Acceleration

Physics

Undersampling

Trajectory

Spiral (railway)

Mathematics

Algorithm

Filter (signal processing)

Astronomy

Iterative reconstruction

Compressed sensing

Mathematical analysis

Sampling (signal processing)

Computer science

Nyquist–Shannon sampling theorem

Computer vision

Classical mechanics

IEEE Transactions on Medical Imaging

The overall duration of acquiring a Nyquist sampled 3D dataset can be significantly shortened by enhancing the efficiency of k-space sampling. This can be achieved by increasing the coverage of k-space for every trajectory interleave. Furthermore, acceleration is possible by making use of advantageous undersampling properties. In this paper, a versatile 3D center-out k-space trajectory based on Jacobian elliptic functions (Seiffert's spiral) is presented. The trajectory leads to a low-discrepancy coverage of k-space using a considerably reduced number of readouts compared with other approaches. Such a coverage is achieved for any number of interleaves, and, therefore, even single-shot trajectories can be constructed to be combined with, for example, hyperpolarized media. Furthermore, acceleration is achievable due to non-coherent undersampling properties of the trajectory in combination with non-linear reconstruction techniques like compressed sensing (CS). Simulations of point-spread functions and discrepancy evaluations compare Seiffert's spiral to the established 3D cones approach. Imaging capabilities are evaluated by comparison of in vivo knee images using Nyquist and undersampled datasets in combination with CS reconstructions.

Efficient 3D Low-Discrepancy ${k}$ -Space Sampling Using Highly Adaptable Seiffert Spirals