Coastal karst aquifers are important water resources, often providing the only source of freshwater to coastal communities for agriculture, industrial usage and human consumption. In order to implement management strategies and preventative measures for future perseveration of this resource, it is imperative to understand how coastal groundwater conditions are controlled by the interaction of freshwater/seawater on local and regional scales, but also over recent and past time periods. However, there is a limited resource of published hydrological data on recent aquifer conditions. In the Yucatán Peninsula and other anchialine environments, this lack of information inhibits the understanding of the spatial and temporal interaction of the meteoric and marine water masses. Documenting how the aquifer is responding to forcing mechanisms such as large precipitation events, seasonal cycles and short-term sea level rise (e.g. storm surge) will assist in understanding modern aquifer condition but also the interpretation of paleo-records. Utilization of water level and salinity sensors in strategic positions in the aquifer demonstrate that meteoric water mass salinity varies over wet and dry seasons with the movement of the halocline, but also on a short-term basis though large rainfall events. Salinity in the meteoric water mass is influenced by mixing with the marine water mass during intense precipitation events associated with Hurricane Ingrid (2013), Tropical Storm Hanna (2014) and a series of unnamed events in 2015. During wet periods, induced flow from increase precipitation causes turbulent mixing with the marine water mass, increasing salinity in the upper meteoric lens. On the contrary, during dry periods, mixing is reduced, therefore making the meteoric lens less saline. This contemporary understanding of meteoric/marine water mass dynamics can be applied to developing and calibrating the geochemical record of calcite rafts, calcite precipitation at the air-water interface of cave pools, as a hydrological proxy for aquifer conditions. Our monitoring of calcite raft formation, deposition and geochemistry shows that raft accumulations (e.g., raft piles/cones) can offer a good paleoenvironmental archive of changing hydrological conditions. Based on a 2-year observational record, results indicate that calcite raft precipitation/formation occurs continuously but with only minor biases with intense rainfall events altering supersaturation conditions in the surface waters. Testing the use of calcite rafts in sediment cores from Hoyo Negro show that geochemical analyses (87Sr/86Sr, δ18O, δ13C, Sr/Ca and Cl/Ca) show that meteoric water mass salinity varied during the Holocene (~ 8.5 Ka – present) likely due to changing rainfall and or cave passage geomorphology, which is coherent with other independent climate records. Prior to this study, calcite rafts have never been considered a paleo-hydrological archive for aquifer conditions, however, the consistency and cross-validation with independent records demonstrates great potential for future paleohydrological reconstructions. / Thesis / Doctor of Philosophy (PhD)

The presence of the sea ice diatom biomarker IP25 in Arctic marine sediments has been used in previous studies as a proxy for past spring sea ice occurrence and as an indicator of wider palaeoenvironmental conditions for different regions of the Arctic over various timescales. The current study describes a number of analytical and palaeoceanographic developments of the IP25 sea ice biomarker. First, IP25 was extracted and purified from Arctic marine sediments. This enabled the structure of IP25 to be confirmed and enabled instrumental (GC-MS) calibrations to be carried out so that quantitative measurements could be performed with greater accuracy. Second, palaeo sea ice reconstructions based on IP25 and other biomarkers were carried out for a suite of sub-Arctic areas within the Greenland, Norwegian and Barents Seas, each of which represent contrasting oceanographic and environmental settings. Further, an evaluation of some combined biomarker approaches (e.g. the PIP25 and DIP25 indices) for quantifying and/or refining definitions of sea ice conditions was carried out. Temporally, particular emphasis was placed on the characterisation of sea ice conditions during the Younger Dryas and the Holocene. Some comparisons with other proxies (e.g. foraminifera, IRD) were also made. A study of a sediment core from Andfjorden (69.16˚N, 16.25˚E), northern Norway, provided unequivocal evidence for the occurrence of seasonal sea ice conditions during the Younger Dryas. The onset (ca. 12.9 cal. kyr BP) and end (ca. 11.5 cal. kyr BP) of this stadial were especially clear in this location, while in a study from the Kveithola Trough (74.52˚N, 16.29˚E), western Barents Sea, these transitions were less apparent. This was attributed to the presence of colder surface waters and the occurrence of seasonal sea ice both before and after this stadial at higher latitudes. Some regional differences regarding the severity of the sea ice conditions were also observed, although an overall general picture was proposed, with more severe sea ice conditions during the early-mid Younger Dryas and less sea ice observed during the late Younger Dryas. A shift in the climate towards ice-free conditions was recorded in northern Norway during the early Holocene (ca. 11.5 – 7.2 cal. kyr BP). Milder conditions were also observed during the Holocene in the western Barents Sea, with three main climate periods observed. During the early Holocene (ca. 11.7 – 9.5 cal. kyr BP), the position of the spring ice edge was close to the study area which resulted in high productivity during summers. During the mid-late Holocene (ca. 9.5 – 1.6 cal. kyr BP), sea ice was mainly absent due to an increased influence of Atlantic waters and northward movement of the Polar Front. During the last ca. 1.6 cal. kyr BP, sea ice conditions were similar to those of the present day. In addition to the outcomes obtained from the Norwegian-Barents Sea region, comparison of biomarker and other proxy data from 3 short cores from Kangerdlugssuaq Trough (Denmark Strait/SE Greenland) with historical climate observations allowed the development of a model of sea ice conditions which was then tested for longer time-scales. It is suggested that the IP25 in sediments from this region is likely derived from drift ice carried from the Arctic Ocean via the East Greenland Current and that two main sea surface scenarios have existed over the last ca. 150 yr. From ca. AD 1850 – 1910, near perennial sea ice conditions resulted in very low primary productivity, while from ca. AD 1910 – 1986, local sea ice conditions were less severe with increased drift ice and enhanced primary productivity. This two-component model was subsequently developed to accommodate different sea surface conditions that existed during the retreat of the Greenland Ice Sheet during the deglaciation (ca. 16.3 – 10.9 cal. kyr BP).

High-resolution records of early Holocene deposits are rare, and as a consequence reconstruction of terrestrial environments very soon after the deglaciation has often been difficult. In this study the palaeoenvironmental conditions of early Holocene (c. 10600-7500 cal. yr BP) are reconstructed in the Värriötunturit area of northeastern Finland, using evidence from plant macrofossils and pollen preserved in a lake sediment sequence retrieved from the small lake Kuutsjärvi. Special emphasis is put on the environment immediately following the deglaciation as the base of the sediment sequence is rich in minerogenic material interpreted to have been deposited by meltwater pulses from the retreating ice sheet. The abundance and variety of fossil remains in these early meltwater deposits provide evidence for a very productive ice-marginal environment in the area between the lake and the ice sheet, and the presence of tree-type Betula macro remains as well as high percentage values of tree-type Betula pollen suggests that a subarctic birch forest established just a few years after the deglaciation. In the following centuries the birch forest around the lake became rich in an under growth of ferns, and at c. 9400 cal. yr BP a transition into a mixed pine and birch forest took place. Due to absence of indicator plant taxa in the sediment it was not possible to reconstruct temperature conditions for any parts of the sequence in this study. However, the rapid colonisation of birch forests suggests that the climate was warm already during deglaciation, which is also in accordance with climatic conditions reconstructed for the early Holocene in the nearby Sokli area just 10 km away, as well as in other parts of Fennoscandia and Russia.

Le refroidissement global et les oscillations entre cycles glaciaires et interglaciaires du Pléistocène inférieur ont pour conséquence une alternance entre milieux steppiques et forestiers, favorisant par là-même renouvellements et dispersions fauniques dont celui du genre Homo.Dans les interprétations paléoenvironnementales basées sur les assemblages fauniques, les cervidés, parmi les plus abondants mammifères, sont classiquement considérés comme forestiers, mais ce paradigme ne reflète pas la complexité de la diversité écologique réelle des cervidés.L'analyse texturale de 921 spécimens représentant les 5 cervidés actuels à l'écologie référencée a permis d'établir une robuste base de données et d'attester du lien significatif entre micro-usure dentaire et ressources végétales. L'analyse de 547 cervidés fossiles issus de 15 localités européennes souligne leur grande diversité écologique. Eucladoceros ctenoides et Metacervoceros rhenanus présentent une alimentation plastique. Leur analyse permet l'identification de réponses alimentaires adaptatives aux modifications environnementales liées aux oscillations climatiques. Ces deux cervidés, eurytopiques, constituent des indicateurs écologiques incontournables. La composante forestière supportée par la présence des cervidés est ici remise en cause ; les cervidés étant plus diversifiés écologiquement. L'analyse de la texture de la micro-usure dentaire des cervidés présents dans des sites européens, où la présence du genre Homo a été avancée, vise à identifier le type potentiel d'habitat favorable à sa dispersion en Eurasie. / The early Pleistocene is a period of global cooling and climatic oscillations punctuated by glacial and interglacial cycles. This period of climatic instability leads to an alternation of steppe and forest habitats resulting in faunal renewals and dispersals, including Homo dispersal.In paleoenvironmental reconstructions based on faunal assemblages, deer, which are among the most abundant mammals, are traditionally considered forest dwellers. However, this paradigm is far from reflecting the real complexity of deer ecological diversity.Via the textural analysis of 921 representatives of the 5 extant European deer with known ecology, a solid reference database has been setup. It attests of the significative link existing between dental micro-wear and vegetal resources. The analysis of 547 fossils from 15 European localities underlines the ecological diversity among fossil deer. Eucladoceros ctenoides and Metacervoceros rhenanus are plastic in their diet. The analysis of such deer allows the identification of dietary adaptive answers to environmental modifications resulting from climatic oscillations. Being eurytopic, they constitute essential proxies for paleoenvironmental reconstructions. The results challenge the link existing between the occurrence of deer and the presence of forest habitats, as deer are ecologically more diversified.The textural analysis of deer from European human bearing localities aims at characterizing potential habitats favorable toward Homo dispersion in Eurasia.

Introduction : la Terre au Trias inférieur et la reconquête après l’extinction fini-PermienneSitué après la limite entre le Paléozoïque et le Mésozoïque, le Trias inférieur est un intervalle court (~4Ma seulement ; Ovtcharova et al., 2006 ; Galfetti et al., 2007a ; Baresel et al., 2017). Lors de la transition entre le Permien et le Trias (PTB), la configuration tectonique de la Terre était différente, et la plupart des masses continentales étaient rassemblées en un seul super continent, la Pangée, lui-même entouré par un unique océan global, la Panthalassa (e.g., Murphy & Nance, 2008 ; Murphy et al., 2009 ; Stampfli et al., 2013).Lors de cette transition et durant le Trias inférieur, un évènement volcanique majeur, la mise en place de la grande province ignée de Sibérie (e.g., Ivanov et al., 2009, 2013), a conduit à l’émission de grande quantité de gaz à effet de serre (e.g., Galfetti et al., 2007b ; Romano et al., 2013). Ceux-ci ont contribué à l’acidification de la colonne d’eau et à l’augmentation des températures consécutivement à l’injection de CO2 dans l’atmosphère (e.g., Galfetti et al., 2007b ; Sun et al., 2012 ; Romano et al., 2013).Les perturbations environnementales qui en découlèrent ont eu des conséquences sur les milieux de dépôts associés à cette période, mais également sur les écosystèmes. Elles sont supposées avoir contribué à la mise en place de conditions délétères pour les organismes et avoir perduré durant tout le Trias inférieur, restreignant ainsi la rediversification biologique d’après-crise (e.g., Pruss & Bottjer, 2004 ; Fraiser & Bottjer, 2007 ; Bottjer et al., 2008 ; Algeo et al., 2011 ; Meyer et al., 2011 ; Bond & Wignall, 2014 ; Song et al., 2014).La limite PT fut le théâtre de la plus importante et la plus destructrice crise biologique du Phanérozoïque, et fut responsable de la disparition de plus de 90% des espèces marines (Raup, 1979), ou encore de la perte d’environ 50% des familles de tétrapodes continentaux (Benton & Newell, 2014), pour ne citer que ces deux exemples. De nombreux groupes ont été oblitérés durant cette extinction, comme par exemple les groupes caractéristiques du Paléozoïque tels que les coraux tabulés ou encore les trilobites (Sepkoski, 2002). Cependant, si la Vie a failli s’éteindre à l’aube du Mésozoïque, celle-ci a tout de même pu se reconstruire, au prix d’une rediversification communément admise comme lente et difficile dans des conditions environnementales délétères (e.g., Twitchett, 1999 ; Fraiser & Bottjer, 2007 ; Meyer et al., 2011 ; Chen & Benton, 2012). De grands paradigmes sont couramment associés à la rediversification du Trias inférieur (illustrés dans la Figure R.1a) :La présence de taxons « désastre », représentant des organismes opportunistes et généralistes qui auraient proliféré à la suite de la libération de niches écologiques laissées vacantes par les métazoaires disparus (e.g. ; Schubert & Bottjer, 1992, 1995 ; Rodland & Bottjer, 2001 ; He et al., 2007) ;Des faciès dit « anachroniques », composés de récifs exclusivement microbiens tels ceux trouvés dans les dépôts Précambriens (e.g., Schubert & Bottjer, 1992 ; Woods et al., 1999 ; Pruss & Bottjer, 2005 ; Pruss et al., 2005 ; Woods, 2009) ;Un effet « Lilliput », soit un nanisme généralisé des faunes présentes (e.g., Urbanek, 1993 ; Hautmann & Nützel, 2005 ; Payne, 2005 ; Twitchett, 2007 ; Fraiser et al., 2011 ; Metcalfe et al., 2011 ; Song et al., 2011) ;Une anoxie/euxinie généralisée dans le domaine marin, y compris littoral (e.g., Isozaki, 1997 ; Meyer et al., 2011 ; Song et al., 2012 ; Grasby et al., 2013).Fig. R.1 : a) Représentation synthétique des principaux paradigmes communément acceptés pour la rediversification biologique au cours du Trias inférieur. b) Représentation synthétique de ces mêmes paradigmes, révisés selon les données récemment recueillies dans le bassin ouest-américain (d’après Brayard, 2015). Inf. : inférieur ; m. : moyen ; s./sup. : supérieur (...). / In the wake of the Mesozoic, the Early Triassic (~251.95 Ma) corresponds to the aftermath of the most severe mass extinction of the Phanerozoic: the end-Permian crisis, when life was nearly obliterated (e.g., 90% of marine species disappeared). Consequences of this mass extinction are thought to have prevailed for several millions of years, implying a delayed recovery lasting the whole Early Triassic, if not more.Several paradigms have been established and associated to a delayed biotic recovery scenario expected to have resulted from harsh and deleterious paleoenvironments. These paradigms include a global anoxia in the marine realm, a “Lilliput” effect, and the presence of “disaster” taxa and “anachronistic” facies. However, recent works have shown a more complex global scheme for the Early Triassic recovery, and that a reevaluation of these paradigms was needed. Especially, new data from the western USA basin were critical in re-addressing these paradigms.The western USA basin is the result of a long tectono-sedimentary history that started 2 Gyr ago by the amalgamation of different lithospheric terranes forming its basement. A succession of orogenies and quiescence phases led to the formation of several successive basins in the studied area, and traces of this important geodynamical activity are still present today. The Sonoma orogeny occurred about 252 Ma in response to the eastward migration of drifting arcs toward the Laurentian craton. As a result, compressive constrains lead to the obduction of the Golconda Allochthon above the west-Pangea margin in present-day Nevada. Emplacement of this topographic load provoked the lithosphere flexuration beneath present-day Utah and Idaho to form the Sonoma Foreland Basin (SFB) studied in this work.The SFB record an excellent fossil and sedimentary record of the Early Triassic. A relatively high and complex biotic diversity has been observed there leading to describe a rapid and explosive recovery for some groups (e.g., ammonoids) in this basin after the end-Permian crisis. The sedimentary record is also well developed and has been studied extensively for a long time. Overall, these studies notably documented a marked difference between the northern and southern sedimentary succession within the basin, whose origin was poorly understood.This work therefore aims to characterize the various depositional settings in the Early Triassic SFB, as well as their paleogeographical distribution. Their controlling factors are also studied based on an original integrated method using sedimentological, paleontological, geochemical, geodynamical, structural and cartographic analyses. Aside the fossil and sedimentary discrepancy between the northern and the southern parts of the SFB, geochemical analyses provide new insights supporting this N/S dichotomy. This study also questions the validity of the geochemical signal as a tool for global correlation, as it appears to mainly reflect local forcing parameters.The geodynamical framework of the SFB was also investigated along with a numerical modelling of the rheological behavior of the basin. This work distinguishes the northern and southern parts of the basin based on markedly distinct tectonic subsidence rates during the Early Triassic: ~500 m/Myr in the northern part vs ~100m/Myr in the southern part. Origin of this remarkable difference is found in inherited properties of the basin basement itself. Indeed, different ages and therefore, rheological behaviors (i.e., rigidity to deformation and flexuration) of the basement lithospheric terranes act as a major controlling factor over the spatial distribution of the subsidence, and therefore of the sedimentary deposition. The lithosphere heritage is thus of paramount importance in the formation, development and spatio-temporal evolution of the SFB.This work leads to a new paleogeographical representation of the Sonoma Foreland Basin and its multi-parameter controlling factors (...).

Les structures de déformation pré-lithification s’enregistrent dans les sédiments meubles. Ces structures sont abondantes dans les domaines sous-glaciaires et marins profonds en raison du développement de surpressions de fluide. A partir de cas d’études choisis dans ces deux environnements, leurs implications sur les (1)reconstructions paléoenvironnementales, leurs impacts sur la (2) morphologie glaciaire, et sur les (3) propriétés pétrophysiques ont pu être définis.(1) L’analyse de ces structures de déformation a permis de mieux contraindre les paléoenvironnements sédimentaires. Ces structures de déformation ont été utilisées comme des «proxy » permettant d’estimer les variations de la vitesse d’écoulement, de l’épaisseur de glace, de la production d’eaux de fonte et de la position de la marge glaciaire.(2) Les séries sédimentaires des vallées tunnels ordoviciennes enregistrent la mise en place de nombreuses structures de déformation liées aux surpressions de fluides. L’analyse de ces structures a permis de proposer un nouveau modèle de creusement des vallées tunnels induits par des pressions de fluides élevées. Ce modèle de creusement, lié aux surpressions de fluide, est favorisé dans les zones d’inter ice-stream. A l’inverse, sous les ice-stream, l’écoulement des eaux de fonte se produit à l’interface glace-substrat et favorise d’autres modèles de formation des vallées tunnels.(3) Les processus de remobilisation sédimentaire ont un impact sur les propriétés pétrophysiques des réservoirs sableux. Les études pétrophysiques menées sur des grès déposés en environnements marins profonds et glaciaires ont permis de mettre en évidence l’impact des surpressions de fluides sur les propriétés réservoirs des sables. Les processus de fluidisation sont capable de créer de bons réservoirs, tandisque les processus d’élutriations ont tendance a réduire la porosité/perméabilité. / Soft-sediment deformation structures (SSDs) occur in unconsolidated sediments, during or shortly after deposition. SSDs are abundant in subglacial and deep-marine environments because of the development of fluid overpressure. Case studies of these two sedimentary environments were used (1) to reconstruct palaeoenvironments from SSDS, and (2) to define the impacts of SSDS on glacial morphologies and (3) petrophysical properties.(1) Analyses of strain regimes, deformation mechanisms, and chronologies in SSDs served to improve palaeoenvironmental reconstructions. These structures were used as proxys to estimate variations of ice flow velocities, ice thickness, meltwater production, and position of the ice margin.(2) The sedimentary series of ordovician tunnel valleys record numerous SSDs induced by fluid overpressure. A new model of tunnel valley formation controlled by the increase of porewater pressure in the bed is proposed. This model of formation occurs in inter-ice stream zones, where meltwater is transferred to the substratum. In ice-stream corridors, meltwater circulates at the ice-bed interface and promotes the formation of tunnel valleys controlled by meltwater processes.(3) Remobilisation processes triggered by the increase of fluid pressure have an impact on the granular framework and on the geometry of reservoirs. Petrophysical studies of subglacial and deep-marine sandstones demonstrated the impact of fluid overpressure on reservoir properties. Processes of fluidisation are responsible for the increase in porosity/permeability, while elutriation processes lead to a decrease in these petrophysical properties.

Much research effort has been devoted to producing algorithms that contribute directly or indirectly to the extraction of 3D information from a wide variety of types of scenes and conditions of image capture. The research work presented in this thesis is aimed at three distinct applications in this area: interactively extracting 3D points from a pair of uncalibrated images in a flexible way; finding corresponding points automatically in high resolution images, particularly those of archaeological scenes captured from a freely moving light aircraft; and improving a correlation approach to dense disparity mapping leading to 3D surface reconstructions. The fundamental concepts required to describe the principles of stereo vision, the camera models, and the epipolar geometry described by the fundamental matrix are introduced, followed by a detailed literature review of existing methods. An interactive system for viewing a scene via a monochrome or colour anaglyph is presented which allows the user to choose the level of compromise between amount of colour and ghosting perceived by controlling colour saturation, and to choose the depth plane of interest. An improved method of extracting 3D coordinates from disparity values when there is significant error is presented. Interactive methods, while very flexible, require significant effort from the user finding and fusing corresponding points and the thesis continues by presenting several variants of existing scale invariant feature transform methods to automatically find correspondences in uncalibrated high resolution aerial images with improved speed and memory requirements. In addition, a contribution to estimating lens distortion correction by a Levenberg Marquard based method is presented; generating data strings for straight lines which are essential input for estimating lens distortion correction. The remainder of the thesis presents correlation based methods for generating dense disparity maps based on single and multiple image rectifications using sets of automatically found correspondences and demonstrates improvements obtained using the latter method. Some example views of point clouds for 3D surfaces produced from pairs of uncalibrated images using the methods presented in the thesis are included.

The decreasing costs of next generation sequencing technologies and the increasing speeds at which they work have lead to an abundance of 'omic datasets. The need for tools and methods to analyze, annotate, and model these datasets to better understand biological systems is growing. Here we present a novel software pipeline to reconstruct the metabolic model of an organism in silico starting from its genome sequence and a novel compilation of biological databases to better serve the generation of metabolic models. We validate these methods using five Gardnerella vaginalis strains and compare the gene annotation results to NCBI and the FBA results to Model SEED models. We found that our gene annotations were larger and highly similar in terms of function and gene types to the gene annotations downloaded from NCBI. Further, we found that our FBA models required a minimal addition of transport reactions, sources, and escapes indicating that our draft pathway models were very complete. We also found that on average our solutions contained more reactions than the models obtained from Model SEED due to a large amount of baseline reactions and gene products found in ASGARD.

Selon le Groupe Intergouvernemental d'experts sur l'Évolution du Climat (GIEC), il est important de connaitre le climat passé afin de replacer le changement climatique actuel dans son contexte. Ainsi, de nombreux chercheurs ont travaillé à l'établissement de procédures permettant de reconstituer les températures ou les précipitations passées à l'aide d'indicateurs climatiques indirects. Ces procédures sont généralement basées sur des méthodes statistiques mais l'estimation des incertitudes associées à ces reconstructions reste une difficulté majeure. L'objectif principal de cette thèse est donc de proposer de nouvelles méthodes statistiques permettant une estimation précise des erreurs commises, en particulier dans le cadre de reconstructions à partir de données sur les cernes d'arbres.De manière générale, les reconstructions climatiques à partir de mesures de cernes d'arbres se déroulent en deux étapes : l'estimation d'une variable cachée, commune à un ensemble de séries de mesures de cernes, et supposée climatique puis l'estimation de la relation existante entre cette variable cachée et certaines variables climatiques. Dans les deux cas, nous avons développé une nouvelle procédure basée sur des modèles bayésiens semi- paramétriques. Tout d'abord, concernant l'extraction du signal commun, nous proposons un modèle hiérarchique semi-paramétrique qui offre la possibilité de capturer les hautes et les basses fréquences contenues dans les cernes d'arbres, ce qui était difficile dans les études dendroclimatologiques passées. Ensuite, nous avons développé un modèle additif généralisé afin de modéliser le lien entre le signal extrait et certaines variables climatiques, permettant ainsi l'existence de relations non-linéaires contrairement aux méthodes classiques de la dendrochronologie. Ces nouvelles méthodes sont à chaque fois comparées aux méthodes utilisées traditionnellement par les dendrochronologues afin de comprendre ce qu'elles peuvent apporter à ces derniers. / As stated by the Intergovernmental Panel on Climate Change (IPCC), it is important to reconstruct past climate to accurately assess the actual climatic change. A large number of researchers have worked to develop procedures to reconstruct past temperatures or precipitation with indirect climatic indicators. These methods are generally based on statistical arguments but the estimation of uncertainties associated to these reconstructions remains an active research field in statistics and in climate studies. The main goal of this thesis is to propose and study novel statistical methods that allow a precise estimation of uncertainties when reconstructing from tree-ring measurements data. Generally, climatic reconstructions from tree-ring observations are based on two steps. Firstly, a hidden environmental hidden variable, common to a collection of tree-ring measurements series, has to be adequately inferred. Secondly, this extracted signal has to be explained with the relevant climatic variables. For these two steps, we have opted to work within a semi-parametric bayesian framework that reduces the number of assumptions and allows to include prior information from the practitioner. Concerning the extraction of the common signal, we propose a model which can catch high and low frequencies contained in tree-rings. This was not possible with previous dendroclimatological methods. For the second step, we have developed a bayesian Generalized Additive Model (GAM) to explore potential links between the extracted signal and some climatic variables. This allows the modeling of non-linear relationships among variables and strongly differs from past dendrochronological methods. From a statistical perspective, a new selection scheme for bayesien GAM was also proposed and studied.

L'imagerie par résonance magnétique (IRM) est une technique d'imagerie non invasive et non ionisante qui permet d'imager et de discriminer les tissus mous grâce à une bonne sensibilité de contraste issue de la variation de paramètres physiques (T$_1$, T$_2$, densité de protons) spécifique à chaque tissu. Les données sont acquises dans l'espace-$k$, correspondant aux fréquences spatiales de l'image. Des contraintes physiques et matérielles contraignent le mode de fonctionnement des gradients de champ magnétique utilisés pour acquérir les données. Ainsi, ces dernières sont obtenues séquentiellement le long de trajectoires assez régulières (dérivée et dérivée seconde bornées). En conséquence, la durée d'acquisition augmente avec la résolution recherchée de l'image. Accélérer l'acquisition des données est crucial pour réduire la durée d'examen et ainsi améliorer le confort du sujet, diminuer les coûts, limiter les distorsions dans l'image~(e.g., dues au mouvement), ou encore augmenter la résolution temporelle en IRM fonctionnelle. L'échantillonnage compressif permet de sous-échantillonner l'espace-$k$, et de reconstruire une image de bonne qualité en utilisant une hypothèse de parcimonie de l'image dans une base d'ondelettes. Les théories d'échantillonnage compressif s'adaptent mal à l'IRM, même si certaines heuristiques ont permis d'obtenir des résultats prometteurs. Les problèmes rencontrés en IRM pour l'application de cette théorie sont i) d'une part, les bases d'acquisition~(Fourier) et de représentation~(ondelettes) sont cohérentes ; et ii) les schémas actuellement couverts par la théorie sont composés de mesures isolées, incompatibles avec l'échantillonnage continu le long de segments ou de courbes. Cette thèse vise à développer une théorie de l'échantillonnage compressif applicable à l'IRM et à d'autres modalités. D'une part, nous proposons une théorie d'échantillonnage à densité variable pour répondre au premier point. Les échantillons les plus informatifs ont une probabilité plus élevée d'être mesurés. D'autre part, nous proposons des schémas et concevons des trajectoires qui vérifient les contraintes d'acquisition tout en parcourant l'espace-$k$ avec la densité prescrite dans la théorie de l'échantillonnage à densité variable. Ce second point étant complexe, il est abordé par une séquence de contributions indépendantes. D'abord, nous proposons des schémas d'échantillonnage à densité variables le long de courbes continues~(marche aléatoire, voyageur de commerce). Ensuite, nous proposons un algorithme de projection sur l'espace des contraintes qui renvoie la courbe physiquement plausible la plus proche d'une courbe donnée~(e.g., une solution du voyageur de commerce). Nous donnons enfin un algorithme de projection sur des espaces de mesures qui permet de trouver la projection d'une distribution quelconque sur l'espace des mesures porté par les courbes admissibles. Ainsi, la courbe obtenue est physiquement admissible et réalise un échantillonnage à densité variable. Les résultats de reconstruction obtenus en simulation à partir de cette méthode dépassent ceux associées aux trajectoires d'acquisition utilisées classiquement~(spirale, radiale) de plusieurs décibels (de l'ordre de 3~dB) et permettent d'envisager une implémentation prochaine à 7~Tesla notamment dans le contexte de l'imagerie anatomique haute résolution. / Magnetic Resonance Imaging~(MRI) is a non-invasive and non-ionizing imaging technique that provides images of body tissues, using the contrast sensitivity coming from the magnetic parameters (T$_1$, T$_2$ and proton density). Data are acquired in the $k$-space, corresponding to spatial Fourier frequencies. Because of physical constraints, the displacement in the $k$-space is subject to kinematic constraints. Indeed, magnetic field gradients and their temporal derivative are upper bounded. Hence, the scanning time increases with the image resolution. Decreasing scanning time is crucial to improve patient comfort, decrease exam costs, limit the image distortions~(eg, created by the patient movement), or decrease temporal resolution in functionnal MRI. Reducing scanning time can be addressed by Compressed Sensing~(CS) theory. The latter is a technique that guarantees the perfect recovery of an image from undersampled data in $k$-space, by assuming that the image is sparse in a wavelet basis. Unfortunately, CS theory cannot be directly cast to the MRI setting. The reasons are: i) acquisition~(Fourier) and representation~(wavelets) bases are coherent and ii) sampling schemes obtained using CS theorems are composed of isolated measurements and cannot be realistically implemented by magnetic field gradients: the sampling is usually performed along continuous or more regular curves. However, heuristic application of CS in MRI has provided promising results. In this thesis, we aim to develop theoretical tools to apply CS to MRI and other modalities. On the one hand, we propose a variable density sampling theory to answer the first inpediment. The more the sample contains information, the more it is likely to be drawn. On the other hand, we propose sampling schemes and design sampling trajectories that fulfill acquisition constraints, while traversing the $k$-space with the sampling density advocated by the theory. The second point is complex and is thus addressed step by step. First, we propose continuous sampling schemes based on random walks and on travelling salesman~(TSP) problem. Then, we propose a projection algorithm onto the space of constraints that returns the closest feasible curve of an input curve~(eg, a TSP solution). Finally, we provide an algorithm to project a measure onto a set of measures carried by parameterizations. In particular, if this set is the one carried by admissible curves, the algorithm returns a curve which sampling density is close to the measure to project. This designs an admissible variable density sampler. The reconstruction results obtained in simulations using this strategy outperform existing acquisition trajectories~(spiral, radial) by about 3~dB. They permit to envision a future implementation on a real 7~T scanner soon, notably in the context of high resolution anatomical imaging.