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Magn Reson Med. 2019 Mar;81(3):2064-2071. doi: 10.1002/mrm.27497. Epub 2018 Oct 17.

Trajectory optimized NUFFT: Faster non-Cartesian MRI reconstruction through prior knowledge and parallel architectures.

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Institute of Imaging Science, Vanderbilt University Medical Center, Nashville, Tennessee.



The non-uniform fast Fourier transform (NUFFT) involves interpolation of non-uniformly sampled Fourier data onto a Cartesian grid, an interpolation that is slowed by complex, non-local data access patterns. A faster NUFFT would increase the clinical relevance of the plethora of advanced non-Cartesian acquisition methods.


Here we customize the NUFFT procedure for a radial trajectory and GPU architecture to eliminate the bottlenecks encountered when allowing for arbitrary trajectories and hardware. We call the result TRON, for TRajectory Optimized NUFFT. We benchmark the speed and accuracy TRON on a Shepp-Logan phantom and on whole-body continuous golden-angle radial MRI.


TRON was 6-30× faster than the closest competitor, depending on test data set, and was the most accurate code tested.


Specialization of the NUFFT algorithm for a particular trajectory yielded significant speed gains. TRON can be easily extended to other trajectories, such as spiral and PROPELLER. TRON can be downloaded at


GPU; MRI; golden angle; gridding; radial

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