GROG-pCS: GRAPPA Operator Gridding with CS-based p-thresholding for Under-sampled Radially Encoded MRI

Major limitation of MRI is long scan time. Compressed Sensing (CS) is a contemporary technique used to accelerate MRI scan time. In CS, fully sampled MRI images are reconstructed from the partially acquired k-space data. In CS MRI, the utilization of a non-linear reconstruction algorithm is one of the key requirements for successful signal recovery. Numerous methods have been used in CS for solving the non-linear problems to get the solution image. In this paper, we proposed GRAPPA Operator gridding (GROG) with CS-based p-thresholding to reconstruct the artefact free MR images from the partially acquired radial k-space data. In this proposed scheme, initially radially acquired under-sampled k-space data is mapped onto Cartesian space using GROG gridding and then CS reconstruction is performed by using iterative p-thresholding. The proposed method is tested on four MRI data sets, (i) simulated Shepp-Logan phantom, (ii) 1.5T human brain data, (iii) 3T human brain, and (iv) 3T short-axial cardiac (SA) radial data. The reconstruction results are compared with the CS-based iterative hard-thresholding and soft-thresholding reconstructions. The quality of the solution images is evaluated by using (i) Artifact Power (AP), (ii) Root Mean Square Error (RMSE), and (iii) Peak Signal-to-Noise Ratio (PSNR).