Sparsity-Promoting Spatiotemporal Regularization for Data Mining in Functional Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) has opened unprecedented avenues to observe the human brain non-invasively. In particular, for about two decades, functional MRI (fMRI) has enabled to monitor brain function using the blood-oxygen-level-dependent (BOLD) contrast as a proxy for neuronal activity. The impact of fMRI on neurosciences, medicine, and psychology is ever increasing and has been mainly focussing on (1) understanding brain organization in terms of segregation (i.e., localized processing) and integration (i.e., distributed processing), specifically, related to sensory processing and cognition; (2) exploring temporal characteristics of brain processes. FMRI provides large spatiotemporal datasets, typically one whole-brain volume with spatial resolution of 1–3 mm in each dimension, every 1–4 seconds during several minutes. The structure of neurophysiological contributions in these data is complex and therefore requires advanced data processing. Conventional fMRI analysis is exploiting timing properties of a stimulation or task paradigm designed by the experimenter; i.e., evidence is sought for the presence of a hypothetical BOLD response. More recently, the community has shown increasing interest in spontaneous brain activity acquired during resting-state fMRI (RS-fMRI). In the absence of any task, data-driven or exploratory methods have found great use. In particular, blind source separation such as independent component analysis (ICA) has been widely applied to RS-fMRI data. One limitation of current data-driven methods is the lack of incorporating knowledge about the hemodynamic system, which governs any activity-related signal component in the fMRI measurements. In this dissertation, we build upon the latest advances in convex optimization and propose a novel framework that can reveal activity-inducing signals at the fMRI timescale. In particular, our regularization strategy, termed “total activation” (TA), allows deconvolving the fMRI signal to remove hemodynamic blur and to improve spatial contrast of activation patterns by incorporating knowledge about meaningful brain regions. The contribution of our method lies in adapting and tailoring state-of-the-art signal processing techniques with specific domain knowledge from fMRI and neurosciences. First, we extend “total variation” (TV), which is a well-recognized method in image processing for edge-preserving regularization. TV favors signals that are piecewise constant, and, therefore, whose derivatives are sparse. We generalize this concept for signals of which the derivative of an additional linear differential operator is sparse, and build a variational formulation for the denoising problem. The recovered signal can be also studied after applying the regularizing operators; e.g., applying the differential operator will lead to the piecewise constant driving signal, while applying an additional derivative reveals a sparse “innovation” signal. Fast and efficient schemes from convex optim