The design of feasible trajectories to traverse the k-space for sampling in magnetic resonance imaging (MRI) is important while considering ways to reduce the scan time. Over the recent years, non-Cartesian trajectories have been observed to result in benign artifacts and being less sensitive to motion. In this paper, we propose a generalized framework that encompasses projection-based methods to generate feasible non-Cartesian k-space trajectories. This framework allows to construct feasible trajectories from both random or structured initial trajectories, e.g., based on the traveling salesman problem (TSP). We evaluate the performance of the proposed methods by simulating the reconstruction of 128 × 128 and 256 × 256 phantom and brain MRI images in terms of structural similarity (SSIM) index and peak signal-to-noise ratio (PSNR) using compressed sensing techniques. It is observed that the TSP-based trajectories from the proposed projection method with constant acceleration parameterization (CAP) result in better reconstruction compared to the projection method with constant velocity parameterization (CVP) and this for a similar read-out time. Further, random-like trajectories are observed to be better than TSP-based trajectories as they reduce the read-out time while providing better reconstruction quality. A reduction in read-out time by upto 67% is achieved using the proposed projection with permutation (PP) method.@en

Variable density sampling of the k-space in MRI is an integral part of trajectory design. It has been observed that data-driven trajectory design methods provide a better image reconstruction as compared to trajectories obtained from a fixed or a parametric density function. In this paper, a data-driven strategy has been proposed to obtain non-Cartesian continuous k-space sampling trajectories for MRI under the compressed sensing framework (greedy non-Cartesian (GNC)). A stochas-tic version of the algorithm (stochastic greedy non-Cartesian (SGNC)) is also proposed that reduces the computation time. We compare the proposed trajectory with a traveling salesman problem (TSP)-based trajectory and an echo planar imaging-like trajectory obtained by a greedy method called stochastic greedy-Cartesian (SGC) algorithm. The training images are taken from knee images of the fastMRI dataset. It is observed that the proposed algorithms outperform the TSP-based and the SGC trajectories for similar read-out times.@en