Jakob Assländer1
1New York University School of Medicine, New York, NY, United States
Synopsis
Today, most clinical scans are performed with Cartesian k-space sampling due to its robustness and ease to implement acquisition and reconstruction. However, there are numerous reasons to use non-Cartesian sampling methods, reasons that range from robustness to motion and flow, to less intrusive undersampling artifacts and more beneficial properties for advanced image reconstruction methods such as compressed sensing. This lecture covers the basics of image reconstruction with the non-uniform FFT. The talk itself discusses the concepts and the underlying theory and is accompanied by exercises that can be done online in a browser (see syllabus for details).
Talk
This lecture focuses on the very basics of non-Cartesian image reconstruction. It discusses the non-uniform fast Fourier transformation (NFFT) [1,2] as an approximation of the discrete Fourier transform and covers its design parameters and implementations, as well as its extensions that account, e.g., for off-resonance effects.Exercises
The more theoretical and conceptual talk is accompanied by exercises that are, on the one hand, intended to recap discussed theory and provide intuition for required design parameters. On the other hand, they are intended to provide a first introduction to the interface of the here used MRIReco.jl [3] Julia package that implements the non-uniform FFT among many other MR image reconstruction tools.
The exercises can be found on github
https://github.com/JakobAsslaender/2021_ISMRM_nonCartesianReconstruction_Exercises
and can either be launched in the cloud with a single click, or you can download the open source Julia programming environment and run the exercise on your local computer. Instructions for that can be found on above linked github page.Acknowledgements
I would like to acknowledge the authors of the Julia packages that implement the non-uniform FFT and reconstruction tools, foremost Tobias Knopp, Mirco Grosser, and Jeff Fessler.References
[1] Jackson, John I., et al. "Selection of a convolution function for Fourier inversion using gridding (computerised tomography application)." IEEE transactions on medical imaging 10.3 (1991): 473-478.
[2] J. A. Fessler and B. P. Sutton, "Nonuniform fast Fourier transforms using min-max interpolation," in IEEE Transactions on Signal Processing, vol. 51, no. 2, pp. 560-574, Feb. 2003, doi: 10.1109/TSP.2002.807005.
[3] Knopp T, Grosser M. MRIReco.jl: An MRI reconstruction framework written in Julia. Magn Reson Med. 2021;00:1– 14. https://doi.org/10.1002/mrm.28792