Contributions en optimisation topologique : extension de la méthode adjointe et applications au traitement d'images

De nos jours, l'optimisation topologique a été largement étudiée en optimisation de structure, problème majeur en conception de systèmes mécaniques pour l'industrie et dans les problèmes inverses avec la détection de défauts et d'inclusions. Ce travail se concentre sur les approches de dérivées topologiques et propose une généralisation plus flexible de cette méthode rendant possible l'investigation de nouvelles applications. Dans une première partie, nous étudions des problèmes classiques en traitement d'images (restauration, inpainting), et exposons une formulation commune à ces problèmes. Nous nous concentrons sur la diffusion anisotrope et considérons un nouveau problème : la super-résolution. Notre approche semble meilleure comparée aux autres méthodes. L'utilisation des dérivées topologiques souffre d'inconvénients : elle est limitée à des problèmes simples, nous ne savons pas comment remplir des trous ... Dans une seconde partie, une nouvelle méthode visant à surmonter ces difficultés est présentée. Cette approche, nommée voûte numérique, est une extension de la méthode adjointe. Ce nouvel outil nous permet de considérer de nouveaux champs d'application et de réaliser de nouvelles investigations théoriques dans le domaine des dérivées topologiques.Nowadays, topology optimization has been extensively studied in structural optimization which is a major interest in the design of mechanical systems in the industry and in inverse problems with the detection of defects or inclusions. This work focuses on the topological derivative approach and proposes a more flexible generalization of this method making it possible to address new applications. In a first part, we study classical image processing problems (restoration, inpainting), and give a common framework to theses problems. We focus on anisotropic diffusion and consider a new problem: super-resolution. Our approach seems to be powerful in comparison with other methods. Topological derivative method has some drawbacks: it is limited to simple problems, we do not know how to fill holes, ... In a second part, to overcome these difficulties, an extension of the adjoint method is presented. Named the numerical vault, it allows us to consider new fields of applications and to explore new theoretical investigations in the area of topological derivative

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Content adaptive single image interpolation based super resolution of compressed images

Image Super resolution is used to upscale the low resolution Images. It is also known as image upscaling .This paper focuses on upscaling of compressed images based on Interpolation techniques. A content adaptive interpolation method of image upscaling has been proposed. This interpolation based scheme is useful for single image based Super-resolution (SR) methods .The presented method works on horizontal, vertical and diagonal directions of an image separately and it is adaptive to the local content of an image. This method relies only on single image and uses the content of the original image only; therefore the proposed method is more practical and realistic. The simulation results have been compared to other standard methods with the help of various performance matrices like PSNR, MSE, MSSIM etc. which indicates the preeminence of the proposed method

MOTION ESTIMATION USING A JOINT OPTIMISATION OF THE MOTION VECTOR FIELD AND A SUPER-RESOLUTION REFERENCE IMAGE

ABSTRACT In many situations, interdependency between motion estimation and other estimation tasks is observable. This is for instance true in the area of Super-Resolution (SR

Elastic image registration using parametric deformation models

The main topic of this thesis is elastic image registration for biomedical applications. We start with an overview and classification of existing registration techniques. We revisit the landmark interpolation which appears in the landmark-based registration techniques and add some generalizations. We develop a general elastic image registration algorithm. It uses a grid of uniform B-splines to describe the deformation. It also uses B-splines for image interpolation. Multiresolution in both image and deformation model spaces yields robustness and speed. First we describe a version of this algorithm targeted at finding unidirectional deformation in EPI magnetic resonance images. Then we present the enhanced and generalized version of this algorithm which is significantly faster and capable of treating multidimensional deformations. We apply this algorithm to the registration of SPECT data and to the motion estimation in ultrasound image sequences. A semi-automatic version of the registration algorithm is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. In the second part of this thesis, we deal with the problem of generalized sampling and variational reconstruction. We explain how to reconstruct an object starting from several measurements using arbitrary linear operators. This comprises the case of traditional as well as generalized sampling. Among all possible reconstructions, we choose the one minimizing an a priori given quadratic variational criterion. We give an overview of the method and present several examples of applications. We also provide the mathematical details of the theory and discuss the choice of the variational criterion to be used

Super-Resolution for Hyperspectral and Multispectral Image Fusion Accounting for Seasonal Spectral Variability

Image fusion combines data from different heterogeneous sources to obtain more precise information about an underlying scene. Hyperspectral-multispectral (HS-MS) image fusion is currently attracting great interest in remote sensing since it allows the generation of high spatial resolution HS images, circumventing the main limitation of this imaging modality. Existing HS-MS fusion algorithms, however, neglect the spectral variability often existing between images acquired at different time instants. This time difference causes variations in spectral signatures of the underlying constituent materials due to different acquisition and seasonal conditions. This paper introduces a novel HS-MS image fusion strategy that combines an unmixing-based formulation with an explicit parametric model for typical spectral variability between the two images. Simulations with synthetic and real data show that the proposed strategy leads to a significant performance improvement under spectral variability and state-of-the-art performance otherwise