Source code for deepmr._vobj.sampling.rosette_proj

"""Three-dimensional rosette projection sampling."""

__all__ = ["rosette_proj"]

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_proj(shape, nviews=None, bending_factor=1.0, order="ga"): r""" Design a 3D rosette projection trajectory. The trajectory consists of a 2D rosette trajectory, whose plane is rotated to cover the 3D k-space. In-plane rotations are sequential. Plane rotation types are specified via the ``order`` argument. Parameters ---------- shape : Iterable[int] Matrix shape ``(in-plane, contrasts=1, echoes=1)``. nviews : int, optional Number of petals (in-plane, radial). The default is ``$\pi$ * (shape[0], shape[1])`` if ``shape[2] == 1``, otherwise it is ``($\pi$ * shape[0], 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``. order : str, optional Rosette plane rotation type. These can be: * ``ga``: Pseudo golden angle variation of periodicity ``377``. * ``ga::multiaxis``: Pseudo golden angle, i.e., same as ``ga`` but views are repeated 3 times on orthogonal axes. * ``ga-sh``: Shuffled pseudo golden angle. * ``ga-sh::multiaxis``: Multiaxis shuffled pseudo golden angle, i.e., same as ``ga-sh`` but views are repeated 3 times on orthogonal axes. The default is ``ga``. Returns ------- head : Header Acquisition header corresponding to the generated sampling pattern. Example ------- >>> import deepmr We can create a Nyquist-sampled 3D rosette trajectory for a matrix of ``(128, 128, 128)`` voxels by: >>> head = deepmr.rosette_proj(128) An undersampled trajectory can be generated by specifying the ``nviews`` argument: >>> head = deepmr.rosette_proj(128, nviews=64) Petals bending can be modified via ``bending_factor``: >>> head = deepmr.rosette_proj(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_proj((128, 420)) >>> head.traj.shape torch.Size([420, 402, 128, 2]) corresponding to 420 different contrasts, each sampled with a different fully sampled plane. Similarly, multiple echoes (with fixed sampling) can be specified as: >>> head = deepmr.rosette_proj((128, 1, 8)) >>> head.traj.shape torch.Size([8, 161604, 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 # expand nviews if needed if np.isscalar(nviews): nviews = [int(math.pi * shape[0]), nviews] else: nviews = list(nviews) # 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) dphi = 360.0 / nviews[0] dtheta = (1 - 233 / 377) * 360.0 # build rotation angles j = np.arange(ncontrasts * nviews[1]) i = np.arange(nviews[0]) j = np.tile(j, nviews[0]) i = np.repeat(i, ncontrasts * nviews[1]) # radial angle if order[:5] == "ga-sh": theta = (i + j) * dtheta else: theta = j * dtheta # in-plane angle phi = i * dphi # convert to radians theta = np.deg2rad(theta) # angles in radians phi = np.deg2rad(phi) # angles in radians # perform rotation axis = np.zeros_like(theta, dtype=int) # rotation axis Rx = _design.angleaxis2rotmat(theta, [1, 0, 0]) # whole-plane rotation about x Rz = _design.angleaxis2rotmat(phi, [0, 0, 1]) # in-plane rotation about z # put together full rotation matrix rot = np.einsum("...ij,...jk->...ik", Rx, Rz) # get trajectory traj = tmp["kr"] * tmp["mtx"] traj = np.concatenate((traj, 0 * traj[..., [0]]), axis=-1) traj = _design.projection(traj[0].T, rot) traj = traj.swapaxes(-2, -1).T traj = traj.reshape(nviews[0], nviews[1], ncontrasts, *traj.shape[-2:]) traj = traj.transpose(2, 1, 0, *np.arange(3, len(traj.shape))) traj = traj.reshape(ncontrasts, -1, *traj.shape[3:]) # get dcf dcf = tmp["dcf"] dcf = _design.angular_compensation(dcf, traj.reshape(-1, *traj.shape[-2:]), axis) dcf = dcf.reshape(*traj.shape[:-1]) # apply multiaxis if order[-9:] == "multiaxis": # expand trajectory traj1 = np.stack((traj[..., 2], traj[..., 0], traj[..., 1]), axis=-1) traj2 = np.stack((traj[..., 1], traj[..., 2], traj[..., 0]), axis=-1) traj = np.concatenate((traj, traj1, traj2), axis=-3) # expand dcf dcf = np.concatenate((dcf, dcf, dcf), axis=-2) # renormalize dcf tabs = (traj[0, 0] ** 2).sum(axis=-1) ** 0.5 k0_idx = np.argmin(tabs) nshots = nviews[0] * nviews[1] * ncontrasts # impose that center of k-space weight is 1 / nshots scale = 1.0 / (dcf[[k0_idx]] + 0.000001) / nshots dcf = scale * dcf # expand echoes nechoes = shape[1] traj = np.repeat(traj, nechoes, axis=0) dcf = np.repeat(dcf, nechoes, axis=0) # get shape shape = [shape[0]] + list(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