"""Three-dimensional stack-of-stars sampling."""
__all__ = ["radial_stack"]
import math
import numpy as np
# this is for stupid Sphinx
try:
from ... import _design
except Exception:
pass
from ..._types import Header
[docs]def radial_stack(shape, nviews=None, accel=1, **kwargs):
r"""
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 : Header
Acquisition header corresponding to the generated sampling pattern.
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`` (:func:`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.
"""
assert len(shape) >= 2, "Please provide at least (in-plane, nslices) as shape."
# expand shape if needed
shape = list(shape)
while len(shape) < 4:
shape = shape + [1]
# default views
if nviews is None:
if shape[2] == 1:
nviews = int(math.pi * shape[0])
else:
nviews = 1
# expand acs if needed
if "acs_shape" in kwargs:
acs_shape = kwargs["acs_shape"]
else:
acs_shape = None
kwargs.pop("acs_shape", None)
# assume 1mm iso
fov = shape[0]
# design single interleaf spiral
tmp, _ = _design.radial(fov, shape[0], 1, 1, **kwargs)
# rotate
ncontrasts = shape[2]
# generate angles
dphi = (1 - 233 / 377) * 360.0
phi = np.arange(ncontrasts * nviews) * dphi # angles in degrees
phi = np.deg2rad(phi) # angles in radians
# build rotation matrix
rot = _design.angleaxis2rotmat(phi, "z")
# get trajectory
traj = tmp["kr"] * tmp["mtx"]
traj = _design.projection(traj[0].T, rot)
traj = traj.swapaxes(-2, -1).T
traj = traj.reshape(nviews, ncontrasts, *traj.shape[-2:])
traj = traj.swapaxes(0, 1)
# expand slices
nz = shape[1]
az = np.arange(-nz // 2, nz // 2, dtype=np.float32)
# accelerate
az = az[::accel]
# add back ACS
if acs_shape is not None:
az = np.concatenate(
(az, np.arange(-acs_shape // 2, acs_shape // 2, dtype=np.float32))
)
az = np.unique(az)
# expand
traj = np.apply_along_axis(np.tile, -3, traj, len(az))
az = np.repeat(az, nviews)
az = az[None, :, None] * np.ones_like(traj[..., 0])
# append new axis
traj = np.concatenate((traj, az[..., None]), axis=-1)
# expand echoes
nechoes = shape[-1]
traj = np.repeat(traj, nechoes, axis=0)
# get dcf
dcf = tmp["dcf"]
# get shape
shape = [shape[1]] + tmp["mtx"]
# get time
t = tmp["t"]
# calculate TE
min_te = float(tmp["te"][0])
TE = np.arange(nechoes, dtype=np.float32) * t[-1] + min_te
# extra args
user = {}
user["acs_shape"] = tmp["acs"]["mtx"]
# get indexes
head = Header(shape, t=t, traj=traj, dcf=dcf, TE=TE, user=user)
head.torch()
return head
