A novel class of k-space trajectories for magnetic resonance imaging (MRI) sampling using space filling curves (SFCs) is presented here. More specifically, Peano, Hilbert and Sierpinski curves are used. We propose 1-shot and 4-shot variable density SFCs by utilizing the space coverage provided by SFCs in different iterations. The proposed trajectories are compared with state-of-the-art echo planar imaging (EPI) trajectories for 128 × 128 and 256 × 256 phantom and brain images. The simulation results show that the readout time is reduced by up to 45% for the 128 × 128 image with little compromise in reconstruction quality. Also, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index are improved by 2.32 dB and 0.1009, respectively, with an 18% shorter readout time using the 4-shot Hilbert SFC trajectory for reconstructing a 256 × 256 brain MRI image.@en

The development of compressed sensing (CS) techniques for magnetic resonance imaging (MRI) is enabling a speedup of MRI scanning. To increase the incoherence in the sampling, a random selection of points on the k-space is deployed and a continuous trajectory is obtained by solving a traveling salesman problem (TSP) through these points. A feasible trajectory satisfying the gradient constraints is then obtained by parameterizing it using state-of-the-art methods. In this paper, a constrained convex optimization based method to obtain feasible trajectories is proposed. The method is motivated by the fact that the readout time is proportional to the number of sample points and includes the lengths of the segments of the trajectory in the cost function to obtain variable length trajectories. The proposed method provides a reduction in readout time by more than 50% for random-like trajectories with an improvement of about 1.5 dB in peak signal-to-noise ratio (PSNR) and 0.0762 in structural similarity (SSIM) index on average for a realistic brain phantom MRI image adopting single-shot trajectories.@en