Exploring subspace-constrained approaches to low-rank fMRI acceleration

Functional magnetic resonance imaging (fMRI) is a medical imaging technique that measures brain activity non-invasively. One of the fundamental quandaries in fMRI is the balance that must be struck between spatial fidelity and temporal resolution. An increase in sampling efficiency could improve either or both of these metrics, allowing images to be created from fewer data points than would otherwise be required. This process is referred to as acceleration. Some degree of acceleration is already standard in fMRI scans. The most common acceleration methods are parallel imaging methods, which utilise the spatial sensitivity profiles of the receiver coils in order to separate the aliased artefacts that result from using fewer data to create each image. However, there are other mathematical properties which can also be incorporated into the reconstruction process in order to allow a higher degree of acceleration. One such property is the inherently low-rank nature of fMRI data, which was introduced by Chiew et al. in 2015 as the k-t FASTER method (fMRI Accelerated in Space-Time via Truncation of Effective Rank). The authors also demonstrated in 2016 that the low-rank information could be combined with the coil sensitivity profiles to achieve a higher acceleration factor than either low-rank information or coil profiles could achieve alone. In this thesis, the k-t FASTER approach is expanded upon by incorporating additional, subspace- specific constraints into the reconstruction process. First, k-t FASTER will be reformulated as an alternating minimisation problem in order to more easily allow subspace-specific regularisation terms. Then, a variety of constraints will be explored in an artificial framework. The constraints being tested are: Tikhonov constraints (which encourage the subspaces to take more minimal energy forms), low-resolution priors (which more greatly weight the oversampled central k-space in radial sampling), and a temporal subspace smoothing constraint (which minimises the variation between frames). These constraints will be applied to real fMRI data acquired with a TURBINE trajectory (Trajectory Using Radially Batched Internal Navigator Echoes), a hybrid radial-Cartesian 3D trajectory with Golden Ratio angle increments in the radial orientation. The aforementioned subspace-constrained approaches could be seen to achieve better classification of the underlying functional activation over a k-t FASTER reconstruction in real data at R=16, or TRvol=0.5s. Ultimately, Tikhonov constraints are found to provide consistently high-quality reconstructions at a range of acceleration factors and SNR values, but in real data with a slow-paradigm task fMRI experiment at high acceleration (R=26, TRvol=0.3s), the temporal subspace smoothing constraints can outperform Tikhonov constraints.