Spatially Adaptive Mixture Modeling for Analysis of fMRI Time Series.

International audienceWithin-subject analysis in fMRI essentially addresses two problems, the detection of brain regions eliciting evoked activity and the estimation of the underlying dynamics. In [1, 2], a detection-estimation framework has been proposed to tackle these problems jointly, since they are connected to one another. In the Bayesian formalism, detection is achieved by modeling activating and non-activating voxels through independent mixture models (IMM) within each region while hemodynamic response estimation is performed at a regional scale in a nonparametric way. Instead of IMMs, in this paper we take advantage of spatial mixture models (SMM) for their non-linear spatial regularizing properties. The proposed method is unsupervised and spatially adaptive in the sense that the amount of spatial correlation is automatically tuned from the data and this setting automatically varies across brain regions. In addition, the level of regularization is specific to each experimental condition since both the signal-to-noise ratio and the activation pattern may vary across stimulus types in a given brain region. These aspects require the precise estimation of multiple partition functions of underlying Ising fields. This is addressed efficiently using first path sampling for a small subset of fields and then using a recently developed fast extrapolation technique for the large remaining set. Simulation results emphasize that detection relying on supervised SMM outperforms its IMM counterpart and that unsupervised spatial mixture models achieve similar results without any hand-tuning of the correlation parameter. On real datasets, the gain is illustrated in a localizer fMRI experiment: brain activations appear more spatially resolved using SMM in comparison with classical General Linear Model (GLM)-based approaches, while estimating a specific parcel-based HRF shape. Our approach therefore validates the treatment of unsmoothed fMRI data without fixed GLM definition at the subject level and makes also the classical strategy of spatial Gaussian filtering deprecated

Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm

This paper addresses the problem of estimating the Potts parameter B jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on B requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method the estimation of B is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating B jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of B. On the other hand, assuming that the value of B is known can degrade estimation performance significantly if this value is incorrect. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images

Statistical modeling and processing of high frequency ultrasound images: application to dermatologic oncology

Cette thèse étudie le traitement statistique des images d’ultrasons de haute fréquence, avec application à l’exploration in-vivo de la peau humaine et l’évaluation non invasive de lésions. Des méthodes Bayésiennes sont considérées pour la segmentation d’images échographiques de la peau. On y établit que les ultrasons rétrodiffusés par la peau convergent vers un processus aléatoire complexe de type Levy-Flight, avec des statistiques non Gaussiennes alpha-stables. L’enveloppe du signal suit une distribution Rayleigh généralisée à queue lourde. A partir de ces résultats, il est proposé de modéliser l’image ultrason de multiples tissus comme un mélange spatialement cohérent de lois Rayleigh à queues lourdes. La cohérence spatiale inhérente aux tissus biologiques est modélisée par un champ aléatoire de Potts-Markov pour représenter la dépendance locale entre les composantes du mélange. Un algorithme Bayésien original combiné à une méthode Monte Carlo par chaine de Markov (MCMC) est proposé pour conjointement estimer les paramètres du modèle et classifier chaque voxel dans un tissu. L’approche proposée est appliquée avec succès à la segmentation de tumeurs de la peau in-vivo dans des images d’ultrasons de haute fréquence en 2D et 3D. Cette méthode est ensuite étendue en incluant l’estimation du paramètre B de régularisation du champ de Potts dans la chaine MCMC. Les méthodes MCMC classiques ne sont pas directement applicables à ce problème car la vraisemblance du champ de Potts ne peut pas être évaluée. Ce problème difficile est traité en adoptant un algorithme Metropolis-Hastings “sans vraisemblance” fondé sur la statistique suffisante du Potts. La méthode de segmentation non supervisée, ainsi développée, est appliquée avec succès à des images échographiques 3D. Finalement, le problème du calcul de la borne de Cramer-Rao (CRB) du paramètre B est étudié. Cette borne dépend des dérivées de la constante de normalisation du modèle de Potts, dont le calcul est infaisable. Ce problème est résolu en proposant un algorithme Monte Carlo original, qui est appliqué avec succès au calcul de la borne CRB des modèles d’Ising et de Potts. ABSTRACT : This thesis studies statistical image processing of high frequency ultrasound imaging, with application to in-vivo exploration of human skin and noninvasive lesion assessment. More precisely, Bayesian methods are considered in order to perform tissue segmentation in ultrasound images of skin. It is established that ultrasound signals backscattered from skin tissues converge to a complex Levy Flight random process with non-Gaussian _-stable statistics. The envelope signal follows a generalized (heavy-tailed) Rayleigh distribution. Based on these results, it is proposed to model the distribution of multiple-tissue ultrasound images as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by a Potts Markov random field. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. The proposed method is successfully applied to the segmentation of in-vivo skin tumors in high frequency 2D and 3D ultrasound images. This method is subsequently extended by including the estimation of the Potts regularization parameter B within the Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because the likelihood of B is intractable. This difficulty is addressed by using a likelihood-free Metropolis-Hastings algorithm based on the sufficient statistic of the Potts model. The resulting unsupervised segmentation method is successfully applied to tridimensional ultrasound images. Finally, the problem of computing the Cramer-Rao bound (CRB) of B is studied. The CRB depends on the derivatives of the intractable normalizing constant of the Potts model. This is resolved by proposing an original Monte Carlo algorithm, which is successfully applied to compute the CRB of the Ising and Potts models

Reconstruction, Classification, and Segmentation for Computational Microscopy

This thesis treats two fundamental problems in computational microscopy: image reconstruction for magnetic resonance force microscopy (MRFM) and image classification for electron backscatter diffraction (EBSD). In MRFM, as in many inverse problems, the true point spread function (PSF) that blurs the image may be only partially known. The image quality may suffer from this possible mismatch when standard image reconstruction techniques are applied. To deal with the mismatch, we develop novel Bayesian sparse reconstruction methods that account for possible errors in the PSF of the microscope and for the inherent sparsity of MRFM images. Two methods are proposed: a stochastic method and a variational method. They both jointly estimate the unknown PSF and unknown image. Our proposed framework for reconstruction has the flexibility to incorporate sparsity inducing priors, thus addressing ill-posedness of this non-convex problem, Markov-Random field priors, and can be extended to other image models. To obtain scalable and tractable solutions, a dimensionality reduction technique is applied to the highly nonlinear PSF space. The experiments clearly demonstrate that the proposed methods have superior performance compared to previous methods. In EBSD we develop novel and robust dictionary-based methods for segmentation and classification of grain and sub-grain structures in polycrystalline materials. Our work is the first in EBSD analysis to use a physics-based forward model, called the dictionary, to use full diffraction patterns, and that efficiently classifies patterns into grains, boundaries, and anomalies. In particular, unlike previous methods, our method incorporates anomaly detection directly into the segmentation process. The proposed approach also permits super-resolution of grain mantle and grain boundary locations. Finally, the proposed dictionary-based segmentation method performs uncertainty quantification, i.e. p-values, for the classified grain interiors and grain boundaries. We demonstrate that the dictionary-based approach is robust to instrument drift and material differences that produce small amounts of dictionary mismatch.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102296/1/seunpark_1.pd

Etude de la variabilité hémodynamique chez l’enfant et l’adulte sains en IRMf

In fMRI, the conclusions of experimental paradigms remain unreliable as far as they supposesome a priori knowledge on the neuro-vascular coupling which is characterized by thehemodynamic response function modeling the link between the stimulus input and the fMRIsignal as output. To improve our understanding of the neuronal and vascular changes inducedby the realization of a cognitive task given in fMRI, it seems thus critical to study thecharacteristics of the hemodynamic response in depth.This thesis gives a new perspective on this topic, supported by an original method for intra-subjectanalysis of fMRI data : the Joint Detection-Estimation (or JDE). The JDE approachmodels the hemodynamic response in a not parametric and multivariate manner, while itjointly detects the cerebral areas which are activated in response to stimulations deliveredalong an experimental paradigm.The first contribution of this thesis is centered on the thorough analysis of the interindividualand inter-regiona hemodynamic variability from a population of young healthyadults. This work has allowed to validate the JDE method at the group level and to highlightthe striking hemodynamic variability in some cerebral regions : parietal, temporal, occipitallobes, motor cortex. This variability is much more important as the region is involved in morecomplex cognitive processes.The second research axis has consisted in focusing on the study of the hemodynamic orga-nizationof a particularly important cerebral area in Humans, the language system. Becausethis function embeds the reading learning ability, groups of healthy children of 6 and 9 yearsold respectively, who were in the process of learning or of strenghting reading, were chosen forthis study. Two important methodological contributions have been proposed. First, a multi-sessionsextension of the JDE approach (until now limited to the processing of mono-sessiondata in fMRI) was worked out in order to improve the robustness and the reproducibility ofthe results. Then, a new framework was developed to overcome the main shortcoming of theJDE approach. The latter indeed relies on a prior parcellation of the data in functionally ho-mogeneousregions, the choice of which is critical for the subsequent inference and impacts thehemodynamic results. In order to avoid this a priori choice, the finalized alternative combinesthe results from various random data fragmentations by using “consensus clustering”.Finally, a second extension of the JDE approach was developed in order to robustly estimatethe shape of the hemodynamic response at the group level. So far, this model was validatedon simulations, and we plan to apply it on children data to improve the study of the BOLDresponse temporal characteristics in the language areas. Thus, this PhD work proposes onone hand new methodological contributions to characterize the hemodynamic response infMRI, and on the other hand a validation and a neuroscientific application of the proposedapproaches.En IRMf, les conclusions de paradigmes expérimentaux restent encore sujettes à caution dans la mesure où elles supposent une connaissance a priori du couplage neuro-vasculaire, c’est-à- dire de la fonction de réponse hémodynamique qui modélise le lien entre la stimulation et le signal mesuré. Afin de mieux appréhender les changements neuronaux et vasculaires induits par la réalisation d’une tâche cognitive en IRMf, il apparaît donc indispensable d’étudier de manière approfondie les caractéristiques de la réponse hémodynamique. Cette thèse apporte un nouvel éclairage sur cette étude, en s’appuyant sur une méthode originale d’analyse intra-sujet des données d’IRMf : la Détection-Estimation Conjointe (« Joint Detection-Estimation » en anglais, ou JDE). L’approche JDE modélise de façon non paramétrique et multivariée la réponse hémodynamique, tout en détectant conjointement les aires cérébrales activées en réponse aux stimulations d’un paradigme expérimental. La première contribution de cette thèse a été centrée sur l’analyse approfondie de la variabilité hémodynamique, tant inter-individuelle qu’inter-régionale, au niveau d’un groupe de jeunes adultes sains. Ce travail a permis de valider la méthode JDE au niveau d’une population et de mettre en évidence la variabilité hémodynamique importante apparaissant dans certaines régions cérébrales : lobes pariétal, temporal, occipital, cortex moteur. Cette variabilité est d’autant plus importante que la région est impliquée dans des processus cognitifs plus complexes.Un deuxième axe de recherche a consisté à se focaliser sur l’étude de l’organisation hémodynamique d’une aire cérébrale particulièrement importante chez les êtres humains, la région du langage. Cette fonction étant liée à la capacité d’apprentissage de la lecture, deux groupes d’enfants sains, âgés respectivement de 6 et 9 ans, en cours d’apprentissage ou de consolidation de la lecture, ont été choisis pour mener cette étude. Deux apports méthodologiques importants ont été proposés. Tout d’abord, une extension multi-sessions de l’approche JDE (jusqu’alors limitée au traitement de données mono-session en IRMf) a été mise au point afin d’améliorer la robustesse et la reproductibilité des résultats. Cette extension a permis de mettre en évidence, au sein de la population d’enfants, l’évolution de la réponse hémodynamique avec l’âge, au sein de la région du sillon temporal supérieur. Ensuite, un nouveau cadre a été développé pour contourner l’une des limitations de l’approche JDE « standard », à savoir la parcellisation a priori des données en régions fonctionnellement homogènes. Cette parcellisation est déterminante pour la suite de l’analyse et a un impact sur les résultats hémodynamiques. Afin de s’affranchir d’un tel choix, l’alternative mise au point combine les résultats issus de différentes parcellisations aléatoires des données en utilisant des techniques de «consensus clustering». Enfin, une deuxième extension de l’approche JDE a été mise en place pour estimer la forme de la réponse hémodynamique au niveau d’un groupe de sujets. Ce modèle a pour l’instant été validé sur simulations, et nous prévoyons de l’appliquer sur les données d’enfant pour améliorer l’étude des caractéristiques temporelles de la réponse BOLD dans les réseaux du langage.Ce travail de thèse propose ainsi d’une part des contributions méthodologiques nouvelles pour caractériser la réponse hémodynamique en IRMf, et d’autre part une validation et une application des approches développées sous un éclairage neuroscientifique

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282