This is the code repository of the Magnetic Resonance Technology and Methods Lab, Institute for Biomedical Engineering, ETH Zurich and University of Zurich

to reproduce the reconstruction results of

[1] K. P. Pruessmann, M. Weiger, P. Börnert, and P. Boesiger (2001), Advances in sensitivity encoding with arbitrary k-space trajectories Magnetic Resonance in Medicine 46(4), 638-651

as put forwards by the ISMRM Reproducible Research Study Group.

The code is largely based on a tutorial developed by Bertram J. Wilm and Klaas P. Pruessmann for an Educational Session on Reconstruction at ESRMRB 2012, in Lisbon, Portugal.

Several people contributed to this repository by code, feedback, review and sharing insights of their cg-SENSE experience:

• Franz Patzig
• Lars Kasper
• Thomas Ulrich
• Maria Engel
• S. Johanna Vannesjo
• Markus Weiger
• David O. Brunner
• Bertram J. Wilm
• Klaas P. Pruessmann

External Code used (from Educational Session ESMRMB):

• Felix Breuer
• Brian Hargreaves

We provide two ways of evaluating our results, depending on whether you have access to Matlab environment on your system:

1. Clone this repository into a project folder of your liking, e.g. via git clone https://github.com/mrtm-zurich/rrsg-arbitrary-sense.git rrsg-arbitrary-sense
   • Note: The data subfolder of the repo already contains the example data from http://www.user.gwdg.de/~muecker1/rrsg_challenge.zip
2. Run code/main.m.
   • The main script calls three functions creating the Figures 4 to 6 from the original paper.
   • They should correspond to figure 4,5, and 6 in the original MRM paper.
   • The created Matlab Figures are saved as PNGs to the results/ subfolder of the project folder.
3. Note: If you just want to try out the reconstruction pipeline (load data, get SENSE map, run recon) for one undersampling factor), run demoRecon.m instead of main.m in the code subfolder of the repository.

If you don't have a Matlab license, you can run this code online on https://CodeOcean.com as a Compute Capsule with its own DOI:

ISMRM 2019 RRSG Challenge: MRI Technology and Methods Lab, ETH Zurich, GitHub Submission

1. Explore the published results on the right tab from a verified run of the code.
2. Press Re-Run to see results unfold for yourself
   • you might have to sign up to CodeOcean to do so

This code is written in Matlab, R2018a, but most likely works with earlier or later versions.

In order to address the goals of the submission, we provide the following result files, reflecting the current state of the repository:

1. The algorithm including gridding and FFT, SENSE map calculation, deapodization, k-space filtering and ringing filter was implemented as in [1]. To try out the pipeline for a single dataset and reconstruction, run demoRecon.m in the main repository folder.
   • Note that the SENSE maps were calculated following

   [2] D. O. Walsh, A. F. Gmitro, and M. W. Marcellin, Adaptive reconstruction of phased array MR imagery, Magnetic Resonance in Medicine, vol. 43, no. 5, pp. 682–690, May 2000.

   • Only the central, fully sampled part of the provided radial data (about 60 samples of each spoke for the brain data) were utilized for this computation. For the heart dataset all samples were used to calculate the SENSE maps.
2. The figure reproducing reconstruction errors of R=2,3,4,5 undersampled brain data is provided in results/Figure4_brain_logDeltaOverIterations.png
   • Note that the upper-case delta, i.e., the relative deviation from the exact solution, cannot be computed in the absence of a ground truth for the imaged object. Therefore, we reconstructed an image with R=1 and picked it as the ground truth for calculating the reconstruction error for R>2.
3. Reconstruction results for R=1,2,3,4 undersampled brain data are stored in two PNG files for better readability, results/Figure5_brain_undersamplingRecon_part{1,2}.png
4. Reconstructions of the provided cardiac data using the first 11,22,33,44,55 spokes (R=5,4,3,2,1 respectively) are provided in results/Figure6_heart_undersamplingRecon.png.