Video super-resolution (VSR) aims to recover a realistic high-resolution (HR) frame from its corresponding center low-resolution (LR) frame and several neighbouring supporting frames. The neighbouring supporting LR frames can provide extra information to help recover the HR frame. However, these frames are not aligned with the center frame due to the motion of objects. Recently, many video super-resolution methods based on deep learning have been proposed with the rapid development of neural networks. Most of these methods utilize motion estimation and compensation models as preprocessing to handle spatio-temporal alignment problem. Therefore, the accuracy of these motion estimation models are critical for predicting the high-resolution frames. Inaccurate results of motion compensation models will lead to artifacts and blurs, which also will damage the recovery of high-resolution frames. We propose an effective wide activated separate 3 dimensional (3D) Convolution Neural Network (CNN) for video super-resolution to overcome the drawback of utilizing motion compensation models. Separate 3D convolution factorizes the 3D convolution into convolutions in the spatial and temporal domain, which have benefit for the optimization of spatial and temporal convolution components. Therefore, our method can capture temporal and spatial information of input frames simultaneously without additional motion evaluation and compensation model. Moreover, the experimental results demonstrated the effectiveness of the proposed wide activated separate 3D CNN.

Video super-resolution (VSR) methods align and fuse consecutive low-resolution frames to generate high-resolution frames. One of the main difficulties for the VSR process is that video contains various motions, and the accuracy of motion estimation dramatically affects the quality of video restoration. However, standard CNNs share the same receptive field in each layer, and it is challenging to estimate diverse motions effectively. Neuroscience research has shown that the receptive fields of biological visual areas will be adjusted according to the input information. Diverse receptive fields in temporal and spatial dimensions have the potential to adapt to various motions, which is rarely paid attention in most known VSR methods. In this thesis, we propose to provide adaptive receptive fields for the VSR model. Firstly, we design a multi-kernel 3D convolution network and integrate it with a multi-kernel deformable convolution network for motion estimation and multiple frames alignment. Secondly, we propose a 2D multi-kernel convolution framework to improve texture restoration quality. Our experimental results show that the proposed framework outperforms the state-of-the-art VSR methods.

Nous affinons le crible asymptotique de Bombieri afin d’obtenir un asymptotique en variables localisées. Comme conséquence, nous démontrons, sous la conjecture d’Elliott-Halberstam, qu’il existe une infinité de nombres presque premiers jumeaux, c’est à dire tels que pour tout ε > 0, p est premier et p−2 est soit premier, soit de la forme p1p2 où p1 < Xε, et nous en donnons un asymptotique. A ce travail s’ajoutent deux chapitres : d’un côté, une preuve montrant comment une méthode sans crible préliminaire donne un résultat plus faible en nécessitant une hypothèse plus forte, ce qui nous permettra de détailler plusieurs estimations et de souligner l’intérêt de notre approche. D’un autre côté une exposition pédagogique d’une méthode donnant un accès facile et explicite à plusieurs estimations de moyennes de fonctions multiplicatives. / We improve Bombieri’s asymptotic sieve to localise the variables. As a consequence, we prove, under a Elliott-Halberstam conjecture, that there exists an infinity of twins almost prime. Those are prime numbers p such that for all ε > 0, p −2 is either a prime number or can be written as p1p2 where p1 and p2 are prime and p1 < Xε, and we give the explicit asymptotic. In addition to this main work, there are two other chapters: the first one gives an asymptotic of prime numbers p such p−2is either a prime number or a product of three primes without using a preliminary sieve and so a stronger conjecture was needed. Hence this part shows the strength of the preliminary sieve and presents a few detailed sommations, most of them involving the Möbius fonction, that could be useful. The second one presents an easy and explicit method to calculate an average order of multiplicative functions.

Aujourd’hui, de nouvelles technologies permettent l’acquisition de scènes 3D volumineuses et précises sous la forme de nuages de points. Les nouvelles applications ouvertes par ces technologies, comme les véhicules autonomes ou la maintenance d'infrastructure, reposent sur un traitement efficace des nuages de points à grande échelle. Les méthodes d'apprentissage profond par convolution ne peuvent pas être utilisées directement avec des nuages de points. Dans le cas des images, les filtres convolutifs ont permis l’apprentissage de nouvelles représentations, jusqu’alors construites « à la main » dans les méthodes de vision par ordinateur plus anciennes. En suivant le même raisonnement, nous présentons dans cette thèse une étude des représentations construites « à la main » utilisées pour le traitement des nuages de points. Nous proposons ainsi plusieurs contributions, qui serviront de base à la conception d’une nouvelle représentation convolutive pour le traitement des nuages de points. Parmi elles, une nouvelle définition de voisinages sphériques multi-échelles, une comparaison avec les k plus proches voisins multi-échelles, une nouvelle stratégie d'apprentissage actif, la segmentation sémantique des nuages de points à grande échelle, et une étude de l'influence de la densité dans les représentations multi-échelles. En se basant sur ces contributions, nous introduisons la « Kernel Point Convolution » (KPConv), qui utilise des voisinages sphériques et un noyau défini par des points. Ces points jouent le même rôle que les pixels du noyau des convolutions en image. Nos réseaux convolutionnels surpassent les approches de segmentation sémantique de l’état de l’art dans presque toutes les situations. En plus de ces résultats probants, nous avons conçu KPConv avec une grande flexibilité et une version déformable. Pour conclure notre réflexion, nous proposons plusieurs éclairages sur les représentations que notre méthode est capable d'apprendre. / In the recent years, new technologies have allowed the acquisition of large and precise 3D scenes as point clouds. They have opened up new applications like self-driving vehicles or infrastructure monitoring that rely on efficient large scale point cloud processing. Convolutional deep learning methods cannot be directly used with point clouds. In the case of images, convolutional filters brought the ability to learn new representations, which were previously hand-crafted in older computer vision methods. Following the same line of thought, we present in this thesis a study of hand-crafted representations previously used for point cloud processing. We propose several contributions, to serve as basis for the design of a new convolutional representation for point cloud processing. They include a new definition of multiscale radius neighborhood, a comparison with multiscale k-nearest neighbors, a new active learning strategy, the semantic segmentation of large scale point clouds, and a study of the influence of density in multiscale representations. Following these contributions, we introduce the Kernel Point Convolution (KPConv), which uses radius neighborhoods and a set of kernel points to play the role of the kernel pixels in image convolution. Our convolutional networks outperform state-of-the-art semantic segmentation approaches in almost any situation. In addition to these strong results, we designed KPConv with a great flexibility and a deformable version. To conclude our argumentation, we propose several insights on the representations that our method is able to learn.

Indiana University-Purdue University Indianapolis (IUPUI) / The word “Perception” seems to be intuitive and maybe the most straightforward problem for the human brain because as a child we have been trained to classify images, detect objects, but for computers, it can be a daunting task. Giving intuition and reasoning to a computer which has mere capabilities to accept commands and process those commands is a big challenge. However, recent leaps in hardware development, sophisticated software frameworks, and mathematical techniques have made it a little less daunting if not easy. There are various applications built around to the concept of “Perception”. These applications require substantial computational resources, expensive hardware, and some sophisticated software frameworks. Building an application for perception for the embedded system is an entirely different ballgame. Embedded system is a culmination of hardware, software and peripherals developed for specific tasks with imposed constraints on memory and power. Therefore, the applications developed should keep in mind the memory and power constraints imposed due to the nature of these systems. Before 2012, the problems related to “Perception” such as classification, object detection were solved using algorithms with manually engineered features. However, in recent years, instead of manually engineering the features, these features are learned through learning algorithms. The game-changing architecture of Convolution Neural Networks proposed in 2012 by Alex K [1], provided a tremendous momentum in the direction of pushing Neural networks for perception. This thesis is an attempt to develop a convolution neural network architecture for embedded systems, i.e. an architecture that has a small model size and competitive accuracy. Recreate state-of-the-art architectures using fire module’s concept to reduce the model size of the architecture. The proposed compact models are feasible for deployment on embedded devices such as the Bluebox 2.0. Furthermore, attempts are made to integrate the compact Convolution Neural Network with object detection pipelines.

A finalidade deste trabalho e calcular a composição de modelos no FBST (the Full Bayesian Signicance Test) descrito por Borges e Stern [6]. Nosso objetivo foi encontrar um método de aproximação numérica mais eficiente que consiga substituir o método de condensação descrita por Kaplan. Três técnicas foram comparadas: a primeira é a aproximação da convolução de Mellin usando discretização e condensação descrita por Kaplan [11], a segunda é a aproximação da convolução de Mellin usando mistura de exponenciais, descrita por Dufresne [8], para calcular a convolução de Fourier mediante a aproximação de mistura de convoluções exponenciais, usando a estrutura algébrica descrita por Hogg [10], mais a aplicação do operador descrito por Collins [7], para transformar a convolução de Fourier para a convolução de Mellin, a terceira é a aproximação da convolução de Mellin usando mistura de exponenciais, descrita por Dufresne [8], para aproximar diretamente via mistura de exponenciais a convolução de Fourier, mais a aplicação do operador descrito por Collins [7], para transformar a convolução de Fourier para a convolução de Mellin. / The purpose of this work is to calculate the compositional models of FBST (the Full Bayesian Signicance Test) studied by Borges and Stern [6]. The objective of this work was to find an approximation method numerically eficient that can replace the condensation methods described by Kaplan. Three techniques were compared: First, the approximation of Mellin convolution using discretization and condensation described by Kaplan [11], second, the approximation of Mellin convolution using mixtures of exponentials, described by Dufresne [8], to calculate the Fourier convolution by approximation of mixtures of exponential convolutions, using the algebraic structure described by Hogg [10], and then to apply the operator described by Collins [7], to transform the usual convolution to Mellin convolution, third, the approximation of Mellin convolution using mixtures of exponentials, described by Dufresne [8], to calculate the Fourier convolution by direct approximation of mixtures of exponentials, and then to apply the operator described by Collins [7], to transform the usual convolution to Mellin convolution.

Na primeira parte desta tese nós estudamos os operadores de convolução Tµ que são tauberianos agindo nas álgebras de grupo L1(G), onde G é um grupo abeliano localmente compacto e µ é uma medida de Borel complexa sobre G. Nós mostramos que esses operadores são invertíveis se o grupo G não é compacto e que eles são de Fredholm quando têm imagem fechada e G é compacto. Além disso, se G é compacto nós provamos que Tµ é de Fredholm se a parte singular contínua de µ respeito à medida de Haar de G é zero. Na segunda parte nós estudamos os operadores de convolução Tµ que são cotauberianos em L1(G). Nós mostramos que esses operadores são tauberianos e são de Fredholm (de índice zero). Além disso, mostramos que Tµ é tauberiano se, e somente se, sua extensão natural à álgebra de medidas M(G) é tauberiano. Mostramos alguns resultados obtidos por dualidade de espaços de Banach para os operadores de convolução tauberianos e cotauberianos agindo sobre C0(G), o espaço de Banach das funções complexas que se anulam no infinito, e L&#8734(G), o espaço de Banach das funções mensuráveis essencialmente limitadas. Finalmente estendemos alguns dos resultados obtidos para álgebras de Banach que possuem uma identidade aproximada limitada. / In the first part of this thesis we study the convolution operators Tµwhich are tauberian as operators acting on the group algebras L1(G), where G is a locally compact abelian group and µ is a complex Borel measure on G. We show that these operators are invertible when G is non-compact, and that they are Fredholm when they have closed range and G is compact. Moreover, if G is compact, we prove that Tµ is Fredholm when the singular continuous part of µ with respect to the Haar measure on G is zero. In the second part we study the convolution operators Tµ which are cotauberian as operators acting on L1(G). We show that these operators are tauberian and Fredholm of index zero. Moreover, we show that Tµ is tauberian as an operator on L1(G) if and only if so is its natural extension to the algebra of measures M(G). We show some results, obtained by duality, about tauberian and cotauberian convolution operators on the Banach spaces L&#8734(G) of equivalence classes of essentially bounded mesurable functions on Gand C0(G) of complex valued continuous functions on Gwhich vanish at infinity. Finally, we extend some results obtained to Banach algebras with a bounded identity approximate.

Na primeira parte desta tese nós estudamos os operadores de convolução Tµ que são tauberianos agindo nas álgebras de grupo L1(G), onde G é um grupo abeliano localmente compacto e µ é uma medida de Borel complexa sobre G. Nós mostramos que esses operadores são invertíveis se o grupo G não é compacto e que eles são de Fredholm quando têm imagem fechada e G é compacto. Além disso, se G é compacto nós provamos que Tµ é de Fredholm se a parte singular contínua de µ respeito à medida de Haar de G é zero. Na segunda parte nós estudamos os operadores de convolução Tµ que são cotauberianos em L1(G). Nós mostramos que esses operadores são tauberianos e são de Fredholm (de índice zero). Além disso, mostramos que Tµ é tauberiano se, e somente se, sua extensão natural à álgebra de medidas M(G) é tauberiano. Mostramos alguns resultados obtidos por dualidade de espaços de Banach para os operadores de convolução tauberianos e cotauberianos agindo sobre C0(G), o espaço de Banach das funções complexas que se anulam no infinito, e L&#8734(G), o espaço de Banach das funções mensuráveis essencialmente limitadas. Finalmente estendemos alguns dos resultados obtidos para álgebras de Banach que possuem uma identidade aproximada limitada. / In the first part of this thesis we study the convolution operators Tµwhich are tauberian as operators acting on the group algebras L1(G), where G is a locally compact abelian group and µ is a complex Borel measure on G. We show that these operators are invertible when G is non-compact, and that they are Fredholm when they have closed range and G is compact. Moreover, if G is compact, we prove that Tµ is Fredholm when the singular continuous part of µ with respect to the Haar measure on G is zero. In the second part we study the convolution operators Tµ which are cotauberian as operators acting on L1(G). We show that these operators are tauberian and Fredholm of index zero. Moreover, we show that Tµ is tauberian as an operator on L1(G) if and only if so is its natural extension to the algebra of measures M(G). We show some results, obtained by duality, about tauberian and cotauberian convolution operators on the Banach spaces L&#8734(G) of equivalence classes of essentially bounded mesurable functions on Gand C0(G) of complex valued continuous functions on Gwhich vanish at infinity. Finally, we extend some results obtained to Banach algebras with a bounded identity approximate.

Nous traitons des problèmes d'interpolation dans les espaces ${\mathcal A}_p(\C)$ des fonctions entières telles que $\sup_{z\in \C}\vert f(z)\vert e^{-Bp(z)}<\infty$, où $p$ est une fonction poids et $B$ est une constante positive qui peut varier. Ces espaces sont des algèbres, qu'on appelle algèbres de Hörmander. Le problème peut être formulé de la manière suivante : étant donnée une suite discrète de nombres complexes $\{\alpha_j\}$ et une suite de valeurs complexes $\{w_j\}$ vérifiant $\sup_j\vert w_j\vert e^{-B'p(\alpha_j)}<\infty$ avec une certaine constante $B'>0$, à quelles conditions existe-t-il une fonction $f\in {\mathcal A}_p(\C)$ telle que, pour tout $j$,$f(\alpha_j)=w_j $?Ce problème a été motivé par ses applications à l'analyse harmonique et particulièrement aux équations de convolution. Nous explorons cet aspect en appliquant certains de nos résultats sur l'interpolation aux fonctions moyenne-périodiques. Nous nous intéressons également à la question de l'interpolation en plusieurs variables complexes.

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