High-Dimensional Matched Subspace Detection When Data are Missing

We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, well-studied problem when the signal is completely observed. High- dimensional testing problems in which it may be prohibitive or impossible to obtain a complete observation motivate this work. The signal is represented as a vector in R^n, but we only observe m << n of its elements. We show that reliable detection is possible, under mild incoherence conditions, as long as m is slightly greater than the dimension of the subspace in question

A likelihood ratio test for functional MRI data analysis to account for colored noise

Abstract. Functional magnetic resonance (fMRI) data are often corrupted with colored noise. To account for this type of noise, many prewhitening and pre-coloring strategies have been proposed to process the fMRI time series prior to statistical inference. In this paper, a generalized likelihood ratio test for brain activation detection is proposed in which the temporal correlation structure of the noise is modelled as an autoregressive (AR) model. The order of the AR model is determined from experimental null data sets. Simulation tests reveal that, for a fixed false alarm rate, the proposed test is slightly (2-3%) better than current tests incorporating colored noise in terms of detection rate

Anatomo-functional magnetic resonance imaging of the spinal cord and its application to the characterization of spinal lesions in cats

Les lésions de la moelle épinière ont un impact significatif sur la qualité de la vie car elles peuvent induire des déficits moteurs (paralysie) et sensoriels. Ces déficits évoluent dans le temps à mesure que le système nerveux central se réorganise, en impliquant des mécanismes physiologiques et neurochimiques encore mal connus. L'ampleur de ces déficits ainsi que le processus de réhabilitation dépendent fortement des voies anatomiques qui ont été altérées dans la moelle épinière. Il est donc crucial de pouvoir attester l'intégrité de la matière blanche après une lésion spinale et évaluer quantitativement l'état fonctionnel des neurones spinaux. Un grand intérêt de l'imagerie par résonance magnétique (IRM) est qu'elle permet d'imager de façon non invasive les propriétés fonctionnelles et anatomiques du système nerveux central. Le premier objectif de ce projet de thèse a été de développer l'IRM de diffusion afin d'évaluer l'intégrité des axones de la matière blanche après une lésion médullaire. Le deuxième objectif a été d'évaluer dans quelle mesure l'IRM fonctionnelle permet de mesurer l'activité des neurones de la moelle épinière. Bien que largement appliquées au cerveau, l'IRM de diffusion et l'IRM fonctionnelle de la moelle épinière sont plus problématiques. Les difficultés associées à l'IRM de la moelle épinière relèvent de sa fine géométrie (environ 1 cm de diamètre chez l'humain), de la présence de mouvements d'origine physiologique (cardiaques et respiratoires) et de la présence d'artefacts de susceptibilité magnétique induits par les inhomogénéités de champ, notamment au niveau des disques intervertébraux et des poumons. L'objectif principal de cette thèse a donc été de développer des méthodes permettant de contourner ces difficultés. Ce développement a notamment reposé sur l'optimisation des paramètres d'acquisition d'images anatomiques, d'images pondérées en diffusion et de données fonctionnelles chez le chat et chez l'humain sur un IRM à 3 Tesla. En outre, diverses stratégies ont été étudiées afin de corriger les distorsions d'images induites par les artefacts de susceptibilité magnétique, et une étude a été menée sur la sensibilité et la spécificité de l'IRM fonctionnelle de la moelle épinière. Les résultats de ces études démontrent la faisabilité d'acquérir des images pondérées en diffusion de haute qualité, et d'évaluer l'intégrité de voies spinales spécifiques après lésion complète et partielle. De plus, l'activité des neurones spinaux a pu être détectée par IRM fonctionnelle chez des chats anesthésiés. Bien qu'encourageants, ces résultats mettent en lumière la nécessité de développer davantage ces nouvelles techniques. L'existence d'un outil de neuroimagerie fiable et robuste, capable de confirmer les paramètres cliniques, permettrait d'améliorer le diagnostic et le pronostic chez les patients atteints de lésions médullaires. Un des enjeux majeurs serait de suivre et de valider l'effet de diverses stratégies thérapeutiques. De telles outils représentent un espoir immense pour nombre de personnes souffrant de traumatismes et de maladies neurodégénératives telles que les lésions de la moelle épinière, les tumeurs spinales, la sclérose en plaques et la sclérose latérale amyotrophique.Spinal cord injury has a significant impact on quality of life since it can lead to motor (paralysis) and sensory deficits. These deficits evolve in time as reorganisation of the central nervous system occurs, involving physiological and neurochemical mechanisms that are still not fully understood. Given that both the severity of the deficit and the successful rehabilitation process depend on the anatomical pathways that have been altered in the spinal cord, it may be of great interest to assess white matter integrity after a spinal lesion and to evaluate quantitatively the functional state of spinal neurons. The great potential of magnetic resonance imaging (MRI) lies in its ability to investigate both anatomical and functional properties of the central nervous system non invasively. To address the problem of spinal cord injury, this project aimed to evaluate the benefits of diffusion-weighted MRI to assess the integrity of white matter axons that remain after spinal cord injury. The second objective was to evaluate to what extent functional MRI can measure the activity of neurons in the spinal cord. Although widely applied to the brain, diffusion-weighted MRI and functional MRI of the spinal cord are not straightforward. Various issues arise from the small cross-section width of the cord, the presence of cardiac and respiratory motions, and from magnetic field inhomogeneities in the spinal region. The main purpose of the present thesis was therefore to develop methodologies to circumvent these issues. This development notably focused on the optimization of acquisition parameters to image anatomical, diffusion-weighted and functional data in cats and humans at 3T using standard coils and pulse sequences. Moreover, various strategies to correct for susceptibility-induced distortions were investigated and the sensitivity and specificity in spinal cord functional MRI was studied. As a result, acquisition of high spatial and angular diffusion-weighted images and evaluation of the integrity of specific spinal pathways following spinal cord injury was achieved. Moreover, functional activations in the spinal cord of anaesthetized cats was detected. Although encouraging, these results highlight the need for further technical and methodological development in the near-future. Being able to develop a reliable neuroimaging tool for confirming clinical parameters would improve diagnostic and prognosis. It would also enable to monitor the effect of various therapeutic strategies. This would certainly bring hope to a large number of people suffering from trauma and neurodegenerative diseases such as spinal cord injury, tumours, multiple sclerosis and amyotrophic lateral sclerosis

Patellofemoral Pain : Where does the pain come from?

My thesis is about patellofemoral pain (PFP), a common knee complaint among physically active young individuals. It is also known as ’anterior knee pain’, ’retropatellar chondropathy’ or more recently suggested ‘theatre or moviegoers knee’. PFP is characterized by retropatellar pain (behind the kneecap) or peripatellar pain (around the kneecap), specifically during knee loading activities, like running, cycling, squatting, stair climbing, and/or during prolonged sitting with the knees flexed in 90 degrees. The majority of people with PFP are treated conservatively with exercise therapy, but the effect of exercise therapy is still unknown. Therefore, this thesis assessed the effects of exercise therapy and aimed to point out the most effective exercise strategy. However, despite the application of a variety of treatment modalities, a substantial group of patients has persistent complaints. The pathophysiology of PFP is considered to be multifactorial, but still widely unknown. Therefore, emphasis has been placed on unraveling the pathophysiology of PFP with advanced MRI techniques. For years it has been suggested that cartilage plays an important role, but this thesis suggests otherwise. Furthermore, an innovative MRI method was developed to study blood perfusion of the patella. It might be that vascular problems are present in patients with knee pain during watching a movie or visiting the theatre in particular. Or maybe, there are no differences between patients and control subjects on MRI, but only differences in pain perception as has been suggested previously......

Neuroinformatics in Functional Neuroimaging

This Ph.D. thesis proposes methods for information retrieval in functional neuroimaging through automatic computerized authority identification, and searching and cleaning in a neuroscience database. Authorities are found through cocitation analysis of the citation pattern among scientific articles. Based on data from a single scientific journal it is shown that multivariate analyses are able to determine group structure that is interpretable as particular “known ” subgroups in functional neuroimaging. Methods for text analysis are suggested that use a combination of content and links, in the form of the terms in scientific documents and scientific citations, respectively. These included context sensitive author ranking and automatic labeling of axes and groups in connection with multivariate analyses of link data. Talairach foci from the BrainMap ™ database are modeled with conditional probability density models useful for exploratory functional volumes modeling. A further application is shown with conditional outlier detection where abnormal entries in the BrainMap ™ database are spotted using kernel density modeling and the redundancy between anatomical labels and spatial Talairach coordinates. This represents a combination of simple term and spatial modeling. The specific outliers that were found in the BrainMap ™ database constituted among others: Entry errors, errors in the article and unusual terminology