Advanced VLBI Imaging

Very Long Baseline Interferometry (VLBI) is an observational technique developed in astronomy for combining multiple radio telescopes into a single virtual instrument with an effective aperture reaching up to many thousand kilometers and enabling measurements at highest angular resolutions. The celebrated examples of applying VLBI to astrophysical studies include detailed, high-resolution images of the innermost parts of relativistic outflows (jets) in active galactic nuclei (AGN) and recent pioneering observations of the shadows of supermassive black holes (SMBH) in the center of our Galaxy and in the galaxy M87. Despite these and many other proven successes of VLBI, analysis and imaging of VLBI data still remain difficult, owing in part to the fact that VLBI imaging inherently constitutes an ill-posed inverse problem. Historically, this problem has been addressed in radio interferometry by the CLEAN algorithm, a matching-pursuit inverse modeling method developed in the early 1970-s and since then established as a de-facto standard approach for imaging VLBI data. In recent years, the constantly increasing demand for improving quality and fidelity of interferometric image reconstruction has resulted in several attempts to employ new approaches, such as forward modeling and Bayesian estimation, for application to VLBI imaging. While the current state-of-the-art forward modeling and Bayesian techniques may outperform CLEAN in terms of accuracy, resolution, robustness, and adaptability, they also tend to require more complex structure and longer computation times, and rely on extensive finetuning of a larger number of non-trivial hyperparameters. This leaves an ample room for further searches for potentially more effective imaging approaches and provides the main motivation for this dissertation and its particular focusing on the need to unify algorithmic frameworks and to study VLBI imaging from the perspective of inverse problems in general. In pursuit of this goal, and based on an extensive qualitative comparison of the existing methods, this dissertation comprises the development, testing, and first implementations of two novel concepts for improved interferometric image reconstruction. The concepts combine the known benefits of current forward modeling techniques, develop more automatic and less supervised algorithms for image reconstruction, and realize them within two different frameworks. The first framework unites multiscale imaging algorithms in the spirit of compressive sensing with a dictionary adapted to the uv-coverage and its defects (DoG-HiT, DoB-CLEAN). We extend this approach to dynamical imaging and polarimetric imaging. The core components of this framework are realized in a multidisciplinary and multipurpose software MrBeam, developed as part of this dissertation. The second framework employs a multiobjective genetic evolutionary algorithm (MOEA/D) for the purpose of achieving fully unsupervised image reconstruction and hyperparameter optimization. These new methods are shown to outperform the existing methods in various metrics such as angular resolution, structural sensitivity, and degree of supervision. We demonstrate the great potential of these new techniques with selected applications to frontline VLBI observations of AGN jets and SMBH. In addition to improving the quality and robustness of image reconstruction, DoG-HiT, DoB-CLEAN and MOEA/D also provide such novel capabilities as dynamic reconstruction of polarimetric images on minute time-scales, or near-real time and unsupervised data analysis (useful in particular for application to large imaging surveys). The techniques and software developed in this dissertation are of interest for a wider range of inverse problems as well. This includes such versatile fields such as Ly-alpha tomography (where we improve estimates of the thermal state of the intergalactic medium), the cosmographic search for dark matter (where we improve forecasted bounds on ultralight dilatons), medical imaging, and solar spectroscopy

Modeling sparse connectivity between underlying brain sources for EEG/MEG

We propose a novel technique to assess functional brain connectivity in EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk between the extracted sources and in this manner we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data, and compare to a number of existing algorithms with excellent results.Comment: 9 pages, 6 figure

Volumetric MRI Reconstruction from 2D Slices in the Presence of Motion

Despite recent advances in acquisition techniques and reconstruction algorithms, magnetic resonance imaging (MRI) remains challenging in the presence of motion. To mitigate this, ultra-fast two-dimensional (2D) MRI sequences are often used in clinical practice to acquire thick, low-resolution (LR) 2D slices to reduce in-plane motion. The resulting stacks of thick 2D slices typically provide high-quality visualizations when viewed in the in-plane direction. However, the low spatial resolution in the through-plane direction in combination with motion commonly occurring between individual slice acquisitions gives rise to stacks with overall limited geometric integrity. In further consequence, an accurate and reliable diagnosis may be compromised when using such motion-corrupted, thick-slice MRI data. This thesis presents methods to volumetrically reconstruct geometrically consistent, high-resolution (HR) three-dimensional (3D) images from motion-corrupted, possibly sparse, low-resolution 2D MR slices. It focuses on volumetric reconstructions techniques using inverse problem formulations applicable to a broad field of clinical applications in which associated motion patterns are inherently different, but the use of thick-slice MR data is current clinical practice. In particular, volumetric reconstruction frameworks are developed based on slice-to-volume registration with inter-slice transformation regularization and robust, complete-outlier rejection for the reconstruction step that can either avoid or efficiently deal with potential slice-misregistrations. Additionally, this thesis describes efficient Forward-Backward Splitting schemes for image registration for any combination of differentiable (not necessarily convex) similarity measure and convex (not necessarily smooth) regularization with a tractable proximal operator. Experiments are performed on fetal and upper abdominal MRI, and on historical, printed brain MR films associated with a uniquely long-term study dating back to the 1980s. The results demonstrate the broad applicability of the presented frameworks to achieve robust reconstructions with the potential to improve disease diagnosis and patient management in clinical practice

Rapid Segmentation Techniques for Cardiac and Neuroimage Analysis

Recent technological advances in medical imaging have allowed for the quick acquisition of highly resolved data to aid in diagnosis and characterization of diseases or to guide interventions. In order to to be integrated into a clinical work flow, accurate and robust methods of analysis must be developed which manage this increase in data. Recent improvements in in- expensive commercially available graphics hardware and General-Purpose Programming on Graphics Processing Units (GPGPU) have allowed for many large scale data analysis problems to be addressed in meaningful time and will continue to as parallel computing technology improves. In this thesis we propose methods to tackle two clinically relevant image segmentation problems: a user-guided segmentation of myocardial scar from Late-Enhancement Magnetic Resonance Images (LE-MRI) and a multi-atlas segmentation pipeline to automatically segment and partition brain tissue from multi-channel MRI. Both methods are based on recent advances in computer vision, in particular max-flow optimization that aims at solving the segmentation problem in continuous space. This allows for (approximately) globally optimal solvers to be employed in multi-region segmentation problems, without the particular drawbacks of their discrete counterparts, graph cuts, which typically present with metrication artefacts. Max-flow solvers are generally able to produce robust results, but are known for being computationally expensive, especially with large datasets, such as volume images. Additionally, we propose two new deformable registration methods based on Gauss-Newton optimization and smooth the resulting deformation fields via total-variation regularization to guarantee the problem is mathematically well-posed. We compare the performance of these two methods against four highly ranked and well-known deformable registration methods on four publicly available databases and are able to demonstrate a highly accurate performance with low run times. The best performing variant is subsequently used in a multi-atlas segmentation pipeline for the segmentation of brain tissue and facilitates fast run times for this computationally expensive approach. All proposed methods are implemented using GPGPU for a substantial increase in computational performance and so facilitate deployment into clinical work flows. We evaluate all proposed algorithms in terms of run times, accuracy, repeatability and errors arising from user interactions and we demonstrate that these methods are able to outperform established methods. The presented approaches demonstrate high performance in comparison with established methods in terms of accuracy and repeatability while largely reducing run times due to the employment of GPU hardware

Integration of magnetic resonance spectroscopic imaging into the radiotherapy treatment planning

L'objectif de cette thèse est de proposer de nouveaux algorithmes pour surmonter les limitations actuelles et de relever les défis ouverts dans le traitement de l'imagerie spectroscopique par résonance magnétique (ISRM). L'ISRM est une modalité non invasive capable de fournir la distribution spatiale des composés biochimiques (métabolites) utilisés comme biomarqueurs de la maladie. Les informations fournies par l'ISRM peuvent être utilisées pour le diagnostic, le traitement et le suivi de plusieurs maladies telles que le cancer ou des troubles neurologiques. Cette modalité se montre utile en routine clinique notamment lorsqu'il est possible d'en extraire des informations précises et fiables. Malgré les nombreuses publications sur le sujet, l'interprétation des données d'ISRM est toujours un problème difficile en raison de différents facteurs tels que le faible rapport signal sur bruit des signaux, le chevauchement des raies spectrales ou la présence de signaux de nuisance. Cette thèse aborde le problème de l'interprétation des données d'ISRM et la caractérisation de la rechute des patients souffrant de tumeurs cérébrales. Ces objectifs sont abordés à travers une approche méthodologique intégrant des connaissances a priori sur les données d'ISRM avec une régularisation spatio-spectrale. Concernant le cadre applicatif, cette thèse contribue à l'intégration de l'ISRM dans le workflow de traitement en radiothérapie dans le cadre du projet européen SUMMER (Software for the Use of Multi-Modality images in External Radiotherapy) financé par la Commission européenne (FP7-PEOPLE-ITN).The aim of this thesis is to propose new algorithms to overcome the current limitations and to address the open challenges in the processing of magnetic resonance spectroscopic imaging (MRSI) data. MRSI is a non-invasive modality able to provide the spatial distribution of relevant biochemical compounds (metabolites) commonly used as biomarkers of disease. Information provided by MRSI can be used as a valuable insight for the diagnosis, treatment and follow-up of several diseases such as cancer or neurological disorders. Obtaining accurate and reliable information from in vivo MRSI signals is a crucial requirement for the clinical utility of this technique. Despite the numerous publications on the topic, the interpretation of MRSI data is still a challenging problem due to different factors such as the low signal-to-noise ratio (SNR) of the signals, the overlap of spectral lines or the presence of nuisance components. This thesis addresses the problem of interpreting MRSI data and characterizing recurrence in tumor brain patients. These objectives are addressed through a methodological approach based on novel processing methods that incorporate prior knowledge on the MRSI data using a spatio-spectral regularization. As an application, the thesis addresses the integration of MRSI into the radiotherapy treatment workflow within the context of the European project SUMMER (Software for the Use of Multi-Modality images in External Radiotherapy) founded by the European Commission (FP7-PEOPLE-ITN framework)