  Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered
as two distinct reconstruction problems. Inspired by recent k-space
interpolation methods, an annihilating filter based low-rank Hankel matrix
approach (ALOHA) is proposed as a general framework for sparsity-driven k-space
interpolation method which unifies pMRI and CS-MRI. Specifically, our framework
is based on the fundamental duality between the transform domain sparsity in
the primary space and the low-rankness of weighted Hankel matrix in the
reciprocal space, which converts pMRI and CS-MRI to a k-space interpolation
problem using structured matrix completion. Using theoretical results from the
latest compressed sensing literatures, we showed that the required sampling
rates for ALOHA may achieve the optimal rate. Experimental results with in vivo
data for single/multi-coil imaging as well as dynamic imaging confirmed that
the proposed method outperforms the state-of-the-art pMRI and CS-MRI.
