Jointly Learning Non-Cartesian k-Space Trajectories and Reconstruction Networks for 2D and 3D MR Imaging through Projection

Compressed sensing in magnetic resonance imaging essentially involves the optimization of (1) the sampling pattern in k-space under MR hardware constraints and (2) image reconstruction from undersampled k-space data. Recently, deep learning methods have allowed the community to address both problems simultaneously, especially in the non-Cartesian acquisition setting. This work aims to contribute to this field by tackling some major concerns in existing approaches. Particularly, current state-of-the-art learning methods seek hardware compliant k-space sampling trajectories by enforcing the hardware constraints through additional penalty terms in the training loss. Through ablation studies, we rather show the benefit of using a projection step to enforce these constraints and demonstrate that the resulting k-space trajectories are more flexible under a projection-based scheme, which results in superior performance in reconstructed image quality. In 2D studies, our novel PROjection for Jointly lEarning non-Cartesian Trajectories while Optimizing Reconstructor (PROJeCTOR) trajectories present an improved image reconstruction quality at a 20-fold acceleration factor on the fastMRI data set with SSIM scores of nearly 0.92–0.95 in our retrospective studies as compared to the corresponding Cartesian reference and also see a 3–4 dB gain in PSNR as compared to earlier state-of-the-art methods. Finally, we extend the algorithm to 3D and by comparing optimization as learning-based projection schemes, we show that data-driven joint learning-based PROJeCTOR trajectories outperform model-based methods such as SPARKLING through a 2 dB gain in PSNR and 0.02 gain in SSIM.