Under-sampled functional MRI using low-rank plus sparse matrix decomposition

High spatial resolution in functional magnetic resonance imaging improves its sensitivity to brain activation signals by reducing partial volume effects. However, the long acquisition times required for high spatial resolution limit the temporal resolution in fMRI studies. Consequently, the low temporal sampling bandwidth leads to increase in physiological noise and poor modeling of the functional activation dynamics. Thus, fast techniques capable of recovering fMRI time-series from under-sampled data are desirable to improve the sensitivity and specificity of fMRI for functional brain mapping. This paper presents an under-sampled fMRI recovery using low-rank plus sparse matrix decomposition signal model. This model is suited for blocked or slow event-related fMRI studies, where the low-rank matrix captures the temporally static T*₂-weighted image patterns and, the sparse matrix captures the pseudo-periodic brain activation signal. The preliminary results of under-sampled recovery on in-vivo fMRI data show recovery of BOLD activation in human superior colliculus with contrast-to-noise ratio ≥ 4.4 (85% of reference) up to acceleration factors of 3.