"""Two-dimensional rosette sampling."""
__all__ = ["rosette"]
import math
import numpy as np
# this is for stupid Sphinx
try:
from ... import _design
except Exception:
pass
from ..._types import Header
[docs]def rosette(shape, nviews=None, bending_factor=1.0):
r"""
Design a rosette trajectory.
The rosette petals 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``.
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``.
bending_factor : float, optional
This is ``0.0`` for radial-like trajectory; increase for maximum coverage per shot.
In real world, must account for hardware and safety limitations.
The default is ``1.0``.
Returns
-------
head : Header
Acquisition header corresponding to the generated sampling pattern.
Example
-------
>>> import deepmr
We can create a Nyquist-sampled rosette trajectory for an in-plane matrix of ``(128, 128)`` pixels by:
>>> head = deepmr.rosette(128)
An undersampled trajectory can be generated by specifying the ``nviews`` argument:
>>> head = deepmr.rosette(128, nviews=64)
Petals bending can be modified via ``bending_factor``:
>>> head = deepmr.rosette(128, bending_factor=1.0) # radial-like trajectory
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.rosette((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.rosette((128, 1, 8)) # 8 echoes
>>> 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`` (: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.
"""
# expand shape if needed
if np.isscalar(shape):
shape = [shape, 1]
else:
shape = list(shape)
while len(shape) < 3:
shape = shape + [1]
# default views
if nviews is None:
if shape[1] == 1:
nviews = int(math.pi * shape[0])
else:
nviews = 1
# assume 1mm iso
fov = shape[0]
# get number of contrasts
ncontrasts = shape[1]
shape[1] = 1
shape = [shape[0], shape[2], shape[1]]
# design single interleaf spiral
tmp, _ = _design.rosette(fov, shape, 1, 1, int(math.pi * shape[0]), bending_factor)
# 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 echoes
nechoes = shape[1]
traj = np.repeat(traj, nechoes, axis=0)
# get dcf
dcf = tmp["dcf"]
# get shape
shape = tmp["mtx"]
# get time
t = tmp["t"]
# calculate TE
TE = tmp["te"]
# get indexes
head = Header(shape, t=t, traj=traj, dcf=dcf, TE=TE)
head.torch()
return head
