A Bayesian approach to GRAPPA parallel fMRI image reconstruction increases SNR and power of task detection

In fMRI, capturing brain activation during a task is dependent on how quickly k-space arrays are obtained. Acquiring full k-space arrays, which are reconstructed into images using the inverse Fourier transform (IFT), that make up volume images can take a considerable amount of scan time. Undersampling k-space reduces the acquisition time but results in aliased, or “folded,” images. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) is a parallel imaging technique that yields full images from subsampled arrays of k-space. GRAPPA uses localized interpolation weights, which are estimated prescan and fixed over time, to fill in the missing spatial frequencies of the subsampled k-space. Here we propose a Bayesian approach to GRAPPA (BGRAPPA) where prior distributions for the unacquired spatial frequencies, localized interpolation weights, and k-space measurement uncertainty are assessed from the a priori calibration k-space arrays. The prior information is utilized to estimate the missing spatial frequency values from the posterior distribution and reconstruct into full field-of-view images. Our BGRAPPA technique successfully reconstructed both a simulated and experimental time series resulting in reduced noise leading to an increased signal-to-noise ratio (SNR) and stronger power of task detection.