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2011-09-30 14:29:35.153

Monitoring the functional connectivity between brain networks is becoming increasingly important in elucidating brain functionality in normal and disease states. Current methods of detecting networks in the recorded EEG such as correlation and coherence are limited by the fact that they assume stationarity of the relationship between channels, and rely on linear dependencies. Here we utilize mutual information (MI) as the metric for determining nonlinear statistical dependencies between electroencephalographic (EEG) channels. Previous work investigating MI between EEG channels in subjects with widespread diseases of the cerebral cortex had subjects simply rest quietly with their eyes closed. In motor disorders such as Parkinson’s disease (PD), abnormalities are only expected during performance of motor tasks, but this makes the assumption of stationarity of relationships between EEG channels untenable. We therefore propose a novel EEG segmentation method based on the temporal dynamics of the cross-spectrogram of the computed Independent Components (ICs). After suitable thresholding of the MI values between channels in the temporally segmented EEG, graphical theoretical analysis approaches are applied to the derived networks. The method was applied to EEG data recorded from six normal subjects and seven PD subjects on and off medication performing a motor task involving either their right hand only or both hands simultaneously. One-way analysis of variance (ANOVA) tests demonstrated statistically significant difference between subject groups. This proposed segmentation/MI network method appears to be a promising approach for EEG analysis. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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).

Iterative processing has been shown to be very effective in multiuser space-time block coding (STBC) systems. The complexity and efficiency of an iterative receiver depend heavily on how the log-likelihood ratios (LLRs) of the coded bits are computed and exchanged at the receiver among its three major components, namely the multiuser detector, the maximum a posterior probability (MAP) demodulators and the MAP channel decoders. This thesis first presents a method to quantitatively measure the system complexities with floating-point operations (FLOPS) and a technique to evaluate the iterative receiver's convergence property based on mutual information and extrinsic information transfer (EXIT) charts.<p>Then, an integrated iterative receiver is developed by applying the sigma mappings for M-ary quadrature amplitude modulation (M-QAM) constellations. Due to the linear relationship between the coded bits and the transmitted channel symbol, the multiuser detector can work on the bit-level and hence improves the convergence property of the iterative receiver. It is shown that the integrated iterative receiver is an attractive candidate to replace the conventional receiver when a few receive antennas and a high-order M-QAM constellation are employed.<p> Finally, a more general two-loop iterative receiver is proposed by introducing an inner iteration loop between the MAP demodulators and the MAP convolutional decoders besides the outer iteration loop that involves the multiuser detection (MUD) as in the conventional iterative receiver. The proposed two-loop iterative receiver greatly improves the iteration efficiency. It is demonstrated that the proposed two-loop iterative receiver can achieve the same asymptotic performance as that of the conventional iterative receiver, but with much less outer-loop iterations.