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 (np.ndarray) – The samples used by the operator.

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

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

• n_coils (int) – The number of coils.

• smaps (np.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.
compute_density	Compute the density compensation weights and set it.
data_consistency	Compute the gradient data consistency.
get_lipschitz_cst	Return the Lipschitz constant of the operator.
op	Non Cartesian MRI forward operator.
with_off_resonnance_correction	Return a new operator with Off Resonnance Correction.

Attributes

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.

op(data, ksp=None)

Non Cartesian MRI forward operator.

Parameters:

• data (np.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

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).

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.

_safe_squeeze(arr)

Squeeze the first two dimensions of shape of the operator.