k-t FASTER: a new method for the acceleration of resting state FMRI data acquisition

Background: Functional MRI has seen a recent resurgence of interest in fast imaging techniques, to harvest statistical benefit from increased degrees of freedom or to provide novel temporal information. However, fast imaging based on sparsity (e.g., compressed sensing) remains largely unexplored in FMRI because the data is not sparse in any of the conventional transform domains. We propose a more appropriate alternative for FMRI, the related concept of matrix completion, which recovers low-rank approximations of under-sampled matrices. This approach is motivated by the wellestablished observation that FMRI data are well represented at low rank, for example when using principal component analysis for dimensionality reduction prior to using independent component analysis (ICA) to identify resting state networks (RSNs). In effect, this dimensionality reduction represents a transform domain under which the space time data can be represented with a small number of spatial maps and their associated timecourses. We propose to take advantage of these properties to accelerate FMRI acquisition by undersampling in the k-t domain and using matrix recovery to estimate the low-rank k-t matrix approximation. We call this approach k-t FASTER: (FMRI Acceleration in Space-time via Truncation of Effective Rank). k-t FASTER is demonstrated on retrospectively undersampled k-t FMRI data using a novel matrix recovery algorithm, iterative hard thresholding with matrix shrinkage (IHT+MS) to produce high fidelity representations of fMRI RSNs at 4x undersampling. Critically, our results are driven entirely by k-t matrix structure, and constitute a fundamentally different approach from time-independent acceleration techniques that reconstruct volumes based on coil information.