MRIStackedNUFFT

class mrinufft.operators.MRIStackedNUFFT(samples: ndarray[tuple[int, ...], dtype[_ScalarType_co]], shape: tuple[int, int, int], backend: str | FourierOperatorBase, smaps: ndarray[tuple[int, ...], dtype[_ScalarType_co]] | None, z_index: Literal['auto'] | ndarray[tuple[int, ...], dtype[_ScalarType_co]] | None = 'auto', n_coils: int = 1, n_batchs: int = 1, squeeze_dims: bool = False, **kwargs)

Bases: FourierOperatorBase

Stacked NUFFT Operator for MRI.

The dimension of stacking is always the last one.

Parameters:

• samples (array-like) – Sample locations in a 2D kspace

• shape (tuple) – Shape of the image.

• z_index (array-like) – Cartesian z index of masked plan. if “auto” the z_index is computed from the samples, if they are 3D, using the last coordinate.

• backend (str or FourierOperatorBase) – Backend to use. If str, a NUFFT operator is initialized with str being a registered backend. If FourierOperatorBase, operator is checked for compatibility and used as is notably one should have: n_coils = self.n_coils*len(z_index), squeeze_dims=True, smaps=None

• smaps (array-like) – Sensitivity maps.

• n_coils (int) – Number of coils.

• n_batchs (int) – Number of batchs.

• **kwargs (dict) – Additional arguments to pass to the backend.

Methods

__init__
adj_op	Adjoint operator.
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.
make_deepinv_phy	Make a new DeepInv Physics with NUFFT operator.
make_linops	Create a Scipy Linear Operator from the NUFFT operator.
op	Forward operator.
pinv_solver	Solves the linear system Ax = y.
update_samples	Update the samples of the NUFFT operator.
with_autograd	Return a Fourier operator with autograd capabilities.
with_off_resonance_correction	Return a new operator with Off Resonnance Correction.

Attributes

autograd_available
available
backend
cpx_dtype	Return complex floating precision of the operator.
density	Density compensation of the operator.
dtype	Return dtype.
img_full_shape	Full image shape with batch and coil dimensions.
interfaces
ksp_full_shape	Full kspace shape with batch and coil dimensions.
n_batchs	Number of coils for the operator.
n_coils	Number of coils for the operator.
n_samples	Return number of samples.
ndim	Number of dimensions in image space of the operator.
norm_factor	Normalization factor of the operator.
samples	Return samples as a N_slice x N_samples x 3 array.
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.

Examples using mrinufft.operators.MRIStackedNUFFT

Stacked NUFFT operator

Stacked NUFFT operator

backend: ClassVar[str] = 'stacked'

available: ClassVar[bool] = True

autograd_available = False

property shape: tuple[int, ...]

Shape of the image space of the operator.

property n_coils: int

Number of coils for the operator.

property n_batchs

Number of coils for the operator.

property smaps

Sensitivity maps of the operator.

static _init_samples(samples: ndarray[tuple[int, ...], dtype[_ScalarType_co]], z_index: Literal['auto'] | ndarray[tuple[int, ...], dtype[_ScalarType_co]] | None, shape: tuple[int, ...]) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]]

Return type:

tuple[ndarray[tuple[int, …], dtype[_ScalarType_co]], ndarray[tuple[int, …], dtype[_ScalarType_co]]]

property dtype

Return dtype.

property n_samples

Return number of samples.

static _fftz(data)

Apply FFT on z-axis.

static _ifftz(data)

Apply IFFT on z-axis.

op(data, ksp=None)

Forward operator.

Note

This function uses numpy for all CPU arrays, and cupy for all on-gpu array. It will convert all its array argument to the respective array library. The outputs will be converted back to the original array module and device.

_op_sense(data, ksp=None)

Apply SENSE operator.

_op_calibless(data, ksp=None)

adj_op(coeffs, img=None)

Adjoint operator.

Note

This function uses numpy for all CPU arrays, and cupy for all on-gpu array. It will convert all its array argument to the respective array library. The outputs will be converted back to the original array module and device.

_adj_op_sense(coeffs, img)

_adj_op_calibless(coeffs, img)

get_lipschitz_cst(max_iter=10)

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.

property samples

Return samples as a N_slice x N_samples x 3 array.

Built from the 2D samples and the z_index normalized to [-0.5, 0.5).

_abc_impl = <_abc._abc_data object>

_safe_squeeze(arr)

Squeeze the first two dimensions of shape of the operator.

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

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

Parameters:

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

• ksp (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.

compute_density(method: Callable[[...], ndarray[tuple[int, ...], dtype[_ScalarType_co]]] | bool | None | str | dict[str, Any] = 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.

compute_smaps(method: ndarray[tuple[int, ...], dtype[_ScalarType_co]] | Callable[[...], ndarray[tuple[int, ...], dtype[_ScalarType_co]]] | str | dict[str, Any] | None = 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)

property cpx_dtype

Return complex floating precision of the operator.

data_consistency(image_data: ndarray[tuple[int, ...], dtype[_ScalarType_co]], obs_data: ndarray[tuple[int, ...], dtype[_ScalarType_co]]) → ndarray[tuple[int, ...], dtype[_ScalarType_co]]

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.

Return type:

ndarray[tuple[int, …], dtype[_ScalarType_co]]

property density: ndarray[tuple[int, ...], dtype[floating]] | None

Density compensation of the operator.

property img_full_shape: tuple[int, ...]

Full image shape with batch and coil dimensions.

interfaces: dict[str, tuple[bool, type[FourierOperatorBase]]] = {'bart': (False, <class 'mrinufft.operators.interfaces.bart.MRIBartNUFFT'>), 'cartesian': (True, <class 'mrinufft.operators.cartesian.MRICartesianOperator'>), 'cufinufft': (True, <class 'mrinufft.operators.interfaces.cufinufft.MRICufiNUFFT'>), 'ducc0': (False, <class 'mrinufft.operators.interfaces.ducc0.MRIDUCC0'>), 'finufft': (True, <class 'mrinufft.operators.interfaces.finufft.MRIfinufft'>), 'gpunufft': (True, <class 'mrinufft.operators.interfaces.gpunufft.MRIGpuNUFFT'>), 'numpy': (True, <class 'mrinufft.operators.interfaces.nudft_numpy.MRInumpy'>), 'pynfft': (False, <class 'mrinufft.operators.interfaces.nfft.MRInfft'>), 'pynufft-cpu': (False, <class 'mrinufft.operators.interfaces.pynufft_cpu.MRIPynufft'>), 'sigpy': (True, <class 'mrinufft.operators.interfaces.sigpy.MRISigpyNUFFT'>), 'stacked': (True, <class 'mrinufft.operators.stacked.MRIStackedNUFFT'>), 'stacked-cufinufft': (True, <class 'mrinufft.operators.stacked.MRIStackedNUFFTGPU'>), 'tensorflow': (False, <class 'mrinufft.operators.interfaces.tfnufft.MRITensorflowNUFFT'>), 'torchkbnufft-cpu': (False, <class 'mrinufft.operators.interfaces.torchkbnufft.TorchKbNUFFTcpu'>), 'torchkbnufft-gpu': (False, <class 'mrinufft.operators.interfaces.torchkbnufft.TorchKbNUFFTgpu'>)}

property ksp_full_shape: tuple[int, int, int]

Full kspace shape with batch and coil dimensions.

make_autograd(*, wrt_data: bool = True, wrt_traj: bool = False, paired_batch: bool = False) → MRINufftAutoGrad

Make a new Operator with autodiff support.

Parameters:

• 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

• paired_batch (int, optional) – If provided, specifies batch size for varying data/smaps pairs. Default is None, which means no batching

Returns:

A NUFFT operator with autodiff capabilities.

Return type:

torch.nn.module

Raises:

ValueError – If autograd is not available.

make_deepinv_phy(*args, **kwargs) → DeepInvPhyNufft

Make a new DeepInv Physics with NUFFT operator.

Parameters:

• 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

• paired_batch (int, optional) – If provided, specifies batch size for varying data/smaps pairs. Default is None, which means no batching

• viewed_as_real (bool, optional) – If True, the DeepInverse physics wrapper accepts and returns real-view tensors with a final dimension of size 2 representing the real and imaginary parts. Default is False.

Returns:

A NUFFT operator with autodiff capabilities.

Return type:

torch.nn.module

Raises:

ValueError – If autograd is not available.

make_linops(*, cupy: bool = False)

Create a Scipy Linear Operator from the NUFFT operator.

We add a _nufft private attribute with the current operator.

Parameters:

cupy (bool, default False) – If True, create a Cupy Linear Operator

See also

-, -

property ndim

Number of dimensions in image space of the operator.

property norm_factor: floating

Normalization factor of the operator.

pinv_solver(kspace_data, optim='lsqr', **kwargs)

Solves the linear system Ax = y.

It uses a least-square optimization solver,

Parameters:

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

• optim (str, default "lsqr") – name of the least-square optimizer to use.

• **kwargs – Extra arguments to pass to the least-square optimizer.

Returns:

Reconstructed image

Return type:

NDArray

update_samples(new_samples: ndarray[tuple[int, ...], dtype[floating]], *, unsafe: bool = False)

Update the samples of the NUFFT operator.

Parameters:

• new_samples (np.ndarray or GPUArray) – The new samples location of shape Nsamples x N_dimensions.

• unsafe (bool, default False) – If True, the original array is used directly without any checks. This should be used with caution as it might lead to unexpected behavior.

Notes

If unsafe is True, the new_samples should be of shape (Nsamples, N_dimensions), F-ordered (column-major) and in the range [-pi, pi]. If not, this will lead to unexpected behavior. You have been warned.

If unsafe is False, this is automatically handled.

property uses_density

Return True if the operator uses density compensation.

property uses_sense

Return True if the operator uses sensitivity maps.

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

Return a Fourier operator with autograd capabilities.

with_off_resonance_correction(readout_time: NDArray, b0_map: NDArray | None = None, r2star_map: NDArray | None = None, mask: NDArray | None = None, interpolator: str | dict | tuple[NDArray, NDArray] = 'svd') → MRIFourierCorrected

Return a new operator with Off Resonnance Correction.

Return type:

MRIFourierCorrected