  In this work we introduce a new method that combines Parallel MRI and
Compressed Sensing (CS) for accelerated image reconstruction from subsampled
k-space data. The method first computes a convolved image, which gives the
convolution between a user-defined kernel and the unknown MR image, and then
reconstructs the image by CS-based image deblurring, in which CS is applied for
removing the inherent blur stemming from the convolution process. This method
is hence termed CORE-Deblur. Retrospective subsampling experiments with data
from a numerical brain phantom and in-vivo 7T brain scans showed that
CORE-Deblur produced high-quality reconstructions, comparable to those of a
conventional CS method, while reducing the number of iterations by a factor of
10 or more. The average Normalized Root Mean Square Error (NRMSE) obtained by
CORE-Deblur for the in-vivo datasets was 0.016. CORE-Deblur also exhibited
robustness regarding the chosen kernel and compatibility with various k-space
subsampling schemes, ranging from regular to random. In summary, CORE-Deblur
enables high quality reconstructions and reduction of the CS iterations number
by 10-fold.
