initialize_3D_floret#

mrinufft.trajectories.inits.floret.initialize_3D_floret(Nc: int, Ns: int, in_out: bool = False, nb_revolutions: float = 1, spiral: str | float = 'fermat', cone_tilt: str | float = 'golden', max_angle: float = 1.5707963267948966, axes: tuple = (2,)) → ndarray[tuple[int, ...], dtype[_ScalarType_co]][source]#

Initialize 3D trajectories with FLORET.

This implementation is based on the work from [Pip+11]. The acronym FLORET stands for Fermat Looped, Orthogonally Encoded Trajectories. It consists of Fermat spirals folded into 3D cones along one or several axes.

Parameters:

  • Nc (int) – Number of shots

  • Ns (int) – Number of samples per shot

  • in_out (bool, optional) – Whether to start from the center or not, by default False

  • nb_revolutions (float, optional) – Number of revolutions of the spirals, by default 1

  • spiral (str, float, optional) – Spiral type, by default “fermat”

  • cone_tilt (str, float, optional) – Tilt of the cones around the \(k_z\)-axis, by default “golden”

  • max_angle (float, optional) – Maximum polar angle starting from the \(k_x-k_y\) plane, by default pi / 2

  • axes (tuple, optional) – Axes over which cones are created, by default (2,)

Returns:

3D FLORET trajectory

Return type:

NDArray

References

[Pip+11]

Pipe, James G., Nicholas R. Zwart, Eric A. Aboussouan, Ryan K. Robison, Ajit Devaraj, and Kenneth O. Johnson. “A new design and rationale for 3D orthogonally oversampled k-space trajectories.” Magnetic resonance in medicine 66, no. 5 (2011): 1303-1311.