Applying the uniform resampling (URS) algorithm to a lissajous trajectory: Fast image reconstruction with optimal gridding

Various kinds of nonrectilinear Cartesian k‐space trajectories have been studied, such as spiral, circular, and rosette trajectories. Although the nonrectilinear Cartesian sampling techniques generally have the advantage of fast data acquisition, the gridding process prior to 2D‐FFT image reconstruction usually requires a number of additional calculations, thus necessitating an increase in the computation time. Further, the reconstructed image often exhibits artifacts resulting from both the k‐space sampling pattern and the gridding procedure. To date, it has been demonstrated in only a few studies that the special geometric sampling patterns of certain specific trajectories facilitate fast image reconstruction. In other words, the inherent link among the trajectory, the sampling scheme, and the associated complexity of the regridding/reconstruction process has been investigated to only a limited extent. In this study, it is demonstrated that a Lissajous trajectory has the special geometric characteristics necessary for rapid reconstruction of nonrectilinear Cartesian k‐space trajectories with constant sampling time intervals. Because of the applicability of a uniform resampling (URS) algorithm, a high‐quality reconstructed image is obtained in a short reconstruction time when compared to other gridding algorithms. Magn Reson Med 44:766–781, 2000. © 2000 Wiley‐Liss, Inc.