Magnetic resonance imaging (MRI) is one of the pillars of modern medical imaging, providing a non-invasive means to generate 3D images of the body with high soft-tissue contrast. Furthermore, the possibilities afforded by the design of MRI sequences enable the signal to be sensitized to a multitude of physiological tissue properties, resulting in a wide variety of distinct MRI modalities for clinical and research use. 

This thesis presents a number of advanced brain MRI applications, which fulfill, to differing extents, two complementary aims. On the one hand, they explore the benefits of a multimodal approach to MRI, combining structural, functional and diffusion MRI, in a variety of contexts. On the other, they emphasize the use of advanced mathematical and computational tools in the analysis of MRI data, such as deep learning, Bayesian statistics, and graph signal processing. 

Paper I introduces an anatomically-adapted extension to previous work in Bayesian spatial priors for functional MRI data, where anatomical information is introduced from a T1-weighted image to compensate for the low anatomical contrast of functional MRI data. 

It has been observed that the spatial correlation structure of the BOLD signal in brain white matter follows the orientation of the underlying axonal fibers. Paper II argues about the implications of this fact on the ideal shape of spatial filters for the analysis of white matter functional MRI data. By using axonal orientation information extracted from diffusion MRI, and leveraging the possibilities afforded by graph signal processing, a graph-based description of the white matter structure is introduced, which, in turn, enables the definition of spatial filters whose shape is adapted to the underlying axonal structure, and demonstrates the increased detection power resulting from their use. 

One of the main clinical applications of functional MRI is functional localization of the eloquent areas of the brain prior to brain surgery. This practice is widespread for various invasive surgeries, but is less common for stereotactic radiosurgery (SRS), a non-invasive surgical procedure wherein tissue is ablated by concentrating several beams of high-energy radiation. Paper III describes an analysis and processing pipeline for functional MRI data that enables its use for functional localization and delineation of organs-at-risk for Elekta GammaKnife SRS procedures. 

Paper IV presents a deep learning model for super-resolution of diffusion MRI fiber ODFs, which outperforms standard interpolation methods in estimating local axonal fiber orientations in white matter. Finally, Paper V demonstrates that some popular methods for anonymizing facial data in structural MRI volumes can be partially reversed by applying generative deep learning models, highlighting one way in which the enormous power of deep learning models can potentially be put to use for harmful purposes.