Des modèles bloc-parcimonieux en multi-modalité : application au problème inverse en EEG/MEG

Three main challenges have been addressed in this thesis, in three chapters.First challenge is about the ineffectiveness of some classic methods in high-dimensional problems. This challenge is partially addressed through the idea of clustering the coherent parts of a dictionary based on the proposed characterisation, in order to create more incoherent atomic entities in the dictionary, which is proposed as a block structure identification framework. The more incoherent atomic entities, the more improvement in the exact recovery conditions. In addition, we applied the mentioned clustering idea to real-world EEG/MEG leadfields to segment the brain source space, without using any information about the brain sources activity and EEG/MEG signals. Second challenge raises when classic recovery conditions cannot be established for the new concept of constraint, i.e., block-sparsity. Therefore, as the second research orientation, we developed a general framework for block-sparse exact recovery conditions, i.e., four theoretical and one algorithmic-dependent conditions, which ensure the uniqueness of the block-sparse solution of corresponding weighted mixed-norm optimisation problem in an underdetermined system of linear equations. The mentioned generality of the framework is in terms of the properties of the underdetermined system of linear equations, extracted dictionary characterisations, optimisation problems, and ultimately the recovery conditions. Finally, the combination of different information of a same phenomenon is the subject of the third challenge, which is addressed in the last part of dissertation with application to brain source space segmentation. More precisely, we showed that by combining the EEG and MEG leadfields and gaining the electromagnetic properties of the head, more refined brain regions appeared.De nombreux phénomènes naturels sont trop complexes pour être pleinement reconnus par un seul instrument de mesure ou par une seule modalité. Par conséquent, le domaine de recherche de la multi-modalité a émergé pour mieux identifier les caractéristiques riches du phénomène naturel de la multi-propriété naturelle, en analysant conjointement les données collectées à partir d’uniques modalités, qui sont en quelque sorte complémentaires. Dans notre étude, le phénomène d’intérêt multi-propriétés est l’activité du cerveau humain et nous nous intéressons à mieux la localiser au moyen de ses propriétés électromagnétiques, mesurables de manière non invasive. En neurophysiologie, l’électroencéphalographie (EEG) et la magnétoencéphalographie (MEG) constituent un moyen courant de mesurer les propriétés électriques et magnétiques de l’activité cérébrale. Notre application dans le monde réel, à savoir le problème de reconstruction de source EEG / MEG, est un problème fondamental en neurosciences, allant des sciences cognitives à la neuropathologie en passant par la planification chirurgicale. Considérant que le problème de reconstruction de source EEG /MEG peut être reformulé en un système d’équations linéaires sous-déterminé, la solution (l’activité estimée de la source cérébrale) doit être suffisamment parcimonieuse pour pouvoir être récupérée de manière unique. La quantité de parcimonie est déterminée par les conditions dites de récupération. Cependant, dans les problèmes de grande dimension, les conditions de récupération conventionnelles sont extrêmement strictes. En regroupant les colonnes cohérentes d’un dictionnaire, on pourrait obtenir une structure plus incohérente. Cette stratégie a été proposée en tant que cadre d’identification de structure de bloc, ce qui aboutit à la segmentation automatique de l’espace source du cerveau, sans utiliser aucune information sur l’activité des sources du cerveau et les signaux EEG / MEG. En dépit du dictionnaire structuré en blocs moins cohérent qui en a résulté, la condition de récupération conventionnelle n’est plus en mesure de calculer la caractérisation de la cohérence. Afin de relever le défi mentionné, le cadre général des conditions de récupération exactes par bloc-parcimonie, comprenant trois conditions théoriques et une condition dépendante de l’algorithme, a été proposé. Enfin, nous avons étudié la multi-modalité EEG et MEG et montré qu’en combinant les deux modalités, des régions cérébrales plus raffinées sont apparue

Recovery guarantees for mixed norm l-(p1, p2) block sparse representations

International audienceIn this work, we propose theoretical and algorithmic-independent recovery conditions which guarantee the uniqueness of block sparse recovery in general dictionaries through a general mixed norm optimization problem. These conditions are derived using the proposed block uncertainty principles and block null space property, based on some newly defined characterizations of block spark, and (p, p)-block mutual incoherence. We show that there is improvement in the recovery condition when exploiting the block structure of the representation. In addition, the proposed recovery condition extends the similar results for block sparse setting by generalizing the criterion for determining the active blocks, generalizing the block sparse recovery condition, and relaxing some constraints on blocks such as linear independency of the columns

Estimates of cortical column orientation improve MEG source inversion

International audienceDetermining the anatomical source of brain activity non-invasively measured from EEG or MEG sensors is challenging. In order to simplify the source localization problem, many techniques introduce the assumption that current sources lie on the cortical surface. Another common assumption is that this current flow is orthogonal to the cortical surface, thereby approximating the orientation of cortical columns. However, it is not clear which cortical surface to use to define the current source locations, and normal vectors computed from a single cortical surface may not be the best approximation to the orientation of cortical columns. We compared three different surface location priors and five different approaches for estimating dipole vector orientation, both in simulations and visual and motor evoked MEG responses. We show that models with source locations on the white matter surface and using methods based on establishing correspondences between white matter and pial cortical surfaces dramatically outperform models with source locations on the pial or combined pial/white surfaces and which use methods based on the geometry of a single cortical surface in fitting evoked visual and motor responses. These methods can be easily implemented and adopted in most M/EEG analysis pipelines, with the potential to significantly improve source localization of evoked responses

Estimates of cortical column orientation improve MEG source inversion

Determining the anatomical source of brain activity non-invasively measured from EEG or MEG sensors is challenging. In order to simplify the source localization problem, many techniques introduce the assumption that current sources lie on the cortical surface. Another common assumption is that this current flow is orthogonal to the cortical surface, thereby approximating the orientation of cortical columns. However, it is not clear which cortical surface to use to define the current source locations, and normal vectors computed from a single cortical surface may not be the best approximation to the orientation of cortical columns. We compared three different surface location priors and five different approaches for estimating dipole vector orientation, both in simulations and visual and motor evoked MEG responses. We show that models with source locations on the white matter surface and using methods based on establishing correspondences between white matter and pial cortical surfaces dramatically outperform models with source locations on the pial or combined pial/white surfaces and which use methods based on the geometry of a single cortical surface in fitting evoked visual and motor responses. These methods can be easily implemented and adopted in most M/EEG analysis pipelines, with the potential to significantly improve source localization of evoked responses