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

Deep learning for accelerated magnetic resonance imaging

Medical imaging has aided the biggest advance in the medical domain in the last century. Whilst X-ray, CT, PET and ultrasound are a form of imaging that can be useful in particular scenarios, they each have disadvantages in cost, image quality, ease-of-use and ionising radiation. MRI is a slow imaging protocol which contributes to its high cost to run. However, MRI is a very versatile imaging protocol allowing images of varying contrast to be easily generated whilst not requiring the use of ionising radiation. If MRI can be made to be more efficient and smart, the effective cost of running MRI may be more affordable and accessible. The focus of this thesis is decreasing the acquisition time involved in MRI whilst maintaining the quality of the generated images and thus diagnosis. In particular, we focus on data-driven deep learning approaches that aid in the image reconstruction process and streamline the diagnostic process. We focus on three particular aspects of MR acquisition. Firstly, we investigate the use of motion estimation in the cine reconstruction process. Motion allows us to combine an abundance of imaging data in a learnt reconstruction model allowing acquisitions to be sped up by up to 50 times in extreme scenarios. Secondly, we investigate the possibility of using under-acquired MR data to generate smart diagnoses in the form of automated text reports. In particular, we investigate the possibility of skipping the imaging reconstruction phase altogether at inference time and instead, directly seek to generate radiological text reports for diffusion-weighted brain images in an effort to streamline the diagnostic process. Finally, we investigate the use of probabilistic modelling for MRI reconstruction without the use of fully-acquired data. In particular, we note that acquiring fully-acquired reference images in MRI can be difficult and nonetheless may still contain undesired artefacts that lead to degradation of the dataset and thus the training process. In this chapter, we investigate the possibility of performing reconstruction without fully-acquired references and furthermore discuss the possibility of generating higher quality outputs than that of the fully-acquired references.Open Acces

Deep learning for fast and robust medical image reconstruction and analysis

Medical imaging is an indispensable component of modern medical research as well as clinical practice. Nevertheless, imaging techniques such as magnetic resonance imaging (MRI) and computational tomography (CT) are costly and are less accessible to the majority of the world. To make medical devices more accessible, affordable and efficient, it is crucial to re-calibrate our current imaging paradigm for smarter imaging. In particular, as medical imaging techniques have highly structured forms in the way they acquire data, they provide us with an opportunity to optimise the imaging techniques holistically by leveraging data. The central theme of this thesis is to explore different opportunities where we can exploit data and deep learning to improve the way we extract information for better, faster and smarter imaging. This thesis explores three distinct problems. The first problem is the time-consuming nature of dynamic MR data acquisition and reconstruction. We propose deep learning methods for accelerated dynamic MR image reconstruction, resulting in up to 10-fold reduction in imaging time. The second problem is the redundancy in our current imaging pipeline. Traditionally, imaging pipeline treated acquisition, reconstruction and analysis as separate steps. However, we argue that one can approach them holistically and optimise the entire pipeline jointly for a specific target goal. To this end, we propose deep learning approaches for obtaining high fidelity cardiac MR segmentation directly from significantly undersampled data, greatly exceeding the undersampling limit for image reconstruction. The final part of this thesis tackles the problem of interpretability of the deep learning algorithms. We propose attention-models that can implicitly focus on salient regions in an image to improve accuracy for ultrasound scan plane detection and CT segmentation. More crucially, these models can provide explainability, which is a crucial stepping stone for the harmonisation of smart imaging and current clinical practice.Open Acces

Modélisation locale en imagerie par résonance magnétique de diffusion : de l'acquisition comprimée au connectome

L’imagerie par résonance magnétique pondérée en diffusion est une modalité d’imagerie médicale non invasive qui permet de mesurer les déplacements microscopiques des molécules d’eau dans les tissus biologiques. Il est possible d’utiliser cette information pour inférer la structure du cerveau. Les techniques de modélisation locale de la diffusion permettent de calculer l’orientation et la géométrie des tissus de la matière blanche. Cette thèse s’intéresse à l’optimisation des métaparamètres utilisés par les modèles locaux. Nous dérivons des paramètres optimaux qui améliorent la qualité des métriques de diffusion locale, de la tractographie de la matière blanche et de la connectivité globale. L’échantillonnage de l’espace-q est un des paramètres principaux qui limitent les types de modèle et d’inférence applicable sur des données acquises en clinique. Dans cette thèse, nous développons une technique d’échantillonnage de l’espace-q permettant d’utiliser l’acquisition comprimée pour réduire le temps d’acquisition nécessaire

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal