Inside standard and hyperspectral low-dose CT variational imaging: parameter identification and material decomposition

The main contribution of this thesis is the proposal of novel strategies for the selection of parameters arising in variational models employed for the solution of inverse problems with data corrupted by Poisson noise. In light of the importance of using a significantly small dose of X-rays in Computed Tomography (CT), and its need of using advanced techniques to reconstruct the objects due to the high level of noise in the data, we will focus on parameter selection principles especially for low photon-counts, i.e. low dose Computed Tomography. For completeness, since such strategies can be adopted for various scenarios where the noise in the data typically follows a Poisson distribution, we will show their performance for other applications such as photography, astronomical and microscopy imaging. More specifically, in the first part of the thesis we will focus on low dose CT data corrupted only by Poisson noise by extending automatic selection strategies designed for Gaussian noise and improving the few existing ones for Poisson. The new approaches will show to outperform the state-of-the-art competitors especially in the low-counting regime. Moreover, we will propose to extend the best performing strategy to the hard task of multi-parameter selection showing promising results. Finally, in the last part of the thesis, we will introduce the problem of material decomposition for hyperspectral CT, which data encodes information of how different materials in the target attenuate X-rays in different ways according to the specific energy. We will conduct a preliminary comparative study to obtain accurate material decomposition starting from few noisy projection data.

Approximation de la distribution a posteriori d'un modèle Gamma-Poisson hiérarchique à effets mixtes

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés.

A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.

Inequalities in the distribution of dental caries among 12-year-old Brazilian schoolchildren

We assessed the inequality in the distribution of dental caries and the association between indicators of socioeconomic status and caries experience in a representative sample of schoolchildren. This study followed a cross-sectional design, with a sample of 792 schoolchildren aged 12 years, representative of this age group in Santa Maria, RS, Brazil. Guardians answered questions on socioeconomic status and a dental examination provided information on the dental caries experience (DMF-T). Inequality in dental caries distribution was measured by the Gini coefficient and the Significant Caries Index (SiC). The assessment of association used Poisson regression models. Socioeconomic factors were associated with prevalence of dental caries for the whole sample and also for individuals with a high-caries level. Children from low-income households had the highest prevalence of dental caries. The Gini coefficient was 0.7 and the SiC Index 2.5. The percentage of caries prevalence was 39.3% (95% CI: 35.8%-42.8%) and the mean for DMF-T was 0.9 (± SD 1.5). Inequalities in the distribution of dental caries were observed and socioeconomic factors were found to be strong predictors of the prevalence of oral disease in children of this age group.

Prevalence and social distribution of risk factors for chronic noncommunicable diseases in Brazil

OBJETIVOS: Evaluar los factores de riesgo de enfermedades crónicas no transmisibles (ECNT) e identificar las desigualdades sociales relacionadas con su distribución en la población adulta brasileña.MÉTODOS: Se estudiaron los factores de riesgo de ECNT (entre ellos el consumo de tabaco, el sobrepeso y la obesidad, el bajo consumo de frutas y vegetales [BCFV], la insuficiente actividad física en el tiempo de ocio [IAFTO], el estilo de vida sedentario y el consumo excesivo de alcohol) en una muestra probabilística de 54369 adultos de 26 capitales estatales de Brasil y el Distrito Federal en 2006. Se utilizó el Sistema de Vigilancia de los Factores Protectores y de Riesgo para Enfermedades Crónicas No Transmisibles por Entrevistas Telefónicas (VIGITEL), un sistema de encuestas telefónicas asistido por computadora, y se calcularon las prevalencias ajustadas por la edad para las tendencias en cuanto al nivel educacional mediante la regresión de Poisson con modelos lineales. RESULTADOS: Los hombres informaron mayor consumo de tabaco, sobrepeso, BCFV, estilo de vida sedentario y consumo excesivo de alcohol que las mujeres, pero menos IAFTO. En los hombres, la educación se asoció con un mayor sobrepeso y un estilo de vida sedentario, pero con un menor consumo de tabaco, BCFV e IAFTO. En las mujeres, la educación se asoció con un menor consumo de tabaco, sobrepeso, obesidad, BCFV e IAFTO, pero aumentó el estilo de vida sedentario CONCLUSIONES: En Brasil, la prevalencia de factores de riesgo para ECNT (excepto IAFTO) es mayor en los hombres que en las mujeres. En ambos sexos, el nivel de educación influye en la prevalencia de los factores de riesgo para ECNT

Temporal evolution and spatial distribution of maternal death

OBJECTIVE To analyze the temporal evolution of maternal mortality and its spatial distribution.METHODS Ecological study with a sample made up of 845 maternal deaths in women between 10 and 49 years, registered from 1999 to 2008 in the state of Rio Grande do Sul, Southern Brazil. Data were obtained from Information System on Mortality of Ministry of Health. The maternal mortality ratio and the specific maternal mortality ratio were calculated from records, and analyzed by the Poisson regression model. In the spatial distribution, three maps of the state were built with the rates in the geographical macro-regions, in 1999, 2003, and 2008.RESULTS There was an increase of 2.0% in the period of ten years (95%CI 1.00;1.04; p = 0.01), with no significant change in the magnitude of the maternal mortality ratio. The Serra macro-region presented the highest maternal mortality ratio (1.15, 95%CI 1.08;1.21; p < 0.001). Most deaths in Rio Grande do Sul were of white women over 40 years, with a lower level of education. The time of delivery/abortion and postpartum are times of increased maternal risk, with a greater negative impact of direct causes such as hypertension and bleeding.CONCLUSIONS The lack of improvement in maternal mortality ratio indicates that public policies had no impact on women’s reproductive and maternal health. It is needed to qualify the attention to women’s health, especially in the prenatal period, seeking to identify and prevent risk factors, as a strategy of reducing maternal death.

Use of Poisson spatiotemporal regression models for the Brazilian Amazon Forest: malaria count data

INTRODUCTION: Malaria is a serious problem in the Brazilian Amazon region, and the detection of possible risk factors could be of great interest for public health authorities. The objective of this article was to investigate the association between environmental variables and the yearly registers of malaria in the Amazon region using Bayesian spatiotemporal methods. METHODS: We used Poisson spatiotemporal regression models to analyze the Brazilian Amazon forest malaria count for the period from 1999 to 2008. In this study, we included some covariates that could be important in the yearly prediction of malaria, such as deforestation rate. We obtained the inferences using a Bayesian approach and Markov Chain Monte Carlo (MCMC) methods to simulate samples for the joint posterior distribution of interest. The discrimination of different models was also discussed. RESULTS: The model proposed here suggests that deforestation rate, the number of inhabitants per km², and the human development index (HDI) are important in the prediction of malaria cases. CONCLUSIONS: It is possible to conclude that human development, population growth, deforestation, and their associated ecological alterations are conducive to increasing malaria risk. We conclude that the use of Poisson regression models that capture the spatial and temporal effects under the Bayesian paradigm is a good strategy for modeling malaria counts.

An extension of the Marsden-Ratiu reduction for Poisson manifolds

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Aplicación de colas de Poisson en procesos de ‘toma de decisiones’ en la gestión de servicios médicos

En este documento se revisa teóricamente la distribución de probabilidad de Poisson como función que asigna a cada suceso definido, sobre una variable aleatoria discreta, la probabilidad de ocurrencia en un intervalo de tiempo o región del espacio disjunto. Adicionalmente se revisa la distribución exponencial negativa empleada para modelar el intervalo de tiempo entre eventos consecutivos de Poisson que ocurren de manera independiente; es decir, en los cuales la probabilidad de ocurrencia de los eventos sucedidos en un intervalo de tiempo no depende de los ocurridos en otros intervalos de tiempo, por esta razón se afirma que es una distribución que no tiene memoria. El proceso de Poisson relaciona la función de Poisson, que representa un conjunto de eventos independientes sucedidos en un intervalo de tiempo o región del espacio con los tiempos dados entre la ocurrencia de los eventos según la distribución exponencial negativa. Los anteriores conceptos se usan en la teoría de colas, rama de la investigación de operaciones que describe y brinda soluciones a situaciones en las que un conjunto de individuos o elementos forman colas en espera de que se les preste un servicio, por lo cual se presentan ejemplos de aplicación en el ámbito médico.

On exact time averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterized by a rate of events, lambda(t), and a magnitude, Phi, following an exponential distribution. We tackle the problem by performing exact time averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.

Use of Poisson spatiotemporal regression models for the Brazilian Amazon Forest: malaria count data

INTRODUÇÃO: A malaria é uma doença endêmica na região da Amazônia Brasileira, e a detecção de possíveis fatores de risco pode ser de grande interesse às autoridades em saúde pública. O objetivo deste artigo é investigar a associação entre variáveis ambientais e os registros anuais de malária na região amazônica usando métodos bayesianos espaço-temporais. MÉTODOS: Utilizaram-se modelos de regressão espaço-temporais de Poisson para analisar os dados anuais de contagem de casos de malária entre os anos de 1999 a 2008, considerando a presença de alguns fatores como a taxa de desflorestamento. em uma abordagem bayesiana, as inferências foram obtidas por métodos Monte Carlo em cadeias de Markov (MCMC) que simularam amostras para a distribuição conjunta a posteriori de interesse. A discriminação de diferentes modelos também foi discutida. RESULTADOS: O modelo aqui proposto sugeriu que a taxa de desflorestamento, o número de habitants por km² e o índice de desenvolvimento humano (IDH) são importantes para a predição de casos de malária. CONCLUSÕES: É possível concluir que o desenvolvimento humano, o crescimento populacional, o desflorestamento e as alterações ecológicas associadas a estes fatores estão associados ao aumento do risco de malária. Pode-se ainda concluir que o uso de modelos de regressão de Poisson que capturam o efeito temporal e espacial em um enfoque bayesiano é uma boa estratégia para modelar dados de contagem de malária.

The Conway-Maxwell-Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

pH at the micellar interface: Synthesis of pH probes derived from salicylic acid, acid-base dissociation in sodium dodecyl sulfate micelles, and Poisson-Boltzmann simulation

The study of the H+ concentration at the micellar interface is a convenient system for modeling the distribution of H+ at interfaces. We have synthesized salicylic acid derivatives to analyze the proton dissociation of both the carboxylic and phenol groups of' the probes, determining spectrophotometrically the apparent pK(a)'s (pK(ap)) in sodium dodecyl Sulfate, SDS, micelles with and without added salt. The synthesized probes were 2-hydroxy-5-(2-trimethylammoniumacetyl)benzoate; 2-hydroxy-5-(2-dimethylhexadecylammoniumacetyl)benzoate- 2-hydroxy-5-(2-dimethylhexadecylammoniumhexanoyl)benzoate-, 2-hydroxy-5-(2-diniethylhexadecylammoniumundecanoyl)betizoate; 2-hydroxy-5-acetylbenzoic acids and 2-hydroxy-5-dodecanoylbenzoic acid. Upon incorporation into SDS micelles the pK(ap)'s of both carboxylic and phenol groups increased by ca. 3 pH units and NaCl addition caused a decrease in the probe-incorporated pKap. The experimental results were fitted with a cell model Poisson-Boltzmann (P-B) equation taking in consideration the effect of salt on the aggregation number of SDS and using the distance of' the dissociating group as a parameter. The conformations of the probes were analyzed theoretically using two dielectric constants, e.g., 2 and 78. Both the P-B analysis and conformation calculations can be interpreted by assuming that the acid groups dissociate very close to, or at, the interface. Our results are consistent with the assumption that the intrinsic pK(a)'s of both carboxylic and phenol groups of the salicylic acid probes used here can be taken as those in water. Using this assumption the micellar and salt effects on the pKap's of the (trialkylammonium)benzoate probes were described accurately using a cell model P-B analysis. (c) 2005 Elsevier B.V. All rights reserved.