Self-calibrated GRAPPA method for 2D and 3D radial data

A fast parallel MRI (pMRI) reconstruction method is presented for 2D and 3D radial trajectories. A limitation of the radial generalized autocalibrating partially parallel acquisitions (GRAPPA) method is the need to acquire training data prior to the actual scan. This can be eliminated by the use of self-calibration when synthesizing the missing data for each coil reconstruction. The training data for each coil are estimated by multiplying the conventionally reconstructed composite image, which contains the aliasing artifacts from undersampling, with each coil's spatial sensitivity profile. An estimate of the individual receiver spatial sensitivity profiles is obtained from the k-space data that fulfill the Nyquist sampling criterion. The frequency domain representation of the training data is then calculated at the acquired k-space sample points and at the unacquired locations at which we desire to synthesize k-space data. Fitting the acquired k-space samples to the unacquired points creates reconstruction weights that are used to synthesize unacquired radial lines. The in vivo feasibility of the method for 2D radial trajectories is illustrated with an example of 2D abdominal imaging. Preliminary results obtained after applying the method on a 3D radial steady-state free precession (SSFP) data set are also demonstrated.