Abstract
This paper analyzes the famous GRAPPA algorithm, which is one of most widely used image reconstruction algorithms for parallel magnetic resonance imaging (pMRI). Inherently the existing GRAPPA type algorithms ignore the physical background of k-space data and treat the image reconstruction problem as a pure data interpolation problem which is solved based on an assumption that the k-space data are shift-invariant autoregressive process. Based on physical principles of MRI, this paper reveals the difficulty of such assumption. New GRAPPA algorithm is developed where the above assumption is relaxed and the missing k-space data are reconstructed based on physical properties of k-space data and coil sensitivity profiles, which can be estimated using Auto-Calibrating Signal (ACS) lines. This proposed algorithm can greatly improve the image quality even at very high acceleration factor. The in vivo examples demonstrate the overwhelming advantages of the proposed algorithm.
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