Num cenário em que dispositivos de aquisição de imagens e vídeo possuem recursos limitados ou as imagens disponíveis não possuem boa qualidade, as técnicas de super-resolução (SR) apresentam uma excelente alternativa para melhorar a qualidade das imagens. Nesta tese é apresentada uma proposta para super-resolução de imagem única que combina os benefícios da interpolação no domínio da transformada DCT e a eficiência dos métodos de reconstrução baseados no conceito de representação esparsa de sinais. A proposta busca aproveitar as melhorias já alcançadas na qualidade e eficiência computacional dos principais algoritmos de super-resolução existentes. O método de super-resolução proposto implementa algumas melhorias nas etapas de treinamento e reconstrução da imagem final. Na etapa de treinamento foi incluída uma nova etapa de extração de características utilizando técnicas de aguçamento por máscara de nitidez e construção de um novo dicionário. Esta estratégia busca extrair mais informações estruturais dos fragmentos de baixa e alta resolução do conjunto de treinamento e ao mesmo tempo reduzir o tamanho dos dicionários. Outra importante contribuição foi a inclusão de um processo iterativo e escalonável no algoritmo, reinserindo no conjunto de treinamento e na etapa de reconstrução, uma imagem de alta resolução obtida numa primeira iteração. Esta solução possibilitou uma melhora na qualidade da imagem de alta resolução final utilizando poucas imagens no conjunto de treinamento. As simulações computacionais demonstraram a capacidade do método proposto em produzir imagens com qualidade e com tempo computacional reduzido. / In a scenario in which the acquisition systems have limited resources or available images do not have good quality, the super-resolution (SR) techniques have become an excellent alternative for improving the image quality. In this thesis, we propose a single-image super-resolution (SR) method that combines the benefits of the DCT interpolation and efficiency of sparse representation method for image reconstruction. Also, the proposed method seeks to take advantage of the improvements already achieved in quality and computational efficiency of the existing SR algorithms. The proposed method implements some improvements in the dictionary training and the reconstruction process. A new dictionary was built by using an unsharp mask technique to characteristics extraction. Simultaneously, this strategy aim to extract more structural information of the low resolution and high resolution patches and reduce the dictionaries size. Another important contribution was the inclusion of an iterative and scalable process by reinserting the HR image obtained of first iteration. This solution aim to improve the quality of the final HR image using a few images in the training set. The results have demonstrated the ability of the proposed method to produce high quality images with reduced computational time.

Current single molecule localisation microscopy methods allow for multicolour imaging of macromolecules in cells, and for a degree quantification on molecule numbers in one colour. However, that has not yet been an attempt to develop tools capable of quantitative imaging with multiple colours in cells. This work addressed this challenge by designing linker peptides with chemospecific groups to allow attachment of activator and emitter dyes for STORM imaging, and a targeting module. The design ensured a stoichiometric ratio of targeting module to activator and emitter dyes. Peptides with HaloTag ligands attached were labelled with various activator and emitter pairs and used to label HaloTag fusions of S. pombe and mouse embryonic stem cells. These peptides were found to bind non-specifically to various areas of both cell types, and did not localise to HaloTag protein, whereas controls did. Another peptide was also labelled with activator-emitter pairs and attached to expressed anti-GFP and ant-mCherry nanobodies via native chemical ligation. The labelled anti-GFP nanobody was to demonstrate ensemble and single molecule imaging in S. pombe, as well as characterisation on single molecule surfaces in comparison to a conventional randomly labelled antibody. The stoichiometrically labelled nanobody had a more consistent number of photons detected per localisation, number of localisation per molecule and number of blinks per molecule, which implied that it could be more useful than randomly labelled nanobodies for counting experiments. It was also shown to be capable of specific laser activation for STORM imaging with both an Alexa405Cy5 and Cy3Cy5 pairs. These anti-GFP and anti-mCherry nanobodies and peptide linker are new tools for both counting and multicolour imaging in super-resolution, which could be widely applied to constructs that are already tagged with GFP or mCherry.

This work explores if combining information from multiple Magnetic Resonance Imaging (MRI) modalities provides improved interpretation of brain biological architecture as each MR modality can reveal different characteristics of underlying anatomical structures. Structural MRI provides a means for high-resolution quantitative study of brain morphometry. Diffusion-weighted MR imaging (DWI) allows for low-resolution modeling of diffusivity properties of water molecules. Structural and diffusion-weighted MRI modalities are commonly used for monitoring the biological architecture of the brain in normal development or neurodegenerative disease processes. Structural MRI provides an overall map of brain tissue organization that is useful for identifying distinct anatomical boundaries that define gross organization of the brain. DWI models provide a reflection of the micro-structure of white matter (WM), thereby providing insightful information for measuring localized tissue properties or for generating maps of brain connectivity. Multispectral information from different structural MR modalities can lead to better delineation of anatomical boundaries, but careful considerations should be taken to deal with increased partial volume effects (PVE) when input modalities are provided in different spatial resolutions. Interpretation of diffusion-weighted MRI is strongly limited by its relatively low spatial resolution. PVE's are an inherent consequence of the limited spatial resolution in low-resolution images like DWI. This work develops novel methods to enhance tissue classification by addressing challenges of partial volume effects encountered from multi-modal data that are provided in different spatial resolutions. Additionally, this project addresses PVE in low-resolution DWI scans by introducing a novel super-resolution reconstruction approach that uses prior information from multi-modal structural MR images provided in higher spatial resolution. The major contributions of this work include: 1) Enhancing multi-modal tissue classification by addressing increased PVE when multispectral information come from different spatial resolutions. A novel method was introduced to find pure spatial samples that are not affected by partial volume composition. Once detecting pure samples, we can safely integrate multi-modal information in training/initialization of the classifier for an enhanced segmentation quality. Our method operates in physical spatial domain and is not limited by the constraints of voxel lattice spaces of different input modalities. 2) Enhancing the spatial resolution of DWI scans by introducing a novel method for super-resolution reconstruction of diffusion-weighted imaging data using high biological-resolution information provided by structural MRI data such that the voxel values at tissue boundaries of the reconstructed DWI image will be in agreement with the actual anatomical definitions of morphological data. We used 2D phantom data and 3D simulated multi-modal MR scans for quantitative evaluation of introduced tissue classification approach. The phantom study result demonstrates that the segmentation error rate is reduced when training samples were selected only from the pure samples. Quantitative results using Dice index from 3D simulated MR scans proves that the multi-modal segmentation quality with low-resolution second modality can approach the accuracy of high-resolution multi-modal segmentation when pure samples are incorporated in the training of classifier. We used high-resolution DWI from Human Connectome Project (HCP) as a gold standard for super-resolution reconstruction evaluation to measure the effectiveness of our method to recover high-resolution extrapolations from low-resolution DWI data using three evaluation approaches consisting of brain tractography, rotationally invariant scalars and tensor properties. Our validation demonstrates a significant improvement in the performance of developed approach in providing accurate assessment of brain connectivity and recovering the high-resolution rotationally invariant scalars (RIS) and tensor property measurements when our approach was compared with two common methods in the literature. The novel methods of this work provide important improvements in tools that assist with improving interpretation of brain biological architecture. We demonstrate an increased sensitivity for volumetric and diffusion measures commonly used in clinical trials to advance our understanding of both normal development and disease induced degeneration. The improved sensitivity may lead to a substantial decrease in the necessary sample size required to demonstrate statistical significance and thereby may reduce the cost of future studies or may allow more clinical and observational trials to be performed in parallel.

Depuis quelques temps, les physiciens théoriciens de la matière condensée sont confrontés à un problème majeur : la puissance de calcul nécessaire pour simuler numériquement et étudier certains systèmes à N corps est insuffisante. Comme le contrôle et l’utilisation des systèmes d’atomes ultra-froids se sont développés de manière importante,principalement durant les deux dernières décennies, nous sommes peut-être en mesure d eproposer une solution alternative : utiliser des atomes ultra-froids piégés dans des réseaux optiques en tant que simulateur quantique. En effet, la physique des électrons se déplaçant sur la structure cristalline d’un solide, ainsi que celle des atomes piégés dans des réseaux optiques, sont toutes les deux décrites par le même modèle de Fermi-Hubbard, qui est une présentation simplifiée du comportement des fermions sur un réseau périodique. Les simulateurs quantiques peuvent donc simuler des propriétés électriques des matériaux, telle sque la conductivité ou le comportement isolant, et potentiellement aussi des propriété smagnétiques telles que l’ordre antiferromagnétique.L’expérience AUFRONS, sur laquelle j’ai travaillé pendant mon doctorat, a pour but d’étudie rla physique des fermions fortement corrélés, avec un simulateur quantique basé sur l’utilisation d’atomes ultra-froids de rubidium 87 et de potassium 40, piégés dans le potentiel nanostructuré des réseaux optiques bidimensionnels, générés en champ proche. Pour détecter la distribution atomique à d’aussi courtes distances, nous avons développé une technique d’imagerie novatrice, qui nous permettra de contourner la limite de diffraction. Une fois terminé, notre système d’imagerie pourrait potentiellement détecter et identifier des sites individuels du réseau optique sub-longueur d’onde.Dans ce manuscrit, je décris le travail que j’ai effectué pour construire l’expérience AUFRONS,ainsi que l’étude de faisabilité que j’ai réalisée pour la technique d’imagerie à super-résolution. / For some time now, theoretical physicists in condensed matter face a majorproblem: the computing power needed to numerically simulate and study some interactingmany-body systems is insufficient. As the control and use of ultracold atomic systems hasexperimented a significant development in recent years, an alternative to this problem is to usecold atoms trapped in optical lattices as a quantum simulator. Indeed, the physics of electronsmoving on a crystalline structure of a solid, and the one of trapped atoms in optical lattices areboth described by the same model, the Fermi-Hubbard model, which is a simplifiedrepresentation of fermions moving on a periodic lattice. The quantum simulators can thusreproduce the electrical properties of materials such as conductivity or insulating behavior, andpotentially also the magnetic ones such as antiferromagnetism.The AUFRONS experiment, in which I worked during my PhD, aims at building a quantumsimulator based on cooled atoms of 87Rb and 40K trapped in near field nanostructured opticalpotentials. In order to detect the atom distribution at such small distances, we have developedan innovative imaging technique for getting around the diffraction limit. This imaging systemcould potentially allow us to detect single-site trapped atoms in a sub-wavelength lattice.In this thesis, I introduce the work I have done for building the AUFRONS experiment, as wellas the feasability study that I did for the super-resolution imaging technique.

La ''super-résolution'' est définie comme une classe de techniques qui améliorent la résolution spatiale d’images. Les méthodes de super-résolution peuvent être subdivisés en méthodes à partir d’une seule image et à partir de multiple images. Cette thèse porte sur le développement d’algorithmes basés sur des théories mathématiques pour résoudre des problèmes de super-résolution à partir d’une seule image. En effet, pour estimer un’image de sortie, nous adoptons une approche mixte : nous utilisons soit un dictionnaire de « patches » avec des contraintes de parcimonie (typique des méthodes basées sur l’apprentissage) soit des termes régularisation (typiques des méthodes par reconstruction). Bien que les méthodes existantes donnent déjà de bons résultats, ils ne prennent pas en compte la géométrie des données dans les différentes tâches. Par exemple, pour régulariser la solution, pour partitionner les données (les données sont souvent partitionnées avec des algorithmes qui utilisent la distance euclidienne comme mesure de dissimilitude), ou pour apprendre des dictionnaires (ils sont souvent appris en utilisant PCA ou K-SVD). Ainsi, les méthodes de l’état de l’art présentent encore certaines limites. Dans ce travail, nous avons proposé trois nouvelles méthodes pour dépasser ces limites. Tout d’abord, nous avons développé SE-ASDS (un terme de régularisation basé sur le tenseur de structure) afin d’améliorer la netteté des bords. SE-ASDS obtient des résultats bien meilleurs que ceux de nombreux algorithmes de l’état de l’art. Ensuite, nous avons proposé les algorithmes AGNN et GOC pour déterminer un sous-ensemble local de données d’apprentissage pour la reconstruction d’un certain échantillon d’entrée, où l’on prend en compte la géométrie sous-jacente des données. Les méthodes AGNN et GOC surclassent dans la majorité des cas la classification spectrale, le partitionnement de données de type « soft », et la sélection de sous-ensembles basée sur la distance géodésique. Ensuite, nous avons proposé aSOB, une stratégie qui prend en compte la géométrie des données et la taille du dictionnaire. La stratégie aSOB surpasse les méthodes PCA et PGA. Enfin, nous avons combiné tous nos méthodes dans un algorithme unique, appelé G2SR. Notre algorithme montre de meilleurs résultats visuels et quantitatifs par rapport aux autres méthodes de l’état de l’art. / Image super-resolution is defined as a class of techniques that enhance the spatial resolution of images. Super-resolution methods can be subdivided in single and multi image methods. This thesis focuses on developing algorithms based on mathematical theories for single image super-resolution problems. Indeed, in order to estimate an output image, we adopt a mixed approach: i.e., we use both a dictionary of patches with sparsity constraints (typical of learning-based methods) and regularization terms (typical of reconstruction-based methods). Although the existing methods already perform well, they do not take into account the geometry of the data to: regularize the solution, cluster data samples (samples are often clustered using algorithms with the Euclidean distance as a dissimilarity metric), learn dictionaries (they are often learned using PCA or K-SVD). Thus, state-of-the-art methods still suffer from shortcomings. In this work, we proposed three new methods to overcome these deficiencies. First, we developed SE-ASDS (a structure tensor based regularization term) in order to improve the sharpness of edges. SE-ASDS achieves much better results than many state-of-the-art algorithms. Then, we proposed AGNN and GOC algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. AGNN and GOC methods outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings. Next, we proposed aSOB strategy which takes into account the geometry of the data and the dictionary size. The aSOB strategy outperforms both PCA and PGA methods. Finally, we combine all our methods in a unique algorithm, named G2SR. Our proposed G2SR algorithm shows better visual and quantitative results when compared to the results of state-of-the-art methods.

Fluorescence correlation spectroscopy has become a standard technique for modern biophysics and single molecule spectroscopy research. Here is presented a novel widefield extension of the established single-point technique. Flow in microfluidic devices was used as a model system for microscopic motion and through widefield fluorescence correlation spectroscopy flow profiles were mapped in three dimensions. The technique presented is shown to be more tolerant to low signal strength, allowing image data with signal-to-noise values as low as 1.4 to produce accurate flow maps as well as utilizing dye-labeled single antibodies as flow tracers. With proper instrumentation flows along the axial direction can also be measured. Widefield fluorescence correlation spectroscopy has also been utilized to produce super-resolution confocal microscopic images relying on the single-molecule microsecond blinking dynamics of fluorescent silver clusters. A method for fluorescence modulation signal extraction as well as synthesis of several novel noble metal fluorophores is also presented.

The cell nucleus is a chemical reactor. Nuclear components interact with each other to express genes, duplicate the chromosomes for cell division, and protect DNA from alteration. These reactions are regulated along the cell cycle and in response to stress. One of the fundamental nuclear processes, transcription, enables the production of a messenger RNA from a template DNA sequence. While mandatory for the cell, transcription nevertheless may involve a very small number of molecules. Indeed, a single gene would have only few copies in the genome. During my PhD, I studied nuclear processes in human cells nuclei at the single molecule level with novel imaging techniques. I developed new statistical tools to quantify nuclear components movement that revealed a dynamic nuclear architecture. Since the 90s, simple methods have been developed for the observation of single molecules in the cell. These experiments can be conducted in an ordinary inverted microscope. We used these methods to monitor nuclear molecules called transcription factors (TF) that regulate transcription. From TF dynamics, we concluded that nuclear exploration by transcription factors is regulated by their chemical interactions with partners. The organization of the components of the nucleus guide transcription factors in their search of a gene. As an example of this organization, we then studied chromatin, the de-condensed form of nuclear DNA, proving that it displays the characteristics of a self-organized fractal structure. This structure changes in response to cellular fate and stress. In yeast, we showed that the interminglement of chromatin constrained DNA locus movement in a reptation regime. All these results show the interdependence of the structure of the nucleus and of its chemical reactions. With combination of realistic modeling and high resolution microscopy, we have enlightened the specificity of the nucleus as a chemical reactor. This thesis has also enabled the development of accurate methods for the statistical analysis of single molecule data.

The cell nucleus is a chemical reactor. Nuclear components interact with each other to express genes, duplicate the chromosomes for cell division, and protect DNA from alteration. These reactions are regulated along the cell cycle and in response to stress. One of the fundamental nuclear processes, transcription, enables the production of a messenger RNA from a template DNA sequence. While mandatory for the cell, transcription nevertheless may involve a very small number of molecules. Indeed, a single gene would have only few copies in the genome. During my PhD, I studied nuclear processes in human cells nuclei at the single molecule level with novel imaging techniques. I developed new statistical tools to quantify nuclear components movement that revealed a dynamic nuclear architecture. Since the 90s, simple methods have been developed for the observation of single molecules in the cell. These experiments can be conducted in an ordinary inverted microscope. We used these methods to monitor nuclear molecules called transcription factors (TF) that regulate transcription. From TF dynamics, we concluded that nuclear exploration by transcription factors is regulated by their chemical interactions with partners. The organization of the components of the nucleus guide transcription factors in their search of a gene. As an example of this organization, we then studied chromatin, the de-condensed form of nuclear DNA, proving that it displays the characteristics of a self-organized fractal structure. This structure changes in response to cellular fate and stress. In yeast, we showed that the interminglement of chromatin constrained DNA locus movement in a reptation regime. All these results show the interdependence of the structure of the nucleus and of its chemical reactions. With combination of realistic modeling and high resolution microscopy, we have enlightened the specificity of the nucleus as a chemical reactor. This thesis has also enabled the development of accurate methods for the statistical analysis of single molecule data.

A surface reconstruction and image enhancement non-linear finite element technique based on minimization of L1 norm of the total variation of the gradient is introduced. Since minimization in the L1 norm is computationally expensive, we seek to improve the performance of this algorithm in two fronts: first, local L1- minimization, which allows parallel implementation; second, application of the Augmented Lagrangian method to solve the minimization problem. We show that local solution of the minimization problem is feasible. Furthermore, the Augmented Lagrangian method can successfully be used to solve the L1 minimization problem. This result is expected to be useful for improving algorithms computing digital elevation maps for natural and urban terrain, fitting surfaces to point-cloud data, and image super-resolution.

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