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FourierOp Norm #542

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FourierOp Norm #542

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614f7e1
test
fzimmermann89 Nov 15, 2024
5c29809
nufft vs fft consistancy
fzimmermann89 Nov 15, 2024
e0407d1
add prod to SpatialDimension
fzimmermann89 Nov 20, 2024
7a0639e
support DCF**.5
fzimmermann89 Nov 20, 2024
23b5f8e
scale by encoding matrix
fzimmermann89 Nov 20, 2024
60668af
change tests
fzimmermann89 Nov 20, 2024
12de434
change tests
fzimmermann89 Nov 20, 2024
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4 changes: 4 additions & 0 deletions src/mrpro/data/SpatialDimension.py
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Expand Up @@ -414,3 +414,7 @@ def shape(self) -> tuple[int, ...]:
return self.x.shape
else:
raise ValueError('Inconsistent shapes')

def prod(self: SpatialDimension[T_co]) -> T_co:
"""Calculate the product x*y*z."""
return self.x * self.y * self.z
7 changes: 7 additions & 0 deletions src/mrpro/operators/DensityCompensationOp.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
"""Class for Density Compensation Operator."""

import torch
from typing_extensions import Self

from mrpro.data.DcfData import DcfData
from mrpro.operators.EinsumOp import EinsumOp
Expand All @@ -25,3 +26,9 @@ def __init__(self, dcf: DcfData | torch.Tensor) -> None:
else:
dcf_tensor = dcf
super().__init__(dcf_tensor, '... k2 k1 k0 ,... coil k2 k1 k0 ->... coil k2 k1 k0')

def __pow__(self, exponent: float) -> Self:
"""Raise the operator to a power."""
if not exponent > 0:
raise NotImplementedError('Can only raise to positive powers')
return type(self)(dcf=self.matrix**exponent)
4 changes: 2 additions & 2 deletions src/mrpro/operators/FastFourierOp.py
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Expand Up @@ -132,10 +132,10 @@ def adjoint(self, y: torch.Tensor) -> tuple[torch.Tensor,]:
-------
IFFT of y
"""
# FFT
return self._pad_op.adjoint(
(x,) = self._pad_op.adjoint(
torch.fft.fftshift(
torch.fft.ifftn(torch.fft.ifftshift(y, dim=self._dim), dim=self._dim, norm='ortho'),
dim=self._dim,
),
)
return (x,)
13 changes: 8 additions & 5 deletions src/mrpro/operators/FourierOp.py
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Expand Up @@ -126,6 +126,7 @@ def get_traj(traj: KTrajectory, dims: Sequence[int]):
self._fwd_nufft_op = None
self._adj_nufft_op = None
self._kshape = traj.broadcasted_shape
self._nufft_scale = torch.tensor(get_spatial_dims(encoding_matrix, self._nufft_dims)).prod().sqrt().reciprocal()

@classmethod
def from_kdata(cls, kdata: KData, recon_shape: SpatialDimension[int] | None = None) -> Self:
Expand Down Expand Up @@ -164,7 +165,6 @@ def forward(self, x: torch.Tensor) -> tuple[torch.Tensor,]:
keep_dims = [-4, *self._nufft_dims] # -4 is always coil
permute = [i for i in range(-x.ndim, 0) if i not in keep_dims] + keep_dims
unpermute = np.argsort(permute)

x = x.permute(*permute)
permuted_x_shape = x.shape
x = x.flatten(end_dim=-len(keep_dims) - 1)
Expand All @@ -174,16 +174,18 @@ def forward(self, x: torch.Tensor) -> tuple[torch.Tensor,]:
omega = omega.broadcast_to(*permuted_x_shape[: -len(keep_dims)], *omega.shape[-len(keep_dims) :])
omega = omega.flatten(end_dim=-len(keep_dims) - 1).flatten(start_dim=-len(keep_dims) + 1)

x = self._fwd_nufft_op(x, omega, norm='ortho')
x = self._fwd_nufft_op(x, omega, norm=None)

shape_nufft_dims = [self._kshape[i] for i in self._nufft_dims]
x = x.reshape(*permuted_x_shape[: -len(keep_dims)], -1, *shape_nufft_dims) # -1 is coils
x = x.permute(*unpermute)

# manual scaling instead of ortho to be independent of oversampling ratio
x = x * self._nufft_scale

if self._fast_fourier_op is not None and self._cart_sampling_op is not None:
# FFT
(x,) = self._cart_sampling_op(self._fast_fourier_op(x)[0])

return (x,)

def adjoint(self, x: torch.Tensor) -> tuple[torch.Tensor,]:
Expand All @@ -209,7 +211,6 @@ def adjoint(self, x: torch.Tensor) -> tuple[torch.Tensor,]:
keep_dims = [-4, *self._nufft_dims] # -4 is coil
permute = [i for i in range(-x.ndim, 0) if i not in keep_dims] + keep_dims
unpermute = np.argsort(permute)

x = x.permute(*permute)
permuted_x_shape = x.shape
x = x.flatten(end_dim=-len(keep_dims) - 1).flatten(start_dim=-len(keep_dims) + 1)
Expand All @@ -218,11 +219,13 @@ def adjoint(self, x: torch.Tensor) -> tuple[torch.Tensor,]:
omega = omega.broadcast_to(*permuted_x_shape[: -len(keep_dims)], *omega.shape[-len(keep_dims) :])
omega = omega.flatten(end_dim=-len(keep_dims) - 1).flatten(start_dim=-len(keep_dims) + 1)

x = self._adj_nufft_op(x, omega, norm='ortho')
x = self._adj_nufft_op(x, omega, norm=None)

x = x.reshape(*permuted_x_shape[: -len(keep_dims)], *x.shape[-len(keep_dims) :])
x = x.permute(*unpermute)

# manual scaling instead of ortho to be independent of oversampling ratio
x = x * self._nufft_scale
return (x,)

@property
Expand Down
92 changes: 53 additions & 39 deletions tests/conftest.py
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Expand Up @@ -240,7 +240,7 @@ def create_traj(k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz):
k_list = []
for spacing, nk in zip([type_kz, type_ky, type_kx], [nkz, nky, nkx], strict=True):
if spacing == 'non-uniform':
k = random_generator.float32_tensor(size=nk, low=-1, high=1) * max(nk)
k = random_generator.float32_tensor(size=nk, low=-max(nk) // 2, high=max(nk) // 2)
elif spacing == 'uniform':
k = create_uniform_traj(nk, k_shape=k_shape)
elif spacing == 'zero':
Expand Down Expand Up @@ -293,10 +293,10 @@ def ismrmrd_cart(ellipse_phantom, tmp_path_factory):
'zero', # type_k2
),
( # (2) 2d non-Cartesian mri with 2 coils
(1, 2, 1, 96, 128), # im_shape
(1, 2, 1, 16, 192), # k_shape
(1, 1, 16, 192), # nkx
(1, 1, 16, 192), # nky
(1, 2, 1, 128, 128), # im_shape
(1, 2, 1, 16, 128), # k_shape
(1, 1, 16, 128), # nkx
(1, 1, 16, 128), # nky
(1, 1, 1, 1), # nkz
'non-uniform', # type_kx
'non-uniform', # type_ky
Expand All @@ -306,7 +306,7 @@ def ismrmrd_cart(ellipse_phantom, tmp_path_factory):
'zero', # type_k2
),
( # (3) 2d Cartesian with irregular sampling
(1, 1, 1, 96, 128), # im_shape
(1, 1, 1, 192, 192), # im_shape
(1, 1, 1, 1, 192), # k_shape
(1, 1, 1, 192), # nkx
(1, 1, 1, 192), # nky
Expand Down Expand Up @@ -344,71 +344,84 @@ def ismrmrd_cart(ellipse_phantom, tmp_path_factory):
'non-uniform', # type_k1
'non-uniform', # type_k2
),
( # (6) 2d non-uniform cine with 8 cardiac phases, 5 coils
(8, 5, 1, 64, 64), # im_shape
(8, 5, 1, 18, 128), # k_shape
(8, 1, 18, 128), # nkx
(8, 1, 18, 128), # nky
(8, 1, 1, 1), # nkz
( # (6) 2d non-uniform cine with 2 cardiac phases, 3 coils
(2, 3, 1, 64, 64), # im_shape
(2, 3, 1, 18, 128), # k_shape
(2, 1, 18, 128), # nkx
(2, 1, 18, 128), # nky
(2, 1, 1, 1), # nkz
'non-uniform', # type_kx
'non-uniform', # type_ky
'zero', # type_kz
'non-uniform', # type_k0
'non-uniform', # type_k1
'zero', # type_k2
),
( # (7) 2d cartesian cine with 9 cardiac phases, 6 coils
(9, 6, 1, 96, 128), # im_shape
(9, 6, 1, 128, 192), # k_shape
(9, 1, 1, 192), # nkx
(9, 1, 128, 1), # nky
(9, 1, 1, 1), # nkz
( # (7) 2d cartesian cine with 2 cardiac phases, 3 coils
(2, 3, 1, 96, 128), # im_shape
(2, 3, 1, 128, 192), # k_shape
(2, 1, 1, 192), # nkx
(2, 1, 128, 1), # nky
(2, 1, 1, 1), # nkz
'uniform', # type_kx
'uniform', # type_ky
'zero', # type_kz
'uniform', # type_k0
'uniform', # type_k1
'zero', # type_k2
),
( # (8) radial phase encoding (RPE), 8 coils, with oversampling in both FFT and non-uniform directions
(2, 8, 64, 32, 48), # im_shape
(2, 8, 8, 64, 96), # k_shape
( # (8) radial phase encoding (RPE), 3 coils, with oversampling in both FFT and non-uniform directions
(2, 3, 64, 32, 48), # im_shape
(2, 3, 8, 64, 96), # k_shape
(2, 1, 1, 96), # nkx
(2, 8, 64, 1), # nky
(2, 8, 64, 1), # nkz
(2, 3, 64, 1), # nky
(2, 3, 64, 1), # nkz
'uniform', # type_kx
'non-uniform', # type_ky
'non-uniform', # type_kz
'uniform', # type_k0
'non-uniform', # type_k1
'non-uniform', # type_k2
),
( # (9) radial phase encoding (RPE), 8 coils with non-Cartesian sampling along readout
(2, 8, 64, 32, 48), # im_shape
(2, 8, 8, 64, 96), # k_shape
( # (9) radial phase encoding (RPE), 3 coils with non-Cartesian sampling along readout
(2, 3, 64, 32, 48), # im_shape
(2, 3, 8, 64, 96), # k_shape
(2, 1, 1, 96), # nkx
(2, 8, 64, 1), # nky
(2, 8, 64, 1), # nkz
(2, 3, 64, 1), # nky
(2, 3, 64, 1), # nkz
'non-uniform', # type_kx
'non-uniform', # type_ky
'non-uniform', # type_kz
'non-uniform', # type_k0
'non-uniform', # type_k1
'non-uniform', # type_k2
),
( # (10) stack of stars, 5 other, 3 coil, oversampling in both FFT and non-uniform directions
(5, 3, 48, 16, 32), # im_shape
(5, 3, 96, 18, 64), # k_shape
(5, 1, 18, 64), # nkx
(5, 1, 18, 64), # nky
(5, 96, 1, 1), # nkz
( # (10) stack of stars, 2 other, 3 coil, oversampling in both FFT and non-uniform directions
(2, 3, 48, 16, 32), # im_shape
(2, 3, 96, 18, 64), # k_shape
(2, 1, 18, 64), # nkx
(2, 1, 18, 64), # nky
(2, 96, 1, 1), # nkz
'non-uniform', # type_kx
'non-uniform', # type_ky
'uniform', # type_kz
'non-uniform', # type_k0
'non-uniform', # type_k1
'uniform', # type_k2
),
( # (11) 2d Cartesian with irregular sampling, oversampling
(1, 1, 1, 96, 128), # im_shape
(1, 1, 1, 1, 192), # k_shape
(1, 1, 1, 192), # nkx
(1, 1, 1, 192), # nky
(1, 1, 1, 1), # nkz
'uniform', # type_kx
'uniform', # type_ky
'zero', # type_kz
'uniform', # type_k0
'zero', # type_k1
'zero', # type_k2
),
],
ids=[
'2d_cartesian_1_coil_no_oversampling',
Expand All @@ -417,10 +430,11 @@ def ismrmrd_cart(ellipse_phantom, tmp_path_factory):
'2d_cartesian_irregular_sampling',
'2d_single_shot_spiral',
'3d_nonuniform_4_coils_2_other',
'2d_nnonuniform_cine_mri_8_cardiac_phases_5_coils',
'2d_cartesian_cine_9_cardiac_phases_6_coils',
'radial_phase_encoding_8_coils_with_oversampling',
'radial_phase_encoding_8_coils_non_cartesian_sampling',
'stack_of_stars_5_other_3_coil_with_oversampling',
'2d_nonuniform_cine_mri_2_cardiac_phases_3_coils',
'2d_cartesian_cine_2_cardiac_phases_3_coils',
'radial_phase_encoding_3_coils_with_oversampling',
'radial_phase_encoding_3_coils_non_cartesian_sampling',
'stack_of_stars_2_other_3_coil_with_oversampling',
'2d_cartesian_irregular_sampling_with_oversampling',
],
)
99 changes: 94 additions & 5 deletions tests/operators/test_fourier_op.py
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Expand Up @@ -3,13 +3,26 @@
import pytest
import torch
from mrpro.data import KData, KTrajectory, SpatialDimension
from mrpro.data.enums import TrajType
from mrpro.data.traj_calculators import KTrajectoryCartesian
from mrpro.operators import FourierOp

from tests import RandomGenerator, dotproduct_adjointness_test
from tests.conftest import COMMON_MR_TRAJECTORIES, create_traj


class NufftTrajektory(KTrajectory):
"""Always returns non-grid trajectory type."""

def _traj_types(
self,
tolerance: float,
) -> tuple[tuple[TrajType, TrajType, TrajType], tuple[TrajType, TrajType, TrajType]]:
true_types = super()._traj_types(tolerance)
modified = tuple([tuple([t & (~TrajType.ONGRID) for t in ts]) for ts in true_types])
return modified


def create_data(im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz):
random_generator = RandomGenerator(seed=0)

Expand Down Expand Up @@ -38,16 +51,92 @@
)
fourier_op = FourierOp(recon_matrix=recon_matrix, encoding_matrix=encoding_matrix, traj=trajectory)

# apply forward operator
(kdata,) = fourier_op(img)

# test adjoint property; i.e. <Fu,v> == <u, F^Hv> for all u,v
random_generator = RandomGenerator(seed=0)
u = random_generator.complex64_tensor(size=img.shape)
v = random_generator.complex64_tensor(size=kdata.shape)
u = random_generator.complex64_tensor(size=im_shape)
v = random_generator.complex64_tensor(size=k_shape)
dotproduct_adjointness_test(fourier_op, u, v)

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test_fourier_op_fwd_adj_property[2d_single_shot_spiral]

AssertionError

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test_fourier_op_fwd_adj_property[radial_phase_encoding_3_coils_with_oversampling]

ValueError: k-space data shape mismatch

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test_fourier_op_fwd_adj_property[radial_phase_encoding_3_coils_non_cartesian_sampling]

AssertionError

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test_fourier_op_fwd_adj_property[2d_single_shot_spiral]

AssertionError

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test_fourier_op_fwd_adj_property[radial_phase_encoding_3_coils_with_oversampling]

ValueError: k-space data shape mismatch

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test_fourier_op_fwd_adj_property[radial_phase_encoding_3_coils_non_cartesian_sampling]

AssertionError

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test_fourier_op_fwd_adj_property[2d_single_shot_spiral]

AssertionError

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test_fourier_op_fwd_adj_property[radial_phase_encoding_3_coils_with_oversampling]

ValueError: k-space data shape mismatch

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test_fourier_op_fwd_adj_property[radial_phase_encoding_3_coils_non_cartesian_sampling]

AssertionError


@COMMON_MR_TRAJECTORIES
def test_fourier_op_norm(im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz, type_k0, type_k1, type_k2):
"""Test operator norm of Fourier Operator, should be 1."""

# generate random images and k-space trajectories
img, trajectory = create_data(im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz)

# create operator
recon_matrix = SpatialDimension(im_shape[-3], im_shape[-2], im_shape[-1])
encoding_matrix = SpatialDimension(
int(trajectory.kz.max() - trajectory.kz.min() + 1),
int(trajectory.ky.max() - trajectory.ky.min() + 1),
int(trajectory.kx.max() - trajectory.kx.min() + 1),
)
fourier_op = FourierOp(recon_matrix=recon_matrix, encoding_matrix=encoding_matrix, traj=trajectory)
(initial_value,) = fourier_op.adjoint(*fourier_op(img))
norm = fourier_op.operator_norm(initial_value, dim=None, max_iterations=4).squeeze()
torch.testing.assert_close(norm, torch.tensor(1.0), atol=0.1, rtol=0.0)

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test_fourier_op_norm[2d_non_cartesian_mri_2_coils]

AssertionError: Scalars are not close!

Expected 1.0 but got 1.4746354818344116.
Absolute difference: 0.4746354818344116 (up to 0.1 allowed)
Relative difference: 0.4746354818344116 (up to 0.0 allowed)

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test_fourier_op_norm[2d_single_shot_spiral]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.7416239380836487.
Absolute difference: 0.2583760619163513 (up to 0.1 allowed)
Relative difference: 0.2583760619163513 (up to 0.0 allowed)

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test_fourier_op_norm[3d_nonuniform_4_coils_2_other]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.6982466578483582.
Absolute difference: 0.30175334215164185 (up to 0.1 allowed)
Relative difference: 0.30175334215164185 (up to 0.0 allowed)

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test_fourier_op_norm[radial_phase_encoding_3_coils_non_cartesian_sampling]

AssertionError: Scalars are not close!

Expected 1.0 but got 1.54142427444458.
Absolute difference: 0.5414242744445801 (up to 0.1 allowed)
Relative difference: 0.5414242744445801 (up to 0.0 allowed)

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test_fourier_op_norm[stack_of_stars_2_other_3_coil_with_oversampling]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.8689930438995361.
Absolute difference: 0.13100695610046387 (up to 0.1 allowed)
Relative difference: 0.13100695610046387 (up to 0.0 allowed)

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test_fourier_op_norm[2d_cartesian_irregular_sampling_with_oversampling]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.6897003650665283.
Absolute difference: 0.3102996349334717 (up to 0.1 allowed)
Relative difference: 0.3102996349334717 (up to 0.0 allowed)

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test_fourier_op_norm[2d_non_cartesian_mri_2_coils]

AssertionError: Scalars are not close!

Expected 1.0 but got 1.4746354818344116.
Absolute difference: 0.4746354818344116 (up to 0.1 allowed)
Relative difference: 0.4746354818344116 (up to 0.0 allowed)

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test_fourier_op_norm[2d_single_shot_spiral]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.7416239380836487.
Absolute difference: 0.2583760619163513 (up to 0.1 allowed)
Relative difference: 0.2583760619163513 (up to 0.0 allowed)

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test_fourier_op_norm[3d_nonuniform_4_coils_2_other]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.6982466578483582.
Absolute difference: 0.30175334215164185 (up to 0.1 allowed)
Relative difference: 0.30175334215164185 (up to 0.0 allowed)

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test_fourier_op_norm[2d_non_cartesian_mri_2_coils]

AssertionError: Scalars are not close!

Expected 1.0 but got 1.4746354818344116.
Absolute difference: 0.4746354818344116 (up to 0.1 allowed)
Relative difference: 0.4746354818344116 (up to 0.0 allowed)

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test_fourier_op_norm[2d_single_shot_spiral]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.7416239380836487.
Absolute difference: 0.2583760619163513 (up to 0.1 allowed)
Relative difference: 0.2583760619163513 (up to 0.0 allowed)

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test_fourier_op_norm[3d_nonuniform_4_coils_2_other]

AssertionError: Scalars are not close!

Expected 1.0 but got 0.6982466578483582.
Absolute difference: 0.30175334215164185 (up to 0.1 allowed)
Relative difference: 0.30175334215164185 (up to 0.0 allowed)


@COMMON_MR_TRAJECTORIES
def test_fourier_op_fft_nufft_forward(
im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz, type_k0, type_k1, type_k2
):
"""Test Nufft vs FFT for Fourier operator."""
if not any(t == 'uniform' for t in [type_kx, type_ky, type_kz]):
return # only test for uniform trajectories

img, trajectory = create_data(im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz)

recon_matrix = SpatialDimension(im_shape[-3], im_shape[-2], im_shape[-1])
encoding_matrix = SpatialDimension(
int(trajectory.kz.max() - trajectory.kz.min() + 1),
int(trajectory.ky.max() - trajectory.ky.min() + 1),
int(trajectory.kx.max() - trajectory.kx.min() + 1),
)
fourier_op = FourierOp(recon_matrix=recon_matrix, encoding_matrix=encoding_matrix, traj=trajectory)

nufft_fourier_op = FourierOp(
recon_matrix=recon_matrix,
encoding_matrix=encoding_matrix,
traj=NufftTrajektory(trajectory.kz, trajectory.ky, trajectory.kx),
nufft_oversampling=8.0,
)

(result_normal,) = fourier_op(img)
(result_nufft,) = nufft_fourier_op(img)
torch.testing.assert_close(result_normal, result_nufft, atol=1e-4, rtol=5e-3)

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test_fourier_op_fft_nufft_forward[radial_phase_encoding_3_coils_with_oversampling]

AssertionError: Tensor-likes are not close!

Mismatched elements: 127 / 110592 (0.1%)
Greatest absolute difference: 0.000497964269015938 at index (1, 2, 1, 53, 70) (up to 0.0001 allowed)
Greatest relative difference: 0.16935928165912628 at index (1, 2, 0, 27, 37) (up to 0.005 allowed)


@COMMON_MR_TRAJECTORIES
def test_fourier_op_fft_nufft_adjoint(
im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz, type_k0, type_k1, type_k2
):
"""Test AdjointNufft vs IFFT for Fourier operator."""
if not any(t == 'uniform' for t in [type_kx, type_ky, type_kz]):
return # only test for uniform trajectories
img, trajectory = create_data(im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz)
recon_matrix = SpatialDimension(im_shape[-3], im_shape[-2], im_shape[-1])
encoding_matrix = SpatialDimension(
int(trajectory.kz.max() - trajectory.kz.min() + 1),
int(trajectory.ky.max() - trajectory.ky.min() + 1),
int(trajectory.kx.max() - trajectory.kx.min() + 1),
)
fourier_op = FourierOp(recon_matrix=recon_matrix, encoding_matrix=encoding_matrix, traj=trajectory)

nufft_fourier_op = FourierOp(
recon_matrix=recon_matrix,
encoding_matrix=encoding_matrix,
traj=NufftTrajektory(trajectory.kz, trajectory.ky, trajectory.kx),
nufft_oversampling=8.0,
)

k = RandomGenerator(0).complex64_tensor(size=k_shape)
(result_normal,) = fourier_op.H(k)

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test_fourier_op_fft_nufft_adjoint[radial_phase_encoding_3_coils_with_oversampling]

ValueError: k-space data shape mismatch
(result_nufft,) = nufft_fourier_op.H(k)
torch.testing.assert_close(result_normal, result_nufft, atol=3e-4, rtol=5e-3)

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test_fourier_op_fft_nufft_adjoint[stack_of_stars_2_other_3_coil_with_oversampling]

AssertionError: Tensor-likes are not close!

Mismatched elements: 227 / 147456 (0.2%)
Greatest absolute difference: 0.0009539038874208927 at index (1, 1, 25, 15, 28) (up to 0.0003 allowed)
Greatest relative difference: 0.18000340461730957 at index (1, 1, 19, 6, 29) (up to 0.005 allowed)


@COMMON_MR_TRAJECTORIES
def test_fourier_op_gram(im_shape, k_shape, nkx, nky, nkz, type_kx, type_ky, type_kz, type_k0, type_k1, type_k2):
"""Test gram of Fourier operator."""
Expand All @@ -64,7 +153,7 @@
(expected,) = (fourier_op.H @ fourier_op)(img)
(actual,) = fourier_op.gram(img)

torch.testing.assert_close(actual, expected, rtol=1e-3, atol=1e-3)

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test_fourier_op_gram[2d_non_cartesian_mri_2_coils]

AssertionError: Tensor-likes are not close!

Mismatched elements: 32768 / 32768 (100.0%)
Greatest absolute difference: 0.5523433089256287 at index (0, 0, 0, 3, 35) (up to 0.001 allowed)
Greatest relative difference: 0.7502065300941467 at index (0, 1, 0, 28, 116) (up to 0.001 allowed)

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test_fourier_op_gram[2d_single_shot_spiral]

AssertionError: Tensor-likes are not close!

Mismatched elements: 23945 / 24576 (97.4%)
Greatest absolute difference: 0.020737048238515854 at index (0, 0, 0, 21, 80) (up to 0.001 allowed)
Greatest relative difference: 0.25013577938079834 at index (0, 1, 0, 71, 127) (up to 0.001 allowed)

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test_fourier_op_gram[radial_phase_encoding_3_coils_with_oversampling]

AssertionError: Tensor-likes are not close!

Mismatched elements: 589559 / 589824 (100.0%)
Greatest absolute difference: 0.17729218304157257 at index (1, 2, 28, 7, 31) (up to 0.001 allowed)
Greatest relative difference: 0.5004300475120544 at index (1, 0, 63, 13, 36) (up to 0.001 allowed)

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test_fourier_op_gram[radial_phase_encoding_3_coils_non_cartesian_sampling]

AssertionError: Tensor-likes are not close!

Mismatched elements: 589632 / 589824 (100.0%)
Greatest absolute difference: 0.2131546139717102 at index (1, 2, 28, 7, 31) (up to 0.001 allowed)
Greatest relative difference: 0.5005220770835876 at index (0, 0, 62, 2, 29) (up to 0.001 allowed)

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test_fourier_op_gram[2d_non_cartesian_mri_2_coils]

AssertionError: Tensor-likes are not close!

Mismatched elements: 32768 / 32768 (100.0%)
Greatest absolute difference: 0.5523433089256287 at index (0, 0, 0, 3, 35) (up to 0.001 allowed)
Greatest relative difference: 0.7502065300941467 at index (0, 1, 0, 28, 116) (up to 0.001 allowed)

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test_fourier_op_gram[2d_single_shot_spiral]

AssertionError: Tensor-likes are not close!

Mismatched elements: 23945 / 24576 (97.4%)
Greatest absolute difference: 0.020737048238515854 at index (0, 0, 0, 21, 80) (up to 0.001 allowed)
Greatest relative difference: 0.25013577938079834 at index (0, 1, 0, 71, 127) (up to 0.001 allowed)


@pytest.mark.parametrize(
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