Deep MR to CT Synthesis for PET/MR Attenuation Correction

Positron Emission Tomography - Magnetic Resonance (PET/MR) imaging combines the functional information from PET with the flexibility of MR imaging. It is essential, however, to correct for photon attenuation when reconstructing PETs, which is challenging for PET/MR as neither modality directly image tissue attenuation properties. Classical MR-based computed tomography (CT) synthesis methods, such as multi-atlas propagation, have been the method of choice for PET attenuation correction (AC), however, these methods are slow and suffer from the poor ability to handle anatomical abnormalities. To overcome this limitation, this thesis explores the rising field of artificial intelligence in order to develop novel methods for PET/MR AC. Deep learning-based synthesis methods such as the standard U-Net architecture are not very stable, accurate, and robust to small variations in image appearance. Thus, the first proposed MR to CT synthesis method deploys a boosting strategy, where multiple weak predictors build a strong predictor providing a significant improvement in CT and PET reconstruction accuracy. Standard deep learning-based methods as well as more advanced methods like the first proposed method show issues in the presence of very complex imaging environments and large images such as whole-body images. The second proposed method learns the image context between whole-body MRs and CTs through multiple resolutions while simultaneously modelling uncertainty. Lastly, as the purpose of synthesizing a CT is to better reconstruct PET data, the use of CT-based loss functions is questioned within this thesis. Such losses fail to recognize the main objective of MR-based AC, which is to generate a synthetic CT that, when used for PET AC, makes the reconstructed PET as close as possible to the gold standard PET. The third proposed method introduces a novel PET-based loss that minimizes CT residuals with respect to the PET reconstruction

A Theory of Justice of John Rawls as Basis for European Fiscal Union

Fiscal policies coordination, macro-stability purposes and provision of European public goods are undoubtedly economic goals of paramount importance when considering the implementation of Fiscal Union at European level. However, there is also a complementary component of moral nature embedded in the constitution of any fiscal system, that is reallocation of resources. The core idea of the paper is that A Theory of Justice of John Rawls can provide a new and compelling basis accounting for the institution of European Fiscal Union in the redistributive perspective since the European Union holds a) a scheme of mutually advantageous cooperation and b) a thick network of institutions which constitute a basic structure. The main outcome of this analysis is a European difference principle. This conclusion is then followed by a corollary: if the European institutions are to be shaped to reflect an arrangement of Rawlsian nature, they should also include Fiscal Union at European level