FourierOperatorCPU

class mrinufft.operators.base.FourierOperatorCPU(samples, shape, density=False, n_coils=1, n_batchs=1, n_trans=1, smaps=None, raw_op=None, squeeze_dims=True)

Bases: FourierOperatorBase

Base class for CPU-based NUFFT operator.

The NUFFT operation will be done sequentially and looped over coils and batches.

Parameters:

• samples (NDArray) – The samples used by the operator.

• shape (tuple) – The shape of the image space (in 2D or 3D)

• density (bool or NDArray) – If True, the density compensation is estimated from the samples. If False, no density compensation is applied. If NDArray, the density compensation is applied from the array.

• n_coils (int) – The number of coils.

• smaps (NDArray) – The sensitivity maps.

• raw_op (object) – An object implementing the NUFFT API. Ut should be responsible to compute a single type 1 /type 2 NUFFT.

Methods

__init__
adj_op	Non Cartesian MRI adjoint operator.
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	Non Cartesian MRI forward 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
cpx_dtype	Return complex floating precision of the operator.
density	Density compensation of the operator.
dtype	Return floating precision of the operator.
interfaces
n_batchs	Number of coils for the operator.
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.FourierOperatorCPU

Minimal example script

Minimal example script

op(data, ksp=None)

Non Cartesian MRI forward operator.

Parameters:

• data (NDArray)

• space. (The uniform (2D or 3D) data in image)

Return type:

Results array on the same device as data.

Notes

this performs for every coil ell: ..math:: mathcal{F}mathcal{S}_ell x

Note

This function uses numpy internally, and will convert all its array argument to numpy arrays. The outputs will be converted back to the original array module and device.

adj_op(coeffs, img=None)

Non Cartesian MRI adjoint operator.

Parameters:

coeffs (np.array or GPUArray)

Return type:

Array in the same memory space of coeffs. (ie on cpu or gpu Memory).

Note

This function uses numpy internally, and will convert all its array argument to numpy arrays. The outputs will be converted back to the original array module and device.

data_consistency(image_data, obs_data)

Compute the gradient data consistency.

This mixes the op and adj_op method to perform F_adj(F(x-y)) on a per coil basis. By doing the computation coil wise, it uses less memory than the naive call to adj_op(op(x)-y)

Parameters:

• image (array) – Image on which the gradient operation will be evaluated. N_coil x Image shape is not using sense.

• obs_data (array) – Observed data.

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.