bartorch.linop.NUFFT

class bartorch.linop.NUFFT(traj, image_shape, kspace_shape=None, weights=None, basis=None, toeplitz=True, oversampling=0.0, width=0.0)

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

Parameters:

• traj (tensor) – Trajectory of shape (..., samples, 3) in grid units, as bartorch.tools.traj() produces. Its third component being zero makes the transform two-dimensional.

• image_shape (tuple of int) – Coil-image shape, C order, for instance (coils, y, x).

• kspace_shape (tuple of int, optional) – Sample shape; by default the trajectory’s, with the coordinate axis replaced by the image’s coil axes.

• weights (tensor, optional) – Diagonal in k-space, applied on the way out and conjugated on the way back.

• basis (tensor, optional) – Subspace basis over frames and coefficients, contracting the image’s coefficients into k-space frames. The weights and the basis are part of the operator because its Toeplitz normal is built over both.

• toeplitz (bool) – Apply the normal as a convolution with a point spread function.

• oversampling (float) – Grid oversampling and kernel width; zero keeps the defaults.

• width (float) – Grid oversampling and kernel width; zero keeps the defaults.

Examples

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

__init__(traj, image_shape, kspace_shape=None, weights=None, basis=None, toeplitz=True, oversampling=0.0, width=0.0)

Methods

A(x, **kwargs)	A x, under deepinv's name.
A_adjoint(y, **kwargs)	A^H y, under deepinv's name, recorded for autograd.
A_adjoint_A(x, **kwargs)	A^H A x, under deepinv's name, recorded for autograd.
A_dagger(y, **kwargs)	The pseudo-inverse, under deepinv's name.
__init__(traj, image_shape[, kspace_shape, ...])
adjoint(y[, out])	A^H y, without recording for autograd.
cogram()	A A^H as an operator.
conj()	conj(A): conjugate the input, apply, conjugate the output.
forward(x[, out])	A x, without recording for autograd.
gram()	A^H A as an operator.
normal(x[, out])	A^H A x.
opnorm()	The spectral norm, by BART's power iteration on A^H A.
pinv(y[, damp])	(A^H A + damp I)^-1 A^H y, the damped least-squares solution.
to_nonlinear()	The same operator as a NonlinearOperator.

Attributes

H	A^H, from BART's own adjoint constructor.
T	A^T, the adjoint without the conjugation, as conj(A).H.
codim_rank	How many axes the codomain has.
codim_shape	The codomain, under pyxu's name for it; the same as oshape.
codim_size	How many elements the codomain holds.
device
dim_rank	How many axes the domain has.
dim_shape	The domain, under pyxu's name for it; the same as ishape.
dim_size	How many elements the domain holds.
ishape
oshape