linop.NUFFT

linop.NUFFT#

class bartorch.linop.NUFFT#

Bases: LinearOperator

Non-uniform FFT from images to samples along a trajectory.

Type-2 transform with a negative exponent, scaled by one over the square root of the number of voxels, as BART’s nufft; computed by FINUFFT (cuFINUFFT on a card) through BART’s nufft_create.

Parameters:

  • traj (tensor) – Trajectory (*encoding, shots, samples, ndim) in grid units (kx, ky[, kz]), as bartorch.tools.traj() returns. A kz that is zero everywhere makes the transform two-dimensional. The encoding axes are any further axes the samples vary along (frames, echoes, cardiac phases).

  • image_shape (tuple of int) – Image shape (*batches, *encoding, [z,] y, x). Leading batch axes (coils, slices) are transformed independently.

  • kspace_shape (tuple of int, default=None) – Sample shape, which must be (*batches, *encoding, shots, samples); None takes it.

  • weights (tensor, default=None) – k-space weighting, broadcast over (*encoding, shots, samples); applied on the forward and conjugated on the adjoint.

  • basis (tensor, default=None) – Temporal subspace basis (coeffs, frames) over the last encoding axis, which has length coeffs in the image and frames in k-space.

  • toeplitz (bool, default=True) – Apply the normal as a convolution with a point spread function rather than as the forward and adjoint transforms. The point spread function includes weights and basis.

  • oversampling (float, default=0.0) – Upsampling factor of FINUFFT’s fine grid, BART’s -o; 0 takes the library setting (1.25 by default). On a card only 2 and 1.25 are accepted.

  • width (float, default=0.0) – Spreading-kernel width in fine-grid points, BART’s -w, converted to the FINUFFT tolerance that gives it and clamped at single precision; 0 keeps the library tolerance.

Raises:

ValueError – When the trajectory, image, sample shape, weights or basis are inconsistent.

Examples

>>> A = NUFFT(traj, image_shape=(8, 128, 128))
>>> A.adjoint(kspace).shape
torch.Size([8, 128, 128])

Also has the methods and properties of LinearOperator.

Examples using NUFFT#

7. Basics of non-Cartesian imaging

7. Basics of non-Cartesian imaging