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.
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