FourierOperatorBase

class mrinufft.operators.base.FourierOperatorBase

Bases: ABC

Base Fourier Operator class.

Every (Linear) Fourier operator inherits from this class, to ensure that we have all the functions rightly implemented as required by ModOpt.

Methods

__init__
adj_op	Compute adjoint operator transform.
cg	Conjugate Gradient method to solve the inverse problem.
check_shape	Validate the shapes of the image or k-space data against operator shapes.
compute_density	Compute the density compensation weights and set it.
compute_smaps	Compute the sensitivity maps and set it.
data_consistency	Compute the gradient data consistency.
get_lipschitz_cst	Return the Lipschitz constant of the operator.
make_autograd	Make a new Operator with autodiff support.
op	Compute operator transform.
with_autograd	Return a Fourier operator with autograd capabilities.
with_off_resonance_correction	Return a new operator with Off Resonnance Correction.

Attributes

autograd_available
cpx_dtype	Return complex floating precision of the operator.
density	Density compensation of the operator.
dtype	Return floating precision of the operator.
interfaces
n_coils	Number of coils for the operator.
n_samples	Return the number of samples used by the operator.
ndim	Number of dimensions in image space of the operator.
norm_factor	Normalization factor of the operator.
samples	Return the samples used by the operator.
shape	Shape of the image space of the operator.
smaps	Sensitivity maps of the operator.
uses_density	Return True if the operator uses density compensation.
uses_sense	Return True if the operator uses sensitivity maps.
backend
available

Examples using mrinufft.operators.base.FourierOperatorBase

Reconstruction with conjugate gradient

Reconstruction with conjugate gradient

Off-resonance corrected NUFFT operator

Off-resonance corrected NUFFT operator

Minimal example script

Minimal example script

Stacked NUFFT operator

Stacked NUFFT operator

Subspace NUFFT Operator

Subspace NUFFT Operator

check_shape(*, image=None, ksp=None)

Validate the shapes of the image or k-space data against operator shapes.

Parameters:

• image (np.ndarray, optional) – If passed, the shape of image data will be checked.

• ksp (np.ndarray or object, optional) – If passed, the shape of the k-space data will be checked.

Raises:

ValueError – If the shape of the provided image does not match the expected operator shape, or if the number of k-space samples does not match the expected number of samples.

abstract op(data)

Compute operator transform.

Parameters:

data (np.ndarray) – input as array.

Returns:

result – operator transform of the input.

Return type:

np.ndarray

abstract adj_op(coeffs)

Compute adjoint operator transform.

Parameters:

x (np.ndarray) – input data array.

Returns:

results – adjoint operator transform.

Return type:

np.ndarray

data_consistency(image_data, obs_data)

Compute the gradient data consistency.

This is the naive implementation using adj_op(op(x)-y). Specific backend can (and should!) implement a more efficient version.

with_off_resonance_correction(B, C, indices)

Return a new operator with Off Resonnance Correction.

compute_smaps(method=None)

Compute the sensitivity maps and set it.

Parameters:

method (callable or dict or array) – The method to use to compute the sensitivity maps. If an array, it should be of shape (NCoils,XYZ) and will be used as is. If a dict, it should have a key ‘name’, to determine which method to use. other items will be used as kwargs. If a callable, it should take the samples and the shape as input. Note that this callable function should also hold the k-space data (use funtools.partial)

make_autograd(wrt_data=True, wrt_traj=False)

Make a new Operator with autodiff support.

Parameters:

• variable (, default data) – variable on which the gradient is computed with respect to.

• wrt_data (bool, optional) – If the gradient with respect to the data is computed, default is true

• wrt_traj (bool, optional) – If the gradient with respect to the trajectory is computed, default is false

Returns:

A NUFFT operator with autodiff capabilities.

Return type:

torch.nn.module

Raises:

ValueError – If autograd is not available.

compute_density(method=None)

Compute the density compensation weights and set it.

Parameters:

method (str or callable or array or dict or bool) –

The method to use to compute the density compensation.

• If a string, the method should be registered in the density registry.

• If a callable, it should take the samples and the shape as input.

• If a dict, it should have a key ‘name’, to determine which method to use.

other items will be used as kwargs. - If an array, it should be of shape (Nsamples,) and will be used as is. - If True, the method pipe is chosen as default estimation method.

Notes

The “pipe” method is only available for the following backends: tensorflow, finufft, cufinufft, gpunufft, torchkbnufft-cpu and torchkbnufft-gpu.

get_lipschitz_cst(max_iter=10, **kwargs)

Return the Lipschitz constant of the operator.

Parameters:

• max_iter (int) – number of iteration to compute the lipschitz constant.

• **kwargs – Extra arguments givent

Returns:

Spectral Radius

Return type:

float

Notes

This uses the Iterative Power Method to compute the largest singular value of a minified version of the nufft operator. No coil or B0 compensation is used, but includes any computed density.

cg(kspace_data, compute_loss=False, **kwargs)

Conjugate Gradient method to solve the inverse problem.

Parameters:

• kspace_data (np.ndarray) – The k-space data to reconstruct.

• computer_loss (bool) – Whether to compute the loss at each iteration. If True, loss is calculated and returned, otherwise, it’s skipped.

• **kwargs – Extra arguments to pass to the conjugate gradient method.

Returns:

• np.ndarray – Reconstructed image

• np.ndarray, optional – array of loss at each iteration, if compute_loss is True.

property uses_sense

Return True if the operator uses sensitivity maps.

property uses_density

Return True if the operator uses density compensation.

property ndim

Number of dimensions in image space of the operator.

property shape

Shape of the image space of the operator.

property n_coils

Number of coils for the operator.

property smaps

Sensitivity maps of the operator.

_check_smaps_shape(smaps)

Check the shape of the sensitivity maps.

property density

Density compensation of the operator.

property dtype

Return floating precision of the operator.

property cpx_dtype

Return complex floating precision of the operator.

property samples

Return the samples used by the operator.

property n_samples

Return the number of samples used by the operator.

property norm_factor

Normalization factor of the operator.

classmethod with_autograd(wrt_data=True, wrt_traj=False, *args, **kwargs)

Return a Fourier operator with autograd capabilities.