On analysis of GRAPPA algorithm for image reconstruction of parallel MRI

Magnetic resonance imaging (MRI) is one of the major imaging modalities in medicine and biology with advantages in imaging soft tissues and great flexibility for various applications. However, its relatively long imaging time has obstructed its further development. To accelerate the imaging process, parallel MRI (pMRI) was proposed which applies multiple receive coils operating in parallel to acquire k-space signals. Unfortunately, because of constraints of image reconstruction algorithms, pMRI can not accelerate the imaging process as much as expected. The purpose of this paper is to analyze the famous GRAPPA algorithm which is the most widely used algorithm for image reconstruction of pMRI in both research and clinic applications. It will be revealed that the difficulty of GRAPPA algorithm lies in its assumption that k-space sequence is an autoregressive (AR) process, which in general is not right necessarily. A condition will be developed for the correctness of this assumption and a measurement will be given to numerically measure the fitness of the AR model identified by GRAPPA. An in vivo example is also studied to demonstrate the proposed theoretical results about GRAPPA algorithm.