Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution

We propose two strategies to improve the quality of tractography results computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both methods are based on the same PDE framework, defined in the coupled space of positions and orientations, associated with a stochastic process describing the enhancement of elongated structures while preserving crossing structures. In the first method we use the enhancement PDE for contextual regularization of a fiber orientation distribution (FOD) that is obtained on individual voxels from high angular resolution diffusion imaging (HARDI) data via constrained spherical deconvolution (CSD). Thereby we improve the FOD as input for subsequent tractography. Secondly, we introduce the fiber to bundle coherence (FBC), a measure for quantification of fiber alignment. The FBC is computed from a tractography result using the same PDE framework and provides a criterion for removing the spurious fibers. We validate the proposed combination of CSD and enhancement on phantom data and on human data, acquired with different scanning protocols. On the phantom data we find that PDE enhancements improve both local metrics and global metrics of tractography results, compared to CSD without enhancements. On the human data we show that the enhancements allow for a better reconstruction of crossing fiber bundles and they reduce the variability of the tractography output with respect to the acquisition parameters. Finally, we show that both the enhancement of the FODs and the use of the FBC measure on the tractography improve the stability with respect to different stochastic realizations of probabilistic tractography. This is shown in a clinical application: the reconstruction of the optic radiation for epilepsy surgery planning

Acquisitions d'IRM de diffusion à haute résolution spatiale : nouvelles perspectives grâce au débruitage spatialement adaptatif et angulaire

Le début des années 2000 a vu la cartographie du génome humain se réaliser après 13 ans de recherche. Le défi du prochain siècle réside dans la construction du connectome humain, qui consiste à cartographier les connexions du cerveau en utilisant l’imagerie par résonance magnétique (IRM) de diffusion. Cette technique permet en effet d’étudier la matière blanche du cerveau de façon complètement non invasive. Bien que le défi soit monumental, la résolution d’une image d’IRM se situe à l’échelle macroscopique et est environ 1000 fois inférieure à la taille des axones qu’il faut cartographier. Pour aider à pallier à ce problème, ce mémoire propose une nouvelle technique de débruitage spécialement conçue pour l’imagerie de diffusion. L’algorithme Non Local Spatial and Angular Matching (NLSAM) se base sur les principes du block matching et du dictionary learning pour exploiter la redondance des données d’IRM de diffusion. Un seuillage sur les voisins angulaire est aussi réalisé à l’aide du sparse coding, où l’erreur de reconstruction en norme l2 est bornée par la variance locale du bruit. L’algorithme est aussi conçu pour gérer le biais du bruit Ricien et Chi non centré puisque les images d’IRM contiennent du bruit non Gaussien. Ceci permet ainsi d’acquérir des données d’IRM de diffusion à une plus grande résolution spatiale que présentement disponible en milieu clinique. Ce travail ouvre donc la voie à un meilleur type d’acquisition, ce qui pourrait contribuer à révéler de nouveaux détails anatomiques non discernables à la résolution spatiale présentement utilisée par la communauté d’IRM de diffusion. Ceci pourrait aussi éventuellement contribuer à identifier de nouveaux biomarqueurs permettant de comprendre les maladies dégénératives telles que la sclérose en plaques, la maladie d’Alzheimer et la maladie de Parkinson

Variable Splitting as a Key to Efficient Image Reconstruction

The problem of reconstruction of digital images from their degraded measurements has always been a problem of central importance in numerous applications of imaging sciences. In real life, acquired imaging data is typically contaminated by various types of degradation phenomena which are usually related to the imperfections of image acquisition devices and/or environmental effects. Accordingly, given the degraded measurements of an image of interest, the fundamental goal of image reconstruction is to recover its close approximation, thereby "reversing" the effect of image degradation. Moreover, the massive production and proliferation of digital data across different fields of applied sciences creates the need for methods of image restoration which would be both accurate and computationally efficient. Developing such methods, however, has never been a trivial task, as improving the accuracy of image reconstruction is generally achieved at the expense of an elevated computational burden. Accordingly, the main goal of this thesis has been to develop an analytical framework which allows one to tackle a wide scope of image reconstruction problems in a computationally efficient manner. To this end, we generalize the concept of variable splitting, as a tool for simplifying complex reconstruction problems through their replacement by a sequence of simpler and therefore easily solvable ones. Moreover, we consider two different types of variable splitting and demonstrate their connection to a number of existing approaches which are currently used to solve various inverse problems. In particular, we refer to the first type of variable splitting as Bregman Type Splitting (BTS) and demonstrate its applicability to the solution of complex reconstruction problems with composite, cross-domain constraints. As specific applications of practical importance, we consider the problem of reconstruction of diffusion MRI signals from sub-critically sampled, incomplete data as well as the problem of blind deconvolution of medical ultrasound images. Further, we refer to the second type of variable splitting as Fuzzy Clustering Splitting (FCS) and show its application to the problem of image denoising. Specifically, we demonstrate how this splitting technique allows us to generalize the concept of neighbourhood operation as well as to derive a unifying approach to denoising of imaging data under a variety of different noise scenarios

Diffusion Weighted Image Denoising using overcomplete Local PCA

Diffusion Weighted Images (DWI) normally shows a low Signal to Noise Ratio (SNR) due to the presence of noise from the measurement process that complicates and biases the estimation of quantitative diffusion parameters. In this paper, a new denoising methodology is proposed that takes into consideration the multicomponent nature of multi-directional DWI datasets such as those employed in diffusion imaging. This new filter reduces random noise in multicomponent DWI by locally shrinking less significant Principal Components using an overcomplete approach. The proposed method is compared with state-of-the-art methods using synthetic and real clinical MR images, showing improved performance in terms of denoising quality and estimation of diffusion parameters.This work has been supported by the Spanish grant TIN2011-26727 from Ministerio de Ciencia e Innovacion. This work has been also partially supported by the French grant "HR-DTI" ANR-10-LABX-57 funded by the TRAIL from the French Agence Nationale de la Recherche within the context of the Investments for the Future program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Manjón Herrera, JV.; Coupé, P.; Concha, L.; Buades, A.; Collins, L.; Robles Viejo, M. (2013). Diffusion Weighted Image Denoising using overcomplete Local PCA. PLoS ONE. 8(9):1-12. https://doi.org/10.1371/journal.pone.0073021S11289Sundgren, P. C., Dong, Q., Gómez-Hassan, D., Mukherji, S. K., Maly, P., & Welsh, R. (2004). Diffusion tensor imaging of the brain: review of clinical applications. Neuroradiology, 46(5), 339-350. doi:10.1007/s00234-003-1114-xJohansen-Berg, H., & Behrens, T. E. (2006). Just pretty pictures? What diffusion tractography can add in clinical neuroscience. 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Spatially Regularized Spherical Reconstruction: A Cross-Domain Filtering Approach for HARDI Signals

Despite the immense advances of science and medicine in recent years, several aspects regarding the physiology and the anatomy of the human brain are yet to be discovered and understood. A particularly challenging area in the study of human brain anatomy is that of brain connectivity, which describes the intricate means by which different regions of the brain interact with each other. The study of brain connectivity is deeply dependent on understanding the organization of white matter. The latter is predominantly comprised of bundles of myelinated axons, which serve as connecting pathways between approximately 10¹¹ neurons in the brain. Consequently, the delineation of fine anatomical details of white matter represents a highly challenging objective, and it is still an active area of research in the fields of neuroimaging and neuroscience, in general. Recent advances in medical imaging have resulted in a quantum leap in our understanding of brain anatomy and functionality. In particular, the advent of diffusion magnetic resonance imaging (dMRI) has provided researchers with a non-invasive means to infer information about the connectivity of the human brain. In a nutshell, dMRI is a set of imaging tools which aim at quantifying the process of water diffusion within the human brain to delineate the complex structural configurations of the white matter. Among the existing tools of dMRI high angular resolution diffusion imaging (HARDI) offers a desirable trade-off between its reconstruction accuracy and practical feasibility. In particular, HARDI excels in its ability to delineate complex directional patterns of the neural pathways throughout the brain, while remaining feasible for many clinical applications. Unfortunately, HARDI presents a fundamental trade-off between its ability to discriminate crossings of neural fiber tracts (i.e., its angular resolution) and the signal-to-noise ratio (SNR) of its associated images. Consequently, given that the angular resolution is of fundamental importance in the context of dMRI reconstruction, there is a need for effective algorithms for de-noising HARDI data. In this regard, the most effective de-noising approaches have been observed to be those which exploit both the angular and the spatial-domain regularity of HARDI signals. Accordingly, in this thesis, we propose a formulation of the problem of reconstruction of HARDI signals which incorporates regularization assumptions on both their angular and their spatial domains, while leading to a particularly simple numerical implementation. Experimental evidence suggests that the resulting cross-domain regularization procedure outperforms many other state of the art HARDI de-noising methods. Moreover, the proposed implementation of the algorithm supersedes the original reconstruction problem by a sequence of efficient filters which can be executed in parallel, suggesting its computational advantages over alternative implementations

WAVELET FRAMES ON THE SPHERE, HIGH ANGULAR RESOLUTION DIFFUSION IMAGINING AND L_1-REGULARIZED OPTIMIZATION ON STIEFEL MANIFOLDS

Ph.DDOCTOR OF PHILOSOPH

Statistical Learning Methods for Diffusion Magnetic Resonance Imaging

Diffusion Magnetic Resonance Imaging (dMRI) is a commonly used imaging technique to reveal white matter (WM) microstructure by probing the diffusion of water molecules. The diffusion of water molecules is constrained by the biological boundaries including nerves and tissues. Thus, quantifying the diffusion process is important to understand the WM microstructure. However, the development of efficient analytical methods for the reconstruction, lifespan structural connectome analysis, and surrogate variable analysis have fallenseriously behind the technological advances. This challenge motivates us to develop new statistical learning methods for dMRI. In the first project, we propose a two-stage sparse and adaptive smoothing model (TSASM) for two major image denoising tasks in neuroimaging data analysis, including image reconstruction from a series of noisy images within each subject and group analysis of images obtained from different subjects. Our TSASM consists of an initial smoothing stage of applying a penalized M-estimator and a refined smoothing stage of applying kernel-based smoothing methods. The key novelties of our TSASM are that it accounts for the sparse structure of imaging signals while preserving piecewise smooth regions with unknown edges. In the second project, we develop a scalable analytical method for mapping the lifespan human structural connectome. Specifically, we develop a novel lifespan population-based structural connectome (LPSC) framework that integrates fiber bundle and functional network information for hierarchically guiding the registration. Our LPSC is applicable to several neuroimaging studies of neuropsychiatric disorders as well as normal brain development. An improved understanding of human structural connectome has the potential to inspire new approaches to prevention, diagnosis, and treatment of many illnesses. In the third project, we propose an eigen-shrinkage projection (ESP) method to perform the surrogate variable analysis and solve the hidden confounder and harmonization problems in the neuroimaging studies. Our ESP can eliminate the signals from primary variable while preserving the eigenvalue-gap between hidden confounder and noises, which enables hidden confounders estimation from the projected data. We then investigate the statistical properties of the estimated hidden confounders and uncover the natural connection with ridge regression. Numerical experiments are used to illustrate the finite-sample performance.Doctor of Philosoph

Imagerie de diffusion en temps-réel (correction du bruit et inférence de la connectivité cérébrale)

La plupart des constructeurs de systèmes d'imagerie par résonance magnétique (IRM) proposent un large choix d'applications de post-traitement sur les données IRM reconstruites a posteriori, mais très peu de ces applications peuvent être exécutées en temps réel pendant l'examen. Mises à part certaines solutions dédiées à l'IRM fonctionnelle permettant des expériences relativement simples ainsi que d'autres solutions pour l'IRM interventionnelle produisant des scans anatomiques pendant un acte de chirurgie, aucun outil n'a été développé pour l'IRM pondérée en diffusion (IRMd). Cependant, comme les examens d'IRMd sont extrêmement sensibles à des perturbations du système hardware ou à des perturbations provoquées par le sujet et qui induisent des données corrompues, il peut être intéressant d'investiguer la possibilité de reconstruire les données d'IRMd directement lors de l'examen. Cette thèse est dédiée à ce projet innovant. La contribution majeure de cette thèse a consisté en des solutions de débruitage des données d'IRMd en temps réel. En effet, le signal pondéré en diffusion peut être corrompu par un niveau élevé de bruit qui n'est plus gaussien, mais ricien ou chi non centré. Après avoir réalisé un état de l'art détaillé de la littérature sur le bruit en IRM, nous avons étendu l'estimateur linéaire qui minimise l'erreur quadratique moyenne (LMMSE) et nous l'avons adapté à notre cadre de temps réel réalisé avec un filtre de Kalman. Nous avons comparé les performances de cette solution à celles d'un filtrage gaussien standard, difficile à implémenter car il nécessite une modification de la chaîne de reconstruction pour y être inséré immédiatement après la démodulation du signal acquis dans l'espace de Fourier. Nous avons aussi développé un filtre de Kalman parallèle qui permet d'appréhender toute distribution de bruit et nous avons montré que ses performances étaient comparables à celles de notre méthode précédente utilisant un filtre de Kalman non parallèle. Enfin, nous avons investigué la faisabilité de réaliser une tractographie en temps-réel pour déterminer la connectivité structurelle en direct, pendant l'examen. Nous espérons que ce panel de développements méthodologiques permettra d'améliorer et d'accélérer le diagnostic en cas d'urgence pour vérifier l'état des faisceaux de fibres de la substance blanche.Most magnetic resonance imaging (MRI) system manufacturers propose a huge set of software applications to post-process the reconstructed MRI data a posteriori, but few of them can run in real-time during the ongoing scan. To our knowledge, apart from solutions dedicated to functional MRI allowing relatively simple experiments or for interventional MRI to perform anatomical scans during surgery, no tool has been developed in the field of diffusion-weighted MRI (dMRI). However, because dMRI scans are extremely sensitive to lots of hardware or subject-based perturbations inducing corrupted data, it can be interesting to investigate the possibility of processing dMRI data directly during the ongoing scan and this thesis is dedicated to this challenging topic. The major contribution of this thesis aimed at providing solutions to denoise dMRI data in real-time. Indeed, the diffusion-weighted signal may be corrupted by a significant level of noise which is not Gaussian anymore, but Rician or noncentral chi. After making a detailed review of the literature, we extended the linear minimum mean square error (LMMSE) estimator and adapted it to our real-time framework with a Kalman filter. We compared its efficiency to the standard Gaussian filtering, difficult to implement, as it requires a modification of the reconstruction pipeline to insert the filter immediately after the demodulation of the acquired signal in the Fourier space. We also developed a parallel Kalman filter to deal with any noise distribution and we showed that its efficiency was quite comparable to the non parallel Kalman filter approach. Last, we addressed the feasibility of performing tractography in real-time in order to infer the structural connectivity online. We hope that this set of methodological developments will help improving and accelerating a diagnosis in case of emergency to check the integrity of white matter fiber bundles.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

IRM de diffusion par encodage tenseur-b : déconvolution sphérique contrainte et décomposition de la variance diffusionnelle

Le cerveau humain est composé de plusieurs milliards de neurones qui forment une multitude de connexions, se regroupant en fibres de matière blanche (WM) sur plus de 160 000 kilomètres au total. L’imagerie par résonance magnétique (IRM) de diffusion (IRMd) tire profit de l’atténuation du signal de résonance magnétique causée par la diffusion des molécules d’eau dans le cerveau pour étudier ces structures sous-jacentes de manière non invasive. Le modèle d’imagerie par tenseur de diffusion (DTI) permet d’accéder à différentes mesures procurant de l’information sur la mésostructure du cerveau à partir de données d'IRMd, en manquant cependant de spécificité face à la nature microscopique du signal. Le modèle de déconvolution sphérique contrainte (CSD) permet de reconstruire une carte des fonctions de distribution d'orientations de fibres (fODF) de WM dans le cerveau de façon précise à partir de l'imagerie de diffusion à haute résolution angulaire (HARDI), ce qui peut être utilisé par un algorithme de tractographie pour cartographier le connectome structurel humain. Afin de surmonter le manque de spécificité présent en DTI, l’IRM de diffusion par encodage tenseur-b a vu le jour dans les années 2000. Cette technique utilise différents encodages de gradients de diffusion (p. ex., encodages linéaire, planaire et sphérique) pour donner accès à des mesures plus fines de la structure microscopique des tissus cérébraux, sous la forme de mesures de microstructure novatrices. Cependant, les données d'IRMd par encodage tenseur-b sont complexes et ne s'appliquent pas directement au modèle de CSD, sans compter que l'impact de ces données sur la reconstruction des fODFs est inconnu. Le présent mémoire vise donc à élaborer les fondations mathématiques et techniques d'une CSD adaptée aux données d'IRMd par encodage tenseur-b. Une évaluation des performances de reconstruction des fODFs par ce modèle est ensuite effectuée sur des données simulées, en parallèle avec des mesures d'efficacité du calcul des mesures de microstructure. L'étude révèle que l'ajout d'un encodage planaire ou sphérique à un encodage linéaire réduit de seulement quelques degrés la résolution angulaire des fODFs reconstruites. De plus, la combinaison d'encodages linéaire et sphérique mène à un calcul précis des mesures de microstructure. Les résultats de ces travaux, incluant la proposition d'un protocole d'IRMd par encodage tenseur-b d'une durée de 10 minutes et 30 secondes, ouvrent la porte à la reconstruction des fODFs jumelée au calcul des précieuses mesures de microstructure