GROG Facilitated Compressed Sensing for Radial MRI

Incoherent k-space sampling plays a critical role in Compressed Sensing MRI (CS-MRI) by facilitating efficient utilization of the limited number of acquired samples to reconstruct high-quality images with reduced acquisition time and improved signal-to-noise ratio. Non-Cartesian sampling like radial, spiral, or randomly sampled trajectories are faster and provide more incoherent k-space compared to Cartesian sampling. However, maintaining the reconstruction quality at high acceleration factors is still challenging with non-Cartesian acquisitions. Addressing these challenges typically involves the use of a GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) operator generated Bunched Phase Encoding data together with a conjugate gradient (CG) reconstruction algorithm, that mimics the functionality of the oscillating gradients required for bunched phase encoding sampling. However, the CG reconstruction method using GRAPPA Operator Gridding (GROG)-generated bunched points is limited to lower acceleration factors ( $AF= 2\sim 6 $ ). In this paper, a novel CS-based reconstruction framework is proposed leveraging enhanced incoherence along with added redundancy of GROG-generated BPE data, to generate artifact-free images from highly undersampled radial acquisitions. In the proposed framework, GRAPPA operator gridding is applied as a first step, on multi-coil undersampled radial data to generate randomly blipped BPE points. The GROG-generated BPE points (non-Cartesian data) are mapped to the Cartesian grid using self-calibrating GRAPPA operator gridding prior to CS-based image reconstruction. To better understand how the GROG-generated bunched points affect the reconstruction quality, sensitivity maps are not explicitly estimated during the CS reconstruction as a first choice. However, incorporating sensitivity maps of multiple channels helps balance data fidelity and regularization; therefore, the performance of the proposed method using coil sensitivity maps has also been investigated. The proposed methods have been validated with both the simulated and in-vivo multi-coil radial datasets. A comparison between the proposed methods and contemporary CS-based reconstruction methods is performed using quantifying parameters such as Artifact Power, Signal-to-Noise ratio, and Root Mean Square Error. The reconstructed images of the proposed method are also subjectively evaluated by expert radiologists. Experimental results show that the proposed methods yield superior performance, both quantitatively and qualitatively at higher acceleration factors ( $ upto~AF= 14$ ) in comparison with the contemporary CS-based image reconstruction techniques.