create_cutoff_decay_density

create_cutoff_decay_density#

mrinufft.trajectories.sampling.create_cutoff_decay_density(shape, cutoff, decay, resolution=None)[source]#

Create a density with central plateau and polynomial decay.

Create a density composed of a central constant-value ellipsis defined by a cutoff ratio, followed by a polynomial decay over outer regions as defined in [Cha+22].

Parameters:

  • shape (tuple of int) – The shape of the density grid, analog to the field-of-view as opposed to resolution below.

  • cutoff (float) – The ratio of the largest k-space dimension between 0 and 1 within which density remains uniform and beyond which it decays.

  • decay (float) – The polynomial decay in density beyond the cutoff ratio.

  • resolution (np.ndarray, optional) – Resolution scaling factors for each dimension of the density grid, by default None.

Returns:

A density array with values decaying based on the specified cutoff ratio and decay rate.

Return type:

np.ndarray

References

[Cha+22]

Chaithya, G. R., Pierre Weiss, Guillaume Daval-Frérot, Aurélien Massire, Alexandre Vignaud, and Philippe Ciuciu. “Optimizing full 3D SPARKLING trajectories for high-resolution magnetic resonance imaging.” IEEE Transactions on Medical Imaging 41, no. 8 (2022): 2105-2117.