Advances in locally constrained k-space-based parallel MRI

In this article, several theoretical and methodological developments regarding k-space-based, locally constrained parallel MRI (pMRI) reconstruction are presented. A connection between Parallel MRI with Adaptive Radius in k-Space (PARS) and GRAPPA methods is demonstrated. The analysis provides a basis for unified treatment of both methods. Additionally, a weighted PARS reconstruction is proposed, which may absorb different weighting strategies for improved image reconstruction. Next, a fast and efficient method for pMRI reconstruction of data sampled on non-Cartesian trajectories is described. In the new technique, the computational burden associated with the numerous matrix inversions in the original PARS method is drastically reduced by limiting direct calculation of reconstruction coefficients to only a few reference points. The rest of the coefficients are found by interpolating between the reference sets, which is possible due to the similar configuration of points participating in reconstruction for highly symmetric trajectories, such as radial and spirals. As a result, the time requirements are drastically reduced, which makes it practical to use pMRI with non-Cartesian trajectories in many applications. The new technique was demonstrated with simulated and actual data sampled on radial trajectories.