nlop.NonlinearSense

nlop.NonlinearSense#

class bartorch.nlop.NonlinearSense#

Bases: NonlinearOperator

Joint image and coil-sensitivity forward model, BART’s noir.

Two inputs, the image and the coil coefficients, and one output. The coil input is not the sensitivity maps but a k-space representation \(\hat{s}\) of them, mapped to the maps by the Sobolev weighting

\[S = \mathcal{F}^{-1} \left[ \, c \, (1 + a |k|^2)^{-b/2} \, \hat{s} \, \right]\]

(BART’s noir_calc_weights), so the coils are smooth by construction and a Gauss-Newton step needs no separate penalty on them. coils maps fitted coefficients to sensitivities.

On a grid the output is k-space. Off the grid, as BART builds the model, the output is the gridded coil images, nufft^H of k-space; prepare() brings a measurement to that form.

Parameters:

  • image_shape (tuple of int) – Coil-image shape (coils, *spatial), C order, as the linear encodings take it. The image input is this shape with one coil.

  • pattern (torch.Tensor, default=None) – Sampling mask on the grid, one at acquired positions; None on a grid is all ones. Off the grid it is passed to BART as is and may not be combined with basis.

  • trajectory (torch.Tensor, default=None) – Trajectory (..., samples, 3) in grid units, as bartorch.tools.traj() produces; selects the non-Cartesian model.

  • kspace_shape (tuple of int, default=None) – Sample shape. Default: image_shape on a grid, (coils, *trajectory.shape[:-1], 1) off it.

  • coil_shape (tuple of int, default=None) – Shapes of the sensitivities and of their coefficients; both default to image_shape.

  • coefficient_shape (tuple of int, default=None) – Shapes of the sensitivities and of their coefficients; both default to image_shape.

  • weights (torch.Tensor, default=None) – k-space diagonal applied to the samples off the grid; its conjugate is applied in the adjoint.

  • basis (torch.Tensor, default=None) – Temporal subspace basis (coefficients, frames) over the last encoding axis; off the grid only.

  • mask (torch.Tensor, default=None) – Support the image is restricted to.

  • sobolev (tuple of float, default=(220.0, 32.0)) – (a, b) of the coil weighting; BART’s defaults.

  • c (float, default=1.0) – Scale of the coil weighting.

  • real (bool, default=False) – Constrain the image to be real.

  • sos (bool, default=False) – BART’s sum-of-squares variant of the coil weighting.

  • oversampling_coils (float, default=None) – Grid oversampling of the coil coefficients; None takes nlinv’s choice, 2 off the grid and 1 on it.

  • oversampled_coils (bool, default=False) – Return the sensitivities on the oversampled grid rather than the image’s.

  • toeplitz (bool, default=True) – Off the grid, apply the normal operator as a convolution with a point spread function rather than as a NUFFT and its adjoint.

  • optimized (bool, default=False) – Off the grid, BART’s noir2_noncart_optimized_create.

Raises:

ValueError – If basis is given on a grid, or with pattern off the grid.

Examples

>>> F = NonlinearSense((8, 128, 128), pattern=mask)
>>> F.ishapes
((1, 128, 128), (8, 128, 128))
>>> image, coefficients = nlop.IRGNM()(kspace, F)
property coils#

Linear operator from coil coefficients to sensitivity maps.

The Sobolev weighting followed by the inverse Fourier transform.

property image#

support mask and real constraint.

Type:

Linear operator applied to the image input

property data#

Linear operator from the model’s output to k-space.

The NUFFT off the grid, whose adjoint is prepare(); the identity on a grid.

property transform#

Linear operator from coil images to k-space, the encoding after the product.

prepare()#

Bring a measurement to the model’s output.

Off the grid this is nufft^H(kspace), as noir2_recon applies it before the first Gauss-Newton step; on a grid kspace is returned unchanged.

Parameters:

kspace (torch.Tensor) – Measurement of kspace_shape.

Returns:

Tensor of oshape.

Return type:

torch.Tensor

Also has the methods and properties of NonlinearOperator.

Examples using NonlinearSense#

4. Joint reconstruction of image and sensitivity maps

4. Joint reconstruction of image and sensitivity maps