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.

Magnetic resonance imaging (MRI) has long become one of the most powerful and accurate tools of medical diagnostic imaging. Central to the diagnostic capabilities of MRI is the notion of contrast, which is determined by the biochemical composition of examined tissue as well as by its morphology. Despite the importance of the prevalent T₁, T₂, and proton density contrast mechanisms to clinical diagnosis, none of them has demonstrated effectiveness in delineating the morphological structure of the white matter - the information which is known to be related to a wide spectrum of brain-related disorders. It is only with the recent advent of diffusion-weighted MRI that scientists have been able to perform quantitative measurements of the diffusivity of white matter, making possible the structural delineation of neural fibre tracts in the human brain. One diffusion imaging technique in particular, namely high angular resolution diffusion imaging (HARDI), has inspired a substantial number of processing methods capable of obtaining the orientational information of multiple fibres within a single voxel while boasting minimal acquisition requirements. HARDI characterization of fibre morphology can be enhanced by increasing spatial and angular resolutions. However, doing so drastically reduces the signal-to-noise ratio. Since pronounced measurement noise tends to obscure and distort diagnostically relevant details of diffusion-weighted MR signals, increasing spatial or angular resolution necessitates application of the efficient and reliable tools of image denoising. The aim of this work is to develop an effective framework for the filtering of HARDI measurement noise which takes into account both the manifold to which the HARDI signal belongs and the statistical nature of MRI noise. These goals are accomplished using an approach rooted in non-local means (NLM) weighted averaging. The average includes samples, and therefore dependencies, from the entire manifold and the result of the average is used to deduce an estimate of the original signal value in accordance with MRI statistics. NLM averaging weights are determined adaptively based on a neighbourhood similarity measure. The novel neighbourhood comparison proposed in this thesis is one of spherical neighbourhoods, which assigns large weights to samples with similar local orientational diffusion characteristics. Moreover, the weights are designed to be invariant to both spatial rotations as well as to the particular sampling scheme in use. This thesis provides a detailed description of the proposed filtering procedure as well as experimental results with synthetic and real-life data. It is demonstrated that the proposed filter has substantially better denoising capabilities as compared to a number of alternative methods.

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.

Magnetic resonance imaging (MRI) has long become one of the most powerful and accurate tools of medical diagnostic imaging. Central to the diagnostic capabilities of MRI is the notion of contrast, which is determined by the biochemical composition of examined tissue as well as by its morphology. Despite the importance of the prevalent T₁, T₂, and proton density contrast mechanisms to clinical diagnosis, none of them has demonstrated effectiveness in delineating the morphological structure of the white matter - the information which is known to be related to a wide spectrum of brain-related disorders. It is only with the recent advent of diffusion-weighted MRI that scientists have been able to perform quantitative measurements of the diffusivity of white matter, making possible the structural delineation of neural fibre tracts in the human brain. One diffusion imaging technique in particular, namely high angular resolution diffusion imaging (HARDI), has inspired a substantial number of processing methods capable of obtaining the orientational information of multiple fibres within a single voxel while boasting minimal acquisition requirements. HARDI characterization of fibre morphology can be enhanced by increasing spatial and angular resolutions. However, doing so drastically reduces the signal-to-noise ratio. Since pronounced measurement noise tends to obscure and distort diagnostically relevant details of diffusion-weighted MR signals, increasing spatial or angular resolution necessitates application of the efficient and reliable tools of image denoising. The aim of this work is to develop an effective framework for the filtering of HARDI measurement noise which takes into account both the manifold to which the HARDI signal belongs and the statistical nature of MRI noise. These goals are accomplished using an approach rooted in non-local means (NLM) weighted averaging. The average includes samples, and therefore dependencies, from the entire manifold and the result of the average is used to deduce an estimate of the original signal value in accordance with MRI statistics. NLM averaging weights are determined adaptively based on a neighbourhood similarity measure. The novel neighbourhood comparison proposed in this thesis is one of spherical neighbourhoods, which assigns large weights to samples with similar local orientational diffusion characteristics. Moreover, the weights are designed to be invariant to both spatial rotations as well as to the particular sampling scheme in use. This thesis provides a detailed description of the proposed filtering procedure as well as experimental results with synthetic and real-life data. It is demonstrated that the proposed filter has substantially better denoising capabilities as compared to a number of alternative methods.

Cette thèse présente les résultats d'observations d'étoiles en rotation rapide menées sur le spectro-interféromètre AMBER du VLTI dans ses modes haute et moyenne résolutions spectrales. Les mesures effectuées sont les visibilités estimées sur trois bases simultanées, les phases différentielles en fonction de la longueur d'onde et des phases de clôtures avec, pour certaines nuits une bonne couverture du plan (u,v). Les données utilisées sont issues de plusieurs campagnes d'observation. Ces dernières étaient fortement dégradées par les défauts optiques d'AMBER, et affectés par des bruits classiques d'interférométrie optique à longue base en IR: défauts du détecteur, bruit de lecture, instabilités du suiveur de franges, ...etc. Leur analyse a nécessité la mise au point d'outils numériques de réduction spécifiques pour atteindre les précisions nécessaires à l'interprétation de mesures interférométriques. Pour interpréter ces mesures j'ai développé un modèle semi-analytique chromatique d'étoile en rotation rapide qui m'a permis d'estimer, à partir des phases différentielles; le degré d'aplatissement, le rayon équatorial, la vitesse de rotation, l'angle d'inclinaison, l'angle position de l'axe de rotation de l'étoile sur le ciel, la distribution de la température effective locale et de la gravité à la surface de l'étoile dans le cadre du théorème de von Zeipel. Les résultats concernant 4 étoiles massives de types spectraux B, A et F m'ont permis de les caractériser pour les mécanismes évoqués ci-dessus et d'ouvrir ainsi la perspective d'études plus systématiques d'objets similaires en étendant ultérieurement ces études à la relation photosphère-enveloppe circumstellaire. / This thesis presents the results of rapidly rotating stars observations conducted on the AMBER spectro-interferometer VLTI in its high average spectral modes and resolutions. The measurements are estimated on three simultaneous visibility bases, differential phases depending on the wavelength and closure phases, with good coverage of the (u, v) plane for some nights. The data used are from several observation campaigns. These were highly degraded by the optical defects of AMBER, and assigned by standard optical interferometry long base IR noises: defects of the detector, reading noise, fringes follower instabilities, ... etc. Their analysis required the development of digital reduction of specific tools to achieve the necessary details to the interpretation of interferometric measurements. In interpreting these measures I developed a chromatic semi-analytical model of rapidly rotating star that allowed me to estimate, from the differential phases; the degree of flattening, the equatorial radius, speed of rotation, angle of inclination, the position angle of the star rotation axis in the sky, the local distribution of the actual temperature and the gravity to the surface of the star within the von Zeipel theorem. The results for four massive stars of spectral type B, A and F have allowed me to characterize the mechanisms discussed above and thus open framework for more systematic studies of similar objects subsequently extending these studies to the relationship photosphere circumstellar envelope.

The existence of other habitable worlds and the possible development of life elsewhere in the Universe have been among mankinds fundamental questions for thousands of years. These interrogations about our origins and place in the Universe are today at the dawn of being answered in scientific terms. The key year was 1995 with the discovery of the first extrasolar planet orbiting around a solar-type star. About 400 extrasolar planets are known today and the possibility to identify habitable worlds and even life among them largely contributes to the growing interest about their nature and properties. However, characterizing planetary systems is a very difficult task due to both the huge contrast and the small angular separation between the host stars and their environment. New techniques have emerged during the past decades with the purpose of tackling these fantastic observational challenges. In that context, infrared interferometry is a very promising technique, since it provides the required angular resolution to separate the emission of the star from that of its environment. This dissertation is devoted to the characterization of extrasolar planetary systems using the high angular resolution and dynamic range capabilities of infrared interferometric techniques. The first part of the present work is devoted to the detection with current interferometric facilities of warm dust within the first few astronomical units of massive debris discs around nearby stars. In order to extend the imaging of planetary systems to fainter discs and to extrasolar planets, we investigate in a second step the performance of future space-based nulling interferometers and make a comparison with ground-based projects. Finally, the third part of this work is dedicated to the impact of exozodiacal discs on the performance of future life-searching space missions, the goal being to characterize extrasolar planets with sizes down to that of the Earth.

Malgré l’existence de modèles précis, notre connaissance des structures à petite échelle des galaxies est toujours limitée par le manque de preuves observationnelles. Les progrès instrumentaux ont permis d’atteindre une haute résolution angulaire à l’aide des nouvelles générations de télescopes, mais celle-ci est restreinte à un faible nombre de cibles extragalactiques à causes des besoins de l’Optique Adaptative (OA). En effet, afin de permettre une mesure efficace du front d’onde, l’OA requiert une source brillante et ponctuelle proche de la cible scientifique, typiquement en dessous de 30 . La partie principale de cette thèse porte sur l’analyse de la dizaine de parsecs centrale des Galaxies à Noyaux Actifs (NAG) à l’aide de différentes techniques observationnelles et numériques. Nous avons dans ce contexte développé un code de transfert radiatif nous permettant d’analyser les données polarimétriques. La seconde partie de ce travail est dédiée à l’analyse d’images en proche infrarouges de galaxies à flambée d’étoiles afin de contraindre les paramètres décrivant les super amas stellaires, jeunes cocons de poussière très massifs abritant une formation d’étoiles très soutenue, à l’aide de données obtenues avec l’instrument CANARY, démonstrateur de nouvelles technologies d’OA. / Despite having strong theoretical models, the current limitation in our understanding of the small-scale structures of galaxies is linked to the lack of observational evidences. Many powerful telescopes and instruments have been developed in the last decades, however one of these strongest tools, namely Adaptive Optics (AO), can only be used on a very limited number of targets. Indeed, for AO to be efficient, a bright star is required close to the scientific target, typically under 30 . This is mandatory for the AO systems to be able to measure the atmospheric turbulence and this condition is rarely satisfied for extended extragalactic targets such as galaxies. The main part of this thesis work consisted in going deeper in the analysis of the inner tens of parsecs of Active Nuclei (AGN) by combining different techniques to obtain and to interpret new data. In this context, we developed a new radiative transfer code to analyse the polarimetric data. A second part of my work was dedicated to a high angular resolution study of Super Star Clusters (SSC) in a new system, thanks to data obtained with the AO demonstrator CANARY instrument.

La recherche de signes de vie extraterrestre par l'observation et la caractérisation d'exoplanètes est, entre autres, l'un des enjeux majeurs de l'astrophysique moderne. Cette quête se traduit de manière instrumentale par le développement de télescopes fournissant des résolutions angulaires supérieures à celles obtenues à l'heure actuelle. C'est pourquoi les projets de futurs très grands télescopes font usage de miroirs primaires dépassant les 30 mètres de diamètre. Leur conception est alors inévitablement basée, pour des raisons techniques et technologiques, sur une géométrie segmentée. De ce fait, la segmentation du miroir primaire implique une complexification des structures pupillaires du télescope. Dans le but d'atteindre les niveaux de qualité optique nécessaires aux applications scientifiques visées, la prise en compte et la correction des effets introduits par un mauvais alignement des segments est de prime importance puisque la résolution angulaire d'un télescope non cophasé serait équivalente à celle obtenue avec un segment individuel. Dans ce contexte, je développe dans cette thèse deux analyseurs de cophasage permettant de mesurer et de corriger les aberrations de piston, tip et tilt présentes sur une pupille segmentée. Le premier, nommé Self-Coherent Camera - Phasing Sensor (SCC-PS), est basé sur une analyse du signal en plan focal. Le second, nommé ZELDA - Phasing Sensor (ZELDA-PS), repose quant à lui sur une analyse du signal en plan pupille. Sont présentés dans ce manuscrit les résultats obtenus à l'aide de simulations numériques ainsi que ceux issus de l'implémentation de la SCC-PS sur un banc d'optique d'essai. / Searching for extraterrestrial life through the observation and characterization of exoplanets is, amongst others, one of the major goal of the modern astrophysics. This quest translate from an instrumental point of view to the development of telescope capable of reaching higher angular resolution that what is actually ongoing. That is why the future projects of extremely large telescopes are using primary mirrors exceeding the 30 meters in diameter. Their conception is consequently based, for technical and technological reasons, on a segmented geometry. The segmentation of the primary mirror therefore implies a growing complexity of the structure of its pupil. In order to reach the optical quality required by the sciences cases of interest, taking into account and correct for the effects introduced by a poor alignment of the segments is mandatory, as the angular resolution of a non-cophased telescope is equivalent to the one obtained with a single segment. In this context, I develop in this manuscript two cophasing sensors allowing to measure and correct for the aberrations of piston, tip and tilt present on a segmented pupil. The first one, the Self-Coherent Camera - Phasing Sensor (SCC-PS), is based on a focal plane analysis of the signal. The second one, the ZELDA - Phasing Sensor (ZELDA-PS), is based on a pupil plane analysis of the signal. The results obtained by means of numerical simulations and the first results coming from the implementation of the SCC-PS on an optical bench are presented in this manuscript.

Diffusion-weighted magnetic resonance imaging (MRI) has allowed unprecedented non-invasive mapping of brain neural connectivity in vivo by means of fiber tractography applications. Fiber tractography has emerged as a useful tool for mapping brain white matter connectivity prior to surgery or in an intraoperative setting. The advent of high angular resolution diffusion-weighted imaging (HARDI) techniques in MRI for fiber tractography has allowed mapping of fiber tracts in areas of complex white matter fiber crossings. Raw HARDI images, as a result of elevated diffusion-weighting, suffer from depressed signal-to-noise ratio (SNR) levels. The accuracy of fiber tractography is dependent on the performance of the various methods extracting dominant fiber orientations from the HARDI-measured noisy diffusivity profiles. These methods will be sensitive to and directly affected by the noise. In the first part of the thesis this issue is addressed by applying an objective and adaptive smoothing to the noisy HARDI data via generalized cross-validation (GCV) by means of the smoothing splines on the sphere method for estimating the smooth diffusivity profiles in three dimensional diffusion space. Subsequently, fiber orientation distribution functions (ODFs) that reveal dominant fiber orientations in fiber crossings are then reconstructed from the smoothed diffusivity profiles using the Funk-Radon transform. Previous ODF smoothing techniques have been subjective and non-adaptive to data SNR. The GCV-smoothed ODFs from our method are accurate and are smoothed without external intervention facilitating more precise fiber tractography. Diffusion-weighted MRI studies in amyotrophic lateral sclerosis (ALS) have revealed significant changes in diffusion parameters in ALS patient brains. With the need for early detection of possibly discrete upper motor neuron (UMN) degeneration signs in patients with early ALS, a HARDI study is applied in order to investigate diffusion-sensitive changes reflected in the diffusion tensor imaging (DTI) measures axial and radial diffusivity as well as the more commonly used measures fractional anisotropy (FA) and mean diffusivity (MD). The hypothesis is that there would be added utility in considering axial and radial diffusivities which directly reflect changes in the diffusion tensors in addition to FA and MD to aid in revealing neurodegenerative changes in ALS. In addition, applying adaptive smoothing via GCV to the HARDI data further facilitates the application of fiber tractography by automatically eliminating spurious noisy peaks in reconstructed ODFs that would mislead fiber tracking.

Cette thèse a pour objectif de comprendre les différents aspects de l'évolution des amas d’étoiles massives NGC3603 et R136 qui possèdent les étoiles les plus massives connues de l'univers local. L'analyse photométrique des noyaux de R136 et NGC3603 utilisant l’imagerie infrarouge de l’instrument SPHERE sur VLT et son système d’optique adaptative extrême de SPHERE, m’a permis de détecter pour la 1ière fois un grand nombre d’étoiles de faibles masse et luminosité au coeur de ces amas et pour la plupart au voisinage des étoiles les plus lumineuses et massives. La comparaison des données de SPHERE de NGC3603 à celles du HST montre l’absence de ségrégation de masse dans le noyau de cet amas. De plus la pente de la fonction de masse de cette région est la même que celle de la région suivante et similaire aux valeurs de la MF correspondant aux régions extérieures de l’amas connues jusqu’ici. L’amas R136 est partiellement résolu par SPHERE/IRDIS dans l’IR. La majorité de ses étoiles massives ont des compagnons visuels. En prenant compte des mesures spectroscopiques et photométriques et leurs erreurs sur l'extinction et l'âge des membres de l’amas, j’ai estimé une gamme de masse pour chaque étoile identifiée. La MF a été calculée pour différents âges ainsi que les erreurs sur les masses stellaires. J’ai simulé des séries d'images de R136 grâce au code Nbody6, et les ai comparées aux observations du HST/WFPC2. Ces simulations permettent de vérifier l'effet de la binarité initiale des étoiles de l’amas, la ségrégation de masse et l'évolution des étoiles sur l'évolution dynamique propre à R136. / This thesis aims at studying 2 massive clusters NGC3603 and R136, and the mechanisms that govern their physics, These clusters host the most massive stars known in the local universe so far and are important clues to understand the formation and fate of very massive star clusters. The manuscript outlines the photometric analysis of the core of R136 and NGC3603 on the basis of HST data in the visible and the VLT high dynamic imaging that I obtained in the infrared thanks to the SPHERE focal instrument operated since 2015 and its extreme Adaptive Optics, In an extensive photometric study of these data I discovered a significantly larger number of faint low-mass stars in the core of both these clusters compared to previous works. These stars are often detected in the vicinity of known massive bright objects. By comparing HST and SPHERE measures, NGC3603 does not show any signature of mass segregation in its core since the MF slope of the very core and the next radial bin are similarly flat and agree well with the MF found in previous works of the outer regions. On the other hand R136 is partially resolved using the SPHERE/IRDIS mode with most of the massive stars having visual companions. Considering the spectroscopic and photometric errors on the extinction and the age of cluster members, I estimate a mass range for each detected star. The MF is plotted at different ages with given errors on stellar masses. Finally I demonstrate that we need more resolution to go further on studying R136 which is 7-8 times further than NGC3603.