initialize_2D_eccentric

initialize_2D_eccentric#

mrinufft.trajectories.inits.eccentric.initialize_2D_eccentric(Nc, Ns, radius_ratio, center_ratio=0.0, nb_revolutions=1.0, min_distance=0.0, seed=None)[source]#

Initialize a 2D ECCENTRIC trajectory.

This is a reproduction of the proposition from [Kla+24]. It creates trajectories as uniformly distributed circles, with a pseudo rosette-like structure at the center to ensure its coverage. ECCENTRIC stands for ECcentric Circle ENcoding TRajectorIes for Compressed sensing.

Notes

This implementation follows the original propositions but decisions were made about missing details and additional features are proposed: - circles are oriented such that their starting points are the closest to the center. It is chosen to avoid sampling the center at radically different times, which would cause contrast discrepancies and signal loss due to dephasing. - the number of circle revolutions is an input instead of sticking to 1, to handle multi-echo sequences or simply benefit from a higher duty cycle.

Parameters:

  • Nc (int) – Number of shots/circles.

  • Ns (int) – Number of samples per shot/circle.

  • radius_ratio (float) – Radius of each circle relatively to the k-space radius, between 0 and 0.5.

  • center_ratio (float, optional) – Proportion between 0 and 1 of shots positioned around the center into a pseudo-rosette pattern. Default to 0.

  • nb_revolutions (float, optional) – Number of revolutions per circle. Defaults to 1.

  • min_distance (float, optional) – Minimum allowed distance between consecutive circles relatively to the k-space radius between 0 and 0.5. Defaults to 0.

  • seed (int | None, optional) – Random seed for reproducibility, used only to draw the circle centers. Defaults to None.

Returns:

The generated 2D trajectory with shape (Nc, Ns, 2).

Return type:

NDArray[np.float64]

References

[Kla+24]

Klauser, Antoine, Bernhard Strasser, Wolfgang Bogner, Lukas Hingerl, Sebastien Courvoisier, Claudiu Schirda, Bruce R. Rosen, Francois Lazeyras, and Ovidiu C. Andronesi. “ECCENTRIC: a fast and unrestrained approach for high-resolution in vivo metabolic imaging at ultra-high field MR”. Imaging Neuroscience 2 (2024): 1-20.

Contents