Blind Source Separation of functional dynamic MRI signals via Dictionary Learning

Magnetic Resonance Imaging (MRI) constitutes a non-invasive medical imaging technique that allows the exploration of the inner anatomy, tissues, and physiological processes of the body. Among the different MRI applications, functional Magnetic Resonance Imaging (fMRI) has slowly become an essential tool for investigating the brain behavior and, nowadays, it plays a fundamental role in clinical and neurophysiological research. Due to its particular nature, specialized signal processing techniques are required in order to analyze the fMRI data properly. Among the various related techniques that have been developed over the years, the General Linear Model (GLM) is one of the most widely used approaches, and it usually appears as a default in many specialized software toolboxes for fMRI. On the other end, Blind Source Separation (BSS) methods constitute the most common alternative to GLM, especially when no prior information regarding the brain activity is available, e.g., in resting-state fMRI experiments. Nevertheless, despite the relatively large volume of potentially suitable alternatives within this framework, Independent Component Analisis (ICA) and Dictionary Learning (DL) are the two most popular approaches. However, although both, ICA and DL, are BSS methods that build upon matrix factorization models, they differ considerably from a theoretical perspective concerning the underlying assumptions, which, in turn, leads to different relative advantages and limitations in practice. In this thesis, we focus our attention on the ICA- and DL-based approaches. After pondering the viability of the most commonly used techniques, we introduce an alternative DL formulation tailored to the fMRI data analysis. Among other merits, this novel formulation complies with the natural sparse structure of the fMRI data, and it naturally paves the way for exploring external information that is available from fMRI experimental evidence. Moreover, we develop a novel DL algorithm to implement this new formulation, referred to as Information Assisted Dictionary Learning (IADL). Unlike conventional alternatives, the proposed IADL turns out to have many advantages, which make it particularly attractive for analyzing fMRI data. Conventional DL-based techniques (as well as some constrained ICA-based alternatives) explicitly require the selection of a particular regularization parameter (or a set of regularization parameters). These parameters usually lack a meaningful interpretation, which renders the corresponding selection a hard task in practice, requiring the use of cross-validation arguments that have no practical meaning when working with fMRI. In contrast, IADL is based on a new set of regularization parameters that bear a direct neurophysiological interpretation, which significantly facilitates their selection in practice. Besides, this natural interpretation allows for exploiting external information that is related to the underlying sparse activity structure of the brain and which is available from other fMRI studies and brain atlases. Furthermore, IADL can naturally incorporate the basic assumption associated with GLM. In words, that of known functional responses of the brain activations. However, in the context of IADL, this can be done in a soft manner via constraints that render this assumption much more realistic. In turn, this allows the combination of GLM with IADL, which leads to an integrated method that shares the enhanced statistical power of GLM and, at the same time, exploits the main advantages of IADL. In order to quantitatively verify the advantages of the proposed alternative compared to more conventional and standard state-of-the-art alternatives, we use a synthetic fMRI-like data set and two real task-related fMRI experiments. The study over these datasets shows that the proposed alternative exhibits improved sensitivity in detecting the significant activation patterns of interest and anatomical reliability compared to more conventional approaches. Furthermore, the study over the synthetic dataset reveals that IADL shows remarkable robustness to the miss-modeling of the associated regularization parameters compared to the more standard methods. Overall, the proposed approach offers a more powerful and reliable alternative that effectively copes with the major limitations of the more conventional DL-based alternatives for the fMRI data analysis. We believe that further scrutiny and wide adoption of the proposed formulation and the use of the introduced IADL algorithm can contribute to improvements in the adoption of the analysis of DL-based techniques for the fMRI data analysis across the corresponding scientific community.