ArbEPI: matlab/pulseq code for generating 3D-EPI sequences from arbitrary 2D sampling masks in the phase-encode-partition (ky-kz) plane

Background

According to compressed sensing, randomly sampling k-space results in incoherent interference in some sparse transform domain e.g. wavelets. This effectively turns the dealiasing problem into a denoising problem, thus allowing the image the be reconstructed from sub-Nyquist sampled k-space. The same principles can be extended to dynamic MRI, where the desired image, when reshaped into a (space x time) matrix, is low-rank in applications like fMRI. By definition, a low-rank matrix is sparse in the singular value domain, thus we want aliasing artifacts that are dense in the singular value domain i.e. high-rank or noise-like when reshaped into a (space x time) matrix. This can be achieved by randomly sampling k-t-space, but there are two obstacles: 1. It is unclear what is the best random sampling strategy. 2. It is technically nontrivial to program the MRI scanner randomly sample k-space. To address these challenges, we present ArbEPI, a framework that accepts arbitrary 2D sampling masks in the phase-encoding-partition (ky-kz) plane and creates fast vendor-agnostic 3D-EPI sequences using the open-source Pulseq library. Examples include: CAIPI, temporally-interleaved CAIPI (TI-CAIPI), Poisson-disc, and Gaussian-weighted random sampling. Tested on GE scanners.

Getting started

1. Set experimental parameters in params.m. The sampling method (samplingMethod) and GE hardware constants are also configured here. Make a copy of this file for each experiment to preserve parameters for reconstruction.
2. Run main.m to generate all four sequences at once:

   main

   Or run individual sequences manually in order:

   omegas = gen_sampling_masks(R);   % Ny x Nz x Nframes logical mask
   ArbEPI(omegas);  % writes ArbEPI.seq/.pge and samp_locs.mat
   EPIcal();        % writes EPIcal.seq/.pge and kxoe<Nx>.mat
   GRE();           % writes GRE.seq/.pge (optional)
   noise();         % writes noise.seq/.pge (optional)

   All outputs go to output/. EPIcal and noise must run after ArbEPI as they load samp_locs.mat.

On the scanner (GE)

1. Set up .pge files by following: https://github.com/jfnielsen/TOPPEpsdSourceCode/tree/UserGuide/v7#running-a-sequence-on-the-scanner (private repo).
2. Run a localizer sequence.
3. Run EPIcal.pge using auto-prescan.
4. Run noise.pge using manual-prescan, keeping the same receiver gain settings from the previous step.
5. Run ArbEPI.pge using manual-prescan, keeping the same receiver gain settings from the previous step.
6. (optional) Run GRE.pge using auto-prescan.

File overview

Root — user-facing files

File	Purpose
params.m	Central configuration: scan geometry, timing, GE hardware constants, sampling method, output directory
main.m	Run all four sequences in order from a single entry point
gen_sampling_masks.m	Generate Ny × Nz × Nframes sampling mask given acceleration factor R
ArbEPI.m	Main 3D-EPI sequence function; takes sampling mask as input
EPIcal.m	Calibration sequence (mirrors ArbEPI, blips zeroed)
GRE.m	Gradient echo reference sequence for sensitivity maps
noise.m	Noise prescan for noise prewhitening
plot_epi.m	Visualization scripts (trajectories, sampling mask, PSF)

lib/ — helper functions (called by the scripts above)

File	Purpose
mask2epi.m	Core algorithm: partition 2D mask into efficient EPI trajectories
caipi_sample.m	Regular CAIPI-shifted sampling masks
ticaipi_sample.m	Temporally-interleaved CAIPI masks (golden-angle frame rotation)
pd_sample.m	Variable-density Poisson-disc sampling masks [1]
rand_sample.m	Weighted random sampling masks
gen_gaussian_pdf.m	2D Gaussian probability density for use with rand_sample
make_fatsat_rf.m	Create fat-saturation RF pulse object
make_excitation_pulse.m	Create slab-selective sinc excitation pulse
make_readout_grads.m	Create EPI readout gradients, blips, and ADC event
make_prephasers.m	Create x/y/z prephaser trapezoids
make_spoilers.m	Create x/y/z spoiler trapezoids
calc_te_tr_delays.m	Compute TE and TR padding delays
plot_kt_mask.m	Interactive viewer for k-t sampling mask (ky, kz, time); scroll wheel, slider, or arrow keys to scrub through frames
write_to_ge.m	Convert Pulseq sequence to GE TOPPE format and write .pge
rf2pulseq.m	Convert RF waveform from Gauss to Hz
check_grad_acoustics.m	Check gradient waveforms for forbidden frequencies

output/ — generated .seq, .pge, and .mat files (gitignored)

Methods overview

1. The core logic is in mask2epi(), which accepts any 2D sampling mask of size (Ny, Nz) and partitions it into efficient 3D-EPI trajectories given the echo train length and number of shots.
2. Sampling mask generators:
   • caipi_sample() — uniformly spaced, CAIPI-shifted masks.
   • ticaipi_sample() — temporally-interleaved CAIPI; the CAIPI shift rotates each frame to improve temporal incoherence.
   • pd_sample() — variable-density Poisson-disc masks based on the SigPy implementation [1]. Density falloff, calibration region size, and corner cropping are configurable via params.m.
   • rand_sample() — random masks weighted by a 2D probability mass function (e.g. gen_gaussian_pdf()). Gaussian sigma is configurable via params.m.
   • All methods are dispatched through gen_sampling_masks(R) via the samplingMethod parameter in params.m.
3. Trajectory generation details:
   • Samples near ky = 0 are distributed evenly across the echo train (center-out ordering) so that the effective echo time is approximately constant across shots.
   • ky is non-decreasing within each echo train so that B0-induced distortion along the phase-encode direction stays coherent.
4. Pulseq implementation details:
   • All ky and kz blips share the same duration and are contained within their readout block, enabling efficient representation as scaled copies of a single waveform.
   • The readout trapezoid is circularly shifted (split and sign-flipped) so that blips fall within the block boundary.
5. Unsolved problems:
   • Acquisition speed is bottlenecked by large k-space jumps between EPI lines. Constraining jump size whilst preserving sampling incoherence is an ongoing research problem.

Notes

The "Arb" in the package name has two meanings:

1. The framework accepts arbitrary sampling masks as input.
2. The package was developed in Ann Arbor, Michigan.

References

1. Ong, F., & Lustig, M. (2019, May). SigPy: a python package for high performance iterative reconstruction. In Proceedings of the ISMRM 27th Annual Meeting, Montreal, Quebec, Canada (Vol. 4819, No. 5).