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deepmr.radial

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deepmr.radial#

deepmr.radial(shape, nviews=None, **kwargs)[source]#

Design a radial trajectory.

The radial spokes are rotated by a pseudo golden angle with period 377 interelaves. Rotations are performed both along view and contrast dimensions. Acquisition is assumed to traverse the contrast dimension first and then the view, i.e., all the contrasts are acquired before moving to the second view. If multiple echoes are specified, final contrast dimensions will have length ncontrasts * nechoes. Echoes are assumed to be acquired sequentially with the same radial spoke.

Parameters:

  • shape (Iterable[int]) – Matrix shape (in-plane, contrasts=1, echoes=1).

  • nviews (int, optional) – Number of spokes. The default is $\pi$ * shape[0] if shape[1] == 1, otherwise it is 1.

Keyword Arguments:

variant (str) –

Type of radial trajectory. Allowed values are:

  • fullspoke: starts at the edge of k-space and ends on the opposite side (default).

  • center-out: starts at the center of k-space and ends at the edge.

Returns:

head – Acquisition header corresponding to the generated sampling pattern.

Return type:

Header

Example

>>> import deepmr

We can create a Nyquist-sampled radial trajectory for an in-plane matrix of (128, 128) pixels by:

>>> head = deepmr.radial(128)

An undersampled trajectory can be generated by specifying the nviews argument:

>>> head = deepmr.radial(128, nviews=64)

Multiple contrasts with different sampling (e.g., for MR Fingerprinting) can be achieved by providing a tuple of ints as the shape argument:

>>> head = deepmr.radial((128, 420))
>>> head.traj.shape
torch.Size([420, 1, 128, 2])

corresponding to 420 different contrasts, each sampled with a different single radial spoke of 128 points. Similarly, multiple echoes (with fixed sampling) can be specified as:

>>> head = deepmr.radial((128, 1, 8))
>>> head.traj.shape
torch.Size([8, 402, 128, 2])

corresponding to a 8-echoes fully sampled k-spaces, e.g., for QSM and T2* mapping.

Notes

The returned head (deepmr.Header()) is a structure with the following fields:

  • shape (torch.Tensor):

    This is the expected image size of shape (nz, ny, nx).

  • t (torch.Tensor):

    This is the readout sampling time (0, t_read) in ms. with shape (nsamples,).

  • traj (torch.Tensor):

    This is the k-space trajectory normalized as (-0.5 * shape, 0.5 * shape) with shape (ncontrasts, nviews, nsamples, 2).

  • dcf (torch.Tensor):

    This is the k-space sampling density compensation factor with shape (ncontrasts, nviews, nsamples).

  • TE (torch.Tensor):

    This is the Echo Times array. Assumes a k-space raster time of 1 us and minimal echo spacing.

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