1,720,984 research outputs found
Stochastic modeling of pharmaco-kinetic processes, applied to PET space-time reconstruction
No full textL'objectif de ce travail est de développer de nouvelles méthodes statistiques de reconstruction d'image spatiale (3D) et spatio-temporelle (3D+t) en Tomographie par Émission de Positons (TEP). Le but est de proposer des méthodes efficaces, capables de reconstruire des images dans un contexte de faibles doses injectées tout en préservant la qualité de l'interprétation. Ainsi, nous avons abordé la reconstruction sous la forme d'un problème inverse spatial et spatio-temporel (à observations ponctuelles) dans un cadre bayésien non paramétrique. La modélisation bayésienne fournit un cadre pour la régularisation du problème inverse mal posé au travers de l'introduction d'une information dite a priori. De plus, elle caractérise les grandeurs à estimer par leur distribution a posteriori, ce qui rend accessible la distribution de l'incertitude associée à la reconstruction. L'approche non paramétrique quant à elle pourvoit la modélisation d'une grande robustesse et d'une grande flexibilité. Notre méthodologie consiste à considérer l'image comme une densité de probabilité dans (pour une reconstruction en k dimensions) et à chercher la solution parmi l'ensemble des densités de probabilité de . La grande dimensionalité des données à manipuler conduit à des estimateurs n'ayant pas de forme explicite. Cela implique l'utilisation de techniques d'approximation pour l'inférence. La plupart de ces techniques sont basées sur les méthodes de Monte-Carlo par chaînes de Markov (MCMC). Dans l'approche bayésienne non paramétrique, nous sommes confrontés à la difficulté majeure de générer aléatoirement des objets de dimension infinie sur un calculateur. Nous avons donc développé une nouvelle méthode d'échantillonnage qui allie à la fois bonnes capacités de mélange et possibilité d'être parallélisé afin de traiter de gros volumes de données. L'approche adoptée nous a permis d'obtenir des reconstructions spatiales 3D sans nécessiter de voxellisation de l'espace, et des reconstructions spatio-temporelles 4D sans discrétisation en amont ni dans l'espace ni dans le temps. De plus, on peut quantifier l'erreur associée à l'estimation statistique au travers des intervalles de crédibilité.The aim of this work is to develop new statistical methods for spatial (3D) and space-time (3D+t) Positron Emission Tomography (PET) reconstruction. The objective is to propose efficient reconstruction methods in a context of low injected doses while maintaining the quality of the interpretation. We tackle the reconstruction problem as a spatial or a space-time inverse problem for point observations in a \Bayesian nonparametric framework. The Bayesian modeling allows to regularize the ill-posed inverse problem via the introduction of a prior information. Furthermore, by characterizing the unknowns with their posterior distributions, the Bayesian context allows to handle the uncertainty associated to the reconstruction process. Being nonparametric offers a framework for robustness and flexibility to perform the modeling. In the proposed methodology, we view the image to reconstruct as a probability density in(for reconstruction in k dimensions) and seek the solution in the space of whole probability densities in . However, due to the size of the data, posterior estimators are intractable and approximation techniques are needed for posterior inference. Most of these techniques are based on Markov Chain Monte-Carlo methods (MCMC). In the Bayesian nonparametric approach, a major difficulty raises in randomly sampling infinite dimensional objects in a computer. We have developed a new sampling method which combines both good mixing properties and the possibility to be implemented on a parallel computer in order to deal with large data sets. Thanks to the taken approach, we obtain 3D spatial reconstructions without any ad hoc space voxellization and 4D space-time reconstructions without any discretization, neither in space nor in time. Furthermore, one can quantify the error associated to the statistical estimation using the credibility intervals
Modélisation stochastique de processus pharmaco-cinétiques, application à la reconstruction tomographique par émission de positrons (TEP) spatio-temporelle
Get PDFThe aim of this work is to develop new statistical methods for spatial (3D) and space-time (3D+t) Positron Emission Tomography (PET) reconstruction. The objective is to propose efficient reconstruction methods in a context of low injected doses while maintaining the quality of the interpretation. We tackle the reconstruction problem as a spatial or a space-time inverse problem for point observations in a \Bayesian nonparametric framework. The Bayesian modeling allows to regularize the ill-posed inverse problem via the introduction of a prior information. Furthermore, by characterizing the unknowns with their posterior distributions, the Bayesian context allows to handle the uncertainty associated to the reconstruction process. Being nonparametric offers a framework for robustness and flexibility to perform the modeling. In the proposed methodology, we view the image to reconstruct as a probability density in(for reconstruction in k dimensions) and seek the solution in the space of whole probability densities in . However, due to the size of the data, posterior estimators are intractable and approximation techniques are needed for posterior inference. Most of these techniques are based on Markov Chain Monte-Carlo methods (MCMC). In the Bayesian nonparametric approach, a major difficulty raises in randomly sampling infinite dimensional objects in a computer. We have developed a new sampling method which combines both good mixing properties and the possibility to be implemented on a parallel computer in order to deal with large data sets. Thanks to the taken approach, we obtain 3D spatial reconstructions without any ad hoc space voxellization and 4D space-time reconstructions without any discretization, neither in space nor in time. Furthermore, one can quantify the error associated to the statistical estimation using the credibility intervals.L'objectif de ce travail est de développer de nouvelles méthodes statistiques de reconstruction d'image spatiale (3D) et spatio-temporelle (3D+t) en Tomographie par Émission de Positons (TEP). Le but est de proposer des méthodes efficaces, capables de reconstruire des images dans un contexte de faibles doses injectées tout en préservant la qualité de l'interprétation. Ainsi, nous avons abordé la reconstruction sous la forme d'un problème inverse spatial et spatio-temporel (à observations ponctuelles) dans un cadre bayésien non paramétrique. La modélisation bayésienne fournit un cadre pour la régularisation du problème inverse mal posé au travers de l'introduction d'une information dite a priori. De plus, elle caractérise les grandeurs à estimer par leur distribution a posteriori, ce qui rend accessible la distribution de l'incertitude associée à la reconstruction. L'approche non paramétrique quant à elle pourvoit la modélisation d'une grande robustesse et d'une grande flexibilité. Notre méthodologie consiste à considérer l'image comme une densité de probabilité dans (pour une reconstruction en k dimensions) et à chercher la solution parmi l'ensemble des densités de probabilité de . La grande dimensionalité des données à manipuler conduit à des estimateurs n'ayant pas de forme explicite. Cela implique l'utilisation de techniques d'approximation pour l'inférence. La plupart de ces techniques sont basées sur les méthodes de Monte-Carlo par chaînes de Markov (MCMC). Dans l'approche bayésienne non paramétrique, nous sommes confrontés à la difficulté majeure de générer aléatoirement des objets de dimension infinie sur un calculateur. Nous avons donc développé une nouvelle méthode d'échantillonnage qui allie à la fois bonnes capacités de mélange et possibilité d'être parallélisé afin de traiter de gros volumes de données. L'approche adoptée nous a permis d'obtenir des reconstructions spatiales 3D sans nécessiter de voxellisation de l'espace, et des reconstructions spatio-temporelles 4D sans discrétisation en amont ni dans l'espace ni dans le temps. De plus, on peut quantifier l'erreur associée à l'estimation statistique au travers des intervalles de crédibilité
QUANTIFYING UNCERTAINTY IN KNEE OSTEOARTHRITIS DIAGNOSIS
No full textInternational audienceKnee OsteoArthritis (OA) is one of the most common causes of physical disability in the world, causing a large personal and socioeconomic burden. Visual assessment of OA still suffers from subjectivity. Deep learning (DL), and in particular convolutional neural networks (CNN), has recently led to remarkable improvements in knee OA detection. However, traditional deep learning-based knee OA classification algorithms lack the ability to quantify decision uncertainty. This is a key point in the medical field where, due to the high cost of labelling, we are faced with a lack of sufficient data to train a learning model. We propose here an alternative approach based on the the concept of Evidential Deep Learning (EDL). Unlike Bayesian neural networks which indirectly infer prediction uncertainty through uncertainties in the network weights, EDL approaches explicitly model this uncertainty using the theory of subjective logic. Experimental results on the Osteoarthritis (OAI) database demonstrate the potential of the proposed approach
QUANTIFYING UNCERTAINTY IN KNEE OSTEOARTHRITIS DIAGNOSIS
No full textInternational audienceKnee OsteoArthritis (OA) is one of the most common causes of physical disability in the world, causing a large personal and socioeconomic burden. Visual assessment of OA still suffers from subjectivity. Deep learning (DL), and in particular convolutional neural networks (CNN), has recently led to remarkable improvements in knee OA detection. However, traditional deep learning-based knee OA classification algorithms lack the ability to quantify decision uncertainty. This is a key point in the medical field where, due to the high cost of labelling, we are faced with a lack of sufficient data to train a learning model. We propose here an alternative approach based on the the concept of Evidential Deep Learning (EDL). Unlike Bayesian neural networks which indirectly infer prediction uncertainty through uncertainties in the network weights, EDL approaches explicitly model this uncertainty using the theory of subjective logic. Experimental results on the Osteoarthritis (OAI) database demonstrate the potential of the proposed approach
Gibbs sampling methods for Pitman-Yor mixture models
No full textWe introduce a new sampling strategy for the two-parameter Poisson-Dirichlet process mixture model, also known as Pitman-Yor process mixture model (PYM). Our sampler is therefore applicable to the well-known Dirichlet process mixture model (DPM). Inference in DPM and PYM is usually performed via Markov Chain Monte Carlo (MCMC) methods, specifi cally the Gibbs sampler. These sampling methods are usually divided in two classes: marginal and conditional algorithms. Each method has its merits and limitations. The aim of this paper is to propose a new sampler that combines the main advantages of each class. The key idea of the proposed sampler consists in replacing the standard posterior updating of the mixing measure based on the stick-breaking representation, with a posterior updating of Pitman(1996) which represents the posterior law under a Pitman-Yor process as the sum of a jump part and a continuous one. We sample the continuous part in two ways, leading to two variants of the proposed sampler. We also propose a threshold to improve mixing in the first variant of our algorithm. The two variants of our sampler are compared with a marginal method, that is the celebrated Algorithm 8 of Neal(2000), and two conditional algorithms based on the stick-breaking representation, namely the efficient slice sampler of Kalli et al. (2011) and the truncated blocked Gibbs sampler of Ishwaran and James (2001). We also investigate e ffects of removing the proposed threshold in the first variant of our algorithm and introducing the threshold in the efficient slice sampler of Kalli et al. (2011). Results on real and simulated data sets illustrate that our algorithms outperform the other conditionals in terms of mixing properties
A Simple and Efficient Method for Sampling Mixture Models based on Dirichlet and Pitman-Yor processes
No full textWe introduce a simple and efficient sampling strategy for the Dirichlet Process Mixture model (DPM) and its two-parameter extension, the Poisson-Dirichlet process mixture model, also known as the Pitman-Yor process Mixture model (PYM). Inference in DPM and PYM is usually performed using Markov Chain Monte Carlo (MCMC) methods, specifically the Gibbs sampler. These sampling methods are usually divided into two classes: marginal and conditional algorithms. Each method has its own merits and limitations. The aim of this paper is to propose a simple and effective strategy that combines the main advantages of each class. Extensive experiments on simulated and real data highlight that the proposed sampler is relevant and performs much better than its competitors
Gibbs sampling methods for Pitman-Yor mixture models
No full textWe introduce a new sampling strategy for the two-parameter Poisson-Dirichlet process mixture model, also known as Pitman-Yor process mixture model (PYM). Our sampler is therefore applicable to the well-known Dirichlet process mixture model (DPM). Inference in DPM and PYM is usually performed via Markov Chain Monte Carlo (MCMC) methods, specifi cally the Gibbs sampler. These sampling methods are usually divided in two classes: marginal and conditional algorithms. Each method has its merits and limitations. The aim of this paper is to propose a new sampler that combines the main advantages of each class. The key idea of the proposed sampler consists in replacing the standard posterior updating of the mixing measure based on the stick-breaking representation, with a posterior updating of Pitman(1996) which represents the posterior law under a Pitman-Yor process as the sum of a jump part and a continuous one. We sample the continuous part in two ways, leading to two variants of the proposed sampler. We also propose a threshold to improve mixing in the first variant of our algorithm. The two variants of our sampler are compared with a marginal method, that is the celebrated Algorithm 8 of Neal(2000), and two conditional algorithms based on the stick-breaking representation, namely the efficient slice sampler of Kalli et al. (2011) and the truncated blocked Gibbs sampler of Ishwaran and James (2001). We also investigate e ffects of removing the proposed threshold in the first variant of our algorithm and introducing the threshold in the efficient slice sampler of Kalli et al. (2011). Results on real and simulated data sets illustrate that our algorithms outperform the other conditionals in terms of mixing properties
A Simple and Efficient Method for Sampling Mixture Models based on Dirichlet and Pitman-Yor processes
No full textWe introduce a simple and efficient sampling strategy for the Dirichlet Process Mixture model (DPM) and its two-parameter extension, the Poisson-Dirichlet process mixture model, also known as the Pitman-Yor process Mixture model (PYM). Inference in DPM and PYM is usually performed using Markov Chain Monte Carlo (MCMC) methods, specifically the Gibbs sampler. These sampling methods are usually divided into two classes: marginal and conditional algorithms. Each method has its own merits and limitations. The aim of this paper is to propose a simple and effective strategy that combines the main advantages of each class. Extensive experiments on simulated and real data highlight that the proposed sampler is relevant and performs much better than its competitors
A Simple and Efficient Method for Sampling Mixture Models based on Dirichlet and Pitman-Yor processes
No full textWe introduce a simple and efficient sampling strategy for the Dirichlet Process Mixture model (DPM) and its two-parameter extension, the Poisson-Dirichlet process mixture model, also known as the Pitman-Yor process Mixture model (PYM). Inference in DPM and PYM is usually performed using Markov Chain Monte Carlo (MCMC) methods, specifically the Gibbs sampler. These sampling methods are usually divided into two classes: marginal and conditional algorithms. Each method has its own merits and limitations. The aim of this paper is to propose a simple and effective strategy that combines the main advantages of each class. Extensive experiments on simulated and real data highlight that the proposed sampler is relevant and performs much better than its competitors
A Bayesian estimation formulation to voxel-based lesion-symptom mapping
No full textInternational audienceStudying brain-injured patients is important for investigating structure-function relationships using neuroimaging techniques. Voxel-based lesion-symptom mapping (VLSM) has increasingly been advocated as a relevant approach to detect structure-function associations in neuroimaging studies. The VLSM method involves mapping the relationship between brain injuries and behavioral performance on a voxel-byvoxel basis. This means that the statistical relationship between damage and behavior (across patients) is computed separately for each voxel. However, one could expect voxels characterizing group differences to be localized into spatially consistent regions rather than randomly distributed over the brain. Thus, in this paper, we propose to depart from conventional models to characterize and exploit this spatial consistency. More precisely, we derive a Bayesian model that explicitly accounts for spatial correlations between neighboring voxels using a Markov random field. Our results highlight that the proposed approach outperforms the conventional ones. Besides, it has the great advantage of possibly reducing the number of patients and identifying new language areas, which are two crucial insights in the targeted medical context
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