A hybrid alternating proximal method for blind video restoration

International audienceOld analog television sequences suffer from a number of degradations. Some of them can be modeled through convolution with a kernel and an additive noise term. In this work, we propose a new blind deconvolution algorithm for the restoration of such sequences based on a variational formulation of the problem. Our method accounts for motion between frames, while enforcing some level of temporal continuity through the use of a novel penalty function involving optical flow operators, in addition to an edge-preserving regularization. The optimization process is performed by a proximal alternating minimization scheme benefiting from theoretical convergence guarantees. Simulation results on synthetic and real video sequences confirm the effectiveness of our method

Restauration super-résolution de séquences d'images : applications aux documents d'archives TV

The last century has witnessed an explosion in the amount of video data stored with holders such as the National Audiovisual Institute whose mission is to preserve and promote the content of French broadcast programs. The cultural impact of these records, their value is increased due to commercial reexploitation through recent visual media. However, the perceived quality of the old data fails to satisfy the current public demand. The purpose of this thesis is to propose new methods for restoring video sequences supplied from television archive documents, using modern optimization techniques with proven convergence properties. In a large number of restoration issues, the underlying optimization problem is made up with several functions which might be convex and non-necessarily smooth. In such instance, the proximity operator, a fundamental concept in convex analysis, appears as the most appropriate tool. These functions may also involve arbitrary linear operators that need to be inverted in a number of optimization algorithms. In this spirit, we developed a new primal-dual algorithm for computing non-explicit proximity operators based on forward-backward iterations. The proposed algorithm is accelerated thanks to the introduction of a preconditioning strategy and a block-coordinate approach in which at each iteration, only a "block" of data is selected and processed according to a quasi-cyclic rule. This approach is well suited to large-scale problems since it reduces the memory requirements and accelerates the convergence speed, as illustrated by some experiments in deconvolution and deinterlacing of video sequences. Afterwards, a close attention is paid to the study of distributed algorithms on both theoretical and practical viewpoints. We proposed an asynchronous extension of the dual forward-backward algorithm, that can be efficiently implemented on a multi-cores architecture. In our distributed scheme, the primal and dual variables are considered as private and spread over multiple computing units, that operate independently one from another. Nevertheless, communication between these units following a predefined strategy is required in order to ensure the convergence toward a consensus solution. We also address in this thesis the problem of blind video deconvolution that consists in inferring from an input degraded video sequence, both the blur filter and a sharp video sequence. Hence, a solution can be reached by resorting to nonconvex optimization methods that estimate alternatively the unknown video and the unknown kernel. In this context, we proposed a new blind deconvolution method that allows us to implement numerous convex and nonconvex regularization strategies, which are widely employed in signal and image processingAu cours du dernier siècle, le volume de vidéos stockées chez des organismes tel que l'Institut National de l'Audiovisuel a connu un grand accroissement. Ces organismes ont pour mission de préserver et de promouvoir ces contenus, car, au-delà de leur importance culturelle, ces derniers ont une vraie valeur commerciale grâce à leur exploitation par divers médias. Cependant, la qualité visuelle des vidéos est souvent moindre comparée à celles acquises par les récents modèles de caméras. Ainsi, le but de cette thèse est de développer de nouvelles méthodes de restauration de séquences vidéo provenant des archives de télévision française, grâce à de récentes techniques d'optimisation. La plupart des problèmes de restauration peuvent être résolus en les formulant comme des problèmes d'optimisation, qui font intervenir plusieurs fonctions convexes mais non-nécessairement différentiables. Pour ce type de problèmes, on a souvent recourt à un outil efficace appelé opérateur proximal. Le calcul de l'opérateur proximal d'une fonction se fait de façon explicite quand cette dernière est simple. Par contre, quand elle est plus complexe ou fait intervenir des opérateurs linéaires, le calcul de l'opérateur proximal devient plus compliqué et se fait généralement à l'aide d'algorithmes itératifs. Une première contribution de cette thèse consiste à calculer l'opérateur proximal d'une somme de plusieurs fonctions convexes composées avec des opérateurs linéaires. Nous proposons un nouvel algorithme d'optimisation de type primal-dual, que nous avons nommé Algorithme Explicite-Implicite Dual par Blocs. L'algorithme proposé permet de ne mettre à jour qu'un sous-ensemble de blocs choisi selon une règle déterministe acyclique. Des résultats de convergence ont été établis pour les deux suites primales et duales de notre algorithme. Nous avons appliqué notre algorithme au problème de déconvolution et désentrelacement de séquences vidéo. Pour cela, nous avons modélisé notre problème sous la forme d'un problème d'optimisation dont la solution est obtenue à l'aide de l'algorithme explicite-implicite dual par blocs. Dans la deuxième partie de cette thèse, nous nous sommes intéressés au développement d'une version asynchrone de notre l'algorithme explicite-implicite dual par blocs. Dans cette nouvelle extension, chaque fonction est considérée comme locale et rattachée à une unité de calcul. Ces unités de calcul traitent les fonctions de façon indépendante les unes des autres. Afin d'obtenir une solution de consensus, il est nécessaire d'établir une stratégie de communication efficace. Un point crucial dans le développement d'un tel algorithme est le choix de la fréquence et du volume de données à échanger entre les unités de calcul, dans le but de préserver de bonnes performances d'accélération. Nous avons évalué numériquement notre algorithme distribué sur un problème de débruitage de séquences vidéo. Les images composant la vidéo sont partitionnées de façon équitable, puis chaque processeur exécute une instance de l'algorithme de façon asynchrone et communique avec les processeurs voisins. Finalement, nous nous sommes intéressés au problème de déconvolution aveugle, qui vise à estimer le noyau de convolution et la séquence originale à partir de la séquence dégradée observée. Nous avons proposé une nouvelle méthode basée sur la formulation d'un problème non-convexe, résolu par un algorithme itératif qui alterne entre l'estimation de la séquence originale et l'identification du noyau. Notre méthode a la particularité de pouvoir intégrer divers types de fonctions de régularisations avec des propriétés mathématiques différentes. Nous avons réalisé des simulations sur des séquences synthétiques et réelles, avec différents noyaux de convolution. La flexibilité de notre approche nous a permis de réaliser des comparaisons entre plusieurs fonctions de régularisation convexes et non-convexes, en terme de qualité d'estimatio

Distributed Algorithms for Scalable Proximity Operator Computation and Application to Video Denoising

Optimization problems arising in signal and image processing involve an increasingly large number of variables. In addition to the curse of dimensionality, another difficulty to overcome is that the cost function usually reads as the sum of several loss/regularization terms, non-necessarily smooth and possibly composed with large-size linear operators. Proximal splitting approaches are fundamental tools to address such problems, with demonstrated efficiency in many applicative fields. In this paper, we present a new distributed algorithm for computing the proximity operator of a sum of non-necessarily smooth convex functions composed with arbitrary linear operators. Our algorithm relies on a primal-dual splitting strategy, and benefits from established convergence guaranties. Each involved function is associated with a node of a hypergraph, with the ability to communicate with neighboring nodes sharing the same hyperedge. Thanks to this structure, our method can be efficiently implemented on modern parallel computing architectures, allowing to distribute computations on different nodes or machines while limiting the need for synchronization steps. Its good numerical performance and scalability properties are illustrated on a problem of video sequence denoising

A Multicore Convex Optimization Algorithm with Applications to Video Restoration

International audienceIn this paper, we present a new distributed algorithm for minimizing a sum of non-necessarily differentiable convex functions composed with arbitrary linear operators. The overall cost function is assumed strongly convex. Each involved function is associated with a node of a hypergraph having the ability to communicate with neighboring nodes sharing the same hyperedge. Our algorithm relies on a primal-dual splitting strategy with established convergence guarantees. We show how it can be efficiently implemented to take full advantage of a multicore architecture. The good numerical performance of the proposed approach is illustrated in a problem of video sequence denoising, where a significant speedup is achieved

Distributed Algorithms for Scalable Proximity Operator Computation and Application to Video Denoising

International audienceOptimization problems arising in signal and image processing involve an increasingly large number of variables. In addition to the curse of dimensionality, another difficulty to overcome is that the cost function usually reads as the sum of several loss/regularization terms, which are non-necessarily smooth and possibly composed with large-size linear operators. Proximal splitting approaches are fundamental tools to address such problems, with demonstrated efficiency in many applicative fields. In this paper, we present a new distributed algorithm for computing the proximity operator of a sum of non-necessarily smooth convex functions composed with arbitrary linear operators. Our algorithm relies on a primal-dual splitting strategy, and benefits from established convergence guaranties. Each involved function is associated with a node of a hypergraph, with the ability to communicate with neighboring nodes sharing the same hyperedge. Thanks to this structure, our method can be efficiently implemented on modern parallel computing architectures, distributing the computations on multiple nodes or machines, with controlled requirements for synchronization steps. Good numerical performance and scalability properties are demonstrated on a problem of video sequence denoising. Our code implemented in Julia is made available at \url{https://github.com/MarinENSTA/distributed_julia_denoising}

A Distributed Strategy for Computing Proximity Operators

International audienceVarious recent iterative optimization methods require to compute the proximity operator of a sum of functions.We address this problem by proposing a new distributed algorithm for a sum of non-necessarily smooth convex functionscomposed with arbitrary linear operators. In our approach, each function is associated with a node of a graph, whichcommunicates with its neighbors. Our algorithm relies on a primal-dual splitting strategy that avoids to invert any linearoperator, thus making it suitable for processing high-dimensional datasets. The proposed algorithm has a wide array of applicationsin signal/image processing and machine learning and its convergence is established

Dual Block Coordinate Forward-Backward Algorithm with Application to Deconvolution and Deinterlacing of Video Sequences

International audienceOptimization methods play a central role in the solution of a wide array of problems encountered in various application fields, such as signal and image processing. Especially when the problems are highly dimensional, proximal methods have shown their efficiency through their capability to deal with composite, possibly nonsmooth objective functions. The cornerstone of these approaches is the proximity operator, which has become a quite popular tool in optimization. In this work, we propose new dual forward-backward formulations for computing the proximity operator of a sum of convex functions involving linear operators. The proposed algorithms are accelerated thanks to the introduction of a block-coordinate strategy combined with a preconditioning technique. Numerical simulations emphasize the good performance of our approach for the problem of jointly deconvoluting and deinterlacing video sequences

An Alternating Proximal Approach for Blind Video Deconvolution

International audienceBlurring occurs frequently in video sequences captured by consumer devices, as a result of various factors such as lens aberrations, defocus, relative camera-scene motion, and camera shake. When it comes to the contents of archive documents such as old films and television shows, the degradations are even more serious due to several physical phenomena happening during the sensing, transmission, recording, and storing processes. We propose in this paper a versatile formulation of blind video deconvolution problems that seeks to estimate both the sharp unknown video sequence and the underlying blur kernel from an observed video. This inverse problem is severely ill-posed, and an appropriate solution can be obtained by modeling it as a nonconvex minimization problem. We provide a novel iterative algorithm to solve it, grounded on the use of recent advances in convex and nonconvex optimization techniques, and having the ability of including numerous well-known regularization strategies