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This thesis addresses different aspects of learning for computational Magnetic Resonance Imaging. The first chapter is an introduction to computational imaging and it illustrates through the case of MRI the developments that have guided this field. It also contains a pedagogical introduction to inverse problems and the associated reconstruction methods. This introduction traces the early linear reconstruction methods, the emergence of non-linear methods and recent advances in reconstruction methods that are learned with neural networks. The following chapters are based on different publications or preprints and, although links are made between the different chapters, they can be read independently of each other. The second chapter deals with spurious minimizers in the optimization of non-uniform Fourier sampling schemes. The motivation is the optimization of MRI sampling schemes for a chosen reconstruction method and for a specific image database. This chapter shows that this type of problem has a combinatorial number of minimizers that can disappear with the large number of images in the training database but that classical MRI databases do not contain enough images to expect this phenomenon to appear. The third chapter proposes a method to globalize the convergence for the optimization of Fourier sampling schemes. This drastically reduces the numerical cost of the optimization while maintaining a significant gain in the image quality. The fourth chapter deals with the training of neural networks that are adaptive to changes in the physics of the acquisition. This formalism allows to solve several blind inverse problems. Finally, the fifth chapter tackles the optimization of neural networks. It proposes a method to scale the learning rate and this opens the way to automate the choice of the hyperparameters during the training phase.; Cette thèse traite d'aspects liés à l'apprentissage pour l'Imagerie par Résonance Magnétique computationnelle. Le premier chapitre est une introduction à l'imagerie computationnelle et illustre à travers le cas de l'IRM les évolutions ayant guidé ce domaine. Il contient aussi une introduction pédagogique aux problèmes inverses et les méthodes de reconstruction associées. Cette introduction retrace les premières méthodes de reconstruction linéaires, l'apparition de méthodes non linéaires et les méthodes récentes de reconstruction apprises à l'aide de réseaux de neurones. Le second chapitre traite des minimiseurs parasites dans l'optimisation de schémas d'échantillonnage de Fourier dont la motivation est l'optimisation de schémas d'échantillonnage pour l'IRM pour une méthode de reconstruction choisie et pour une base de données d'images spécifique. Ce chapitre montre que ce type de problème a un nombre combinatoire de minimiseurs qui peuvent disparaître avec le grand nombre d'images dans la base de données mais que les bases de données classiques d'IRM ne contiennent pas assez d'images pour espérer voir apparaître ce phénomène. Le troisième chapitre propose une méthode de globalisation de la convergence pour l'optimisation de schémas de Fourier. Cela permet de grandement réduire le coût numérique de l'optimisation tout en conservant un gain dans l'amélioration des images. Le quatrième chapitre traite de l'entraînement de réseaux de neurones "unrolled" adaptatifs à des changements dans la physique de l'acquisition. Ce formalisme permet de résoudre plusieurs problèmes inverses aveugles. Enfin, le cinquième chapitre traite des méthodes d'optimisation pour des réseaux de neurones de manière générale. Il propose une méthode permettant d'introduire une mise à l'échelle du pas pour l'optimisation de réseaux de neurones. Cela ouvre la voie à une automatisation du choix des hyperparamètres lors de l'entraînement.

Neural networks are full of promises for the resolution of ill-posed inverse problems. In particular, physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms, for their superior quality. The aim of this paper is twofold. First we show a limitations of these networks: when trained on a given forward operator, they do not generalize well to a different one. Second, we show that training the network with a family of forward operators allows to solve the adaptivity problem without compromising the reconstruction quality significantly. All our experiments are carefully devised on partial Fourier sampling problems arising in magnetic resonance imaging (MRI).

Chemically, biologically, or radiologically contaminated surfaces can be treated using colloidal “vacuumable” gels containing alumina particles as a thickening agent, decontaminating solutions to inhibit/eliminate biological and chemical contaminants, and Pluronic PE 6200 as a surfactant to adjust the gel’s physicochemical properties. These gels have been shown to remain efficient even after prolonged storage. In the present study, the properties of gels with different surfactant concentrations were monitored over several months using rheological analyses, contact angle measurements, and ion chromatography. Results show that the surfactant reacts with the hypochlorite ions in the decontaminating solution. This leads to sedimentation, which modifies the rheological properties of the gel. Increasing the surfactant concentration ensures the physicochemical properties of the gel are preserved for longer, but because the surfactant reacts with the hypochlorite ions, the concentration of the latter decreases drastically and thus so do the decontamination properties of the gel. There is therefore a trade-off between the efficiency of the gel against chemical and biological contamination at a given time and how long its physicochemical properties are preserved, with the optimal balance depending on its intended use.

International audience; Chemically, biologically or radiologically-contaminated surfaces can be treated using colloidal "vacuumable" gels containing alumina particles as a thickening agent, decontaminating solutions to inhibit/eliminate biological and chemical contaminants, and Pluronic PE 6200 as a surfactant to adjust the gel's physicochemical properties. These gels have been shown to remain efficient even after prolonged storage. In the present study, the properties of gels with different surfactant concentrations were monitored over several months using rheological analyses, contact angle measurements and ion chromatography. Results show that the surfactant reacts with the hypochlorite ions in the decontaminating solution. This leads to sedimentation, which modifies the rheological properties of the gel. Increasing the surfactant concentration ensures the physicochemical properties of the gel are preserved for longer, but because the surfactant reacts with the hypochlorite ions, the concentration of the latter decreases drastically and thus so do the decontamination properties of the gel. There is therefore a trade-off between the efficiency of the gel against chemical and biological contamination at a given time and how long its physicochemical properties are preserved, the optimal balance depending on its intended use.

International audience; Chemical, biological, radiological and nuclear (CBRN) accidents or attacks typically disseminate contaminants inside and outside buildings and structures whose surfaces have to be decontaminated. This paper describes an innovative colloidal gel formulation and its effects against CBR threat agents and also against prion contaminations. The gel’s rheological properties ensure it remains attached even to vertical surfaces. The gel then dries with the contaminants trapped inside, leaving behind non-dusting solid residues that are easy to recover by brushing or vacuum cleaning. The results obtained here on different formulations show that decontamination proceeds in two steps. Contaminants are first solubilized or absorbed into the gel thanks to the efficient wetting of the surface by the gel. Chemical and biological agents are then neutralized by the NaOH and hypochlorite ions in the gel. This article demonstrates the efficiency of this CBR gel against Bacillus anthracis, the chemical agents sulfur mustard, VX, and soman, 137Cs, and prion proteins.