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deepmr.radial_stack

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deepmr.radial_stack#

deepmr.radial_stack(shape, nviews=None, accel=1, **kwargs)[source]#

Design a stack-of-stars trajectory.

As in the 2D radial case, 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 spoke.

Finally, slice dimension is assumed to be the outermost loop.

Parameters:

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

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

  • accel (int, optional) – Slice acceleration factor. Ranges from 1 (fully sampled) to nslices. The default is 1.

Keyword Arguments:

  • acs_shape (int) – Matrix size for inner (coil sensitivity estimation) region along slice encoding direction. The default is None.

  • 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 stack-of-stars trajectory for a (128, 128, 120) voxels matrix by:

>>> head = deepmr.radial_stack((128, 120))

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

>>> head = deepmr.radial_stack((128, 120), nviews=64)

Slice acceleration can be specified using the accel argument. For example, the following

>>> head = deepmr.radial_stack((128, 120), accel=2)

will generate the following trajectory:

>>> head.traj.shape
torch.Size([1, 24120, 128, 3])

i.e., a Nyquist-sampled stack-of-stars trajectory with a slice acceleration of 2 (i.e., 60 encodings).

Parallel imaging calibration region can be specified using acs_shape argument:

>>> head = deepmr.radial_stack((128, 120), accel=2, acs_shape=32)

The generated stack will have an inner 32-wide fully sampled k-space region.

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_stack((128, 120, 420))
>>> head.traj.shape
torch.Size([420, 120, 128, 3])

corresponding to 420 different contrasts, each sampled with a single radial spoke of 128 points, repeated for 120 slice encodings. Similarly, multiple echoes (with fixed sampling) can be specified as:

>>> head = deepmr.radial_stack((128, 120, 1, 8))
>>> head.traj.shape
torch.Size([8, 48240, 128, 3])

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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